Optimized Path Planning User Guide — ManipulaPy 1.1.0 Documentation
Description: This guide covers the highly optimized trajectory planning capabilities in ManipulaPy, including adaptive GPU/CPU execution, memory pooling, batch processing, and advanced performance optimizations...

# Optimized Path Planning User Guide

This guide covers the highly optimized trajectory planning capabilities in ManipulaPy, including adaptive GPU/CPU execution, memory pooling, batch processing, and advanced performance optimizations for robotic manipulators.

## Introduction

The optimized TrajectoryPlanning class (now OptimizedTrajectoryPlanning) provides comprehensive trajectory generation and execution capabilities with significant performance improvements through CUDA acceleration and intelligent adaptive execution strategies.

Key Optimizations: - Adaptive GPU/CPU execution based on problem size and hardware availability - Memory pooling to reduce allocation overhead and improve performance - Batch processing for multiple trajectories with optimized kernel launches - Fused kernels to minimize memory bandwidth requirements - Intelligent fallback to CPU when beneficial for small problems - 2D parallelization for better GPU utilization - Pinned memory transfers for faster host-device communication

Enhanced Features: - Automatic performance tuning and statistics collection - Smart threshold adaptation based on execution patterns - Comprehensive error handling and graceful degradation - Advanced profiling and benchmarking capabilities - Backward compatibility with existing TrajectoryPlanning interface

### Mathematical Background

The mathematical foundation remains the same as the original implementation, with optimizations focused on computational efficiency rather than algorithmic changes. The core time-scaling functions, dynamics computations, and collision avoidance methods are preserved while being accelerated through parallel execution.

Key Computational Optimizations:

1. Parallel Time-Scaling: Joint trajectory computation parallelized across both time steps and joints using 2D CUDA grids

2. Vectorized Operations: All mathematical operations vectorized for SIMD execution on both CPU and GPU

3. Memory Coalescing: Data layouts optimized for efficient memory access patterns

4. Kernel Fusion: Multiple operations combined into single kernel launches to reduce overhead

## Getting Started

### Basic Setup with Optimizations

    from ManipulaPy.path_planning import OptimizedTrajectoryPlanning, create_optimized_planner
    from ManipulaPy.urdf_processor import URDFToSerialManipulator
    import numpy as np

    # Load robot model
    processor = URDFToSerialManipulator("robot.urdf")
    robot = processor.serial_manipulator
    dynamics = processor.dynamics

    # Define joint and torque limits
    joint_limits = [(-np.pi, np.pi)] * 6  # 6-DOF robot
    torque_limits = [(-50, 50)] * 6       # ±50 N⋅m per joint

    # Method 1: Use factory function with auto-optimization
    planner = create_optimized_planner(
        serial_manipulator=robot,
        urdf_path="robot.urdf",
        dynamics=dynamics,
        joint_limits=joint_limits,
        torque_limits=torque_limits,
        gpu_memory_mb=512,        # Allocate 512MB GPU memory pool
        enable_profiling=True     # Enable performance profiling
    )

    # Method 2: Direct instantiation with custom settings
    planner_custom = OptimizedTrajectoryPlanning(
        serial_manipulator=robot,
        urdf_path="robot.urdf",
        dynamics=dynamics,
        joint_limits=joint_limits,
        torque_limits=torque_limits,
        use_cuda=None,            # Auto-detect (None/True/False)
        cuda_threshold=100,       # Min problem size for GPU
        memory_pool_size_mb=256,  # GPU memory pool size
        enable_profiling=False    # Disable profiling for production
    )

    print(f"CUDA available: {planner.cuda_available}")
    print(f"GPU properties: {planner.gpu_properties}")

### Backward Compatibility

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    Backward Compatibility
    ~~~~~~~~~~~~~~~~~~~~~

The optimized planner maintains full backward compatibility:

    # Existing code works unchanged - automatically uses optimizations
    from ManipulaPy.path_planning import TrajectoryPlanning

    # This now creates an OptimizedTrajectoryPlanning instance
    planner = TrajectoryPlanning(
        serial_manipulator=robot,
        urdf_path="robot.urdf",
        dynamics=dynamics,
        joint_limits=joint_limits,
        torque_limits=torque_limits
    )

    # All existing methods work exactly the same
    trajectory = planner.joint_trajectory(
        theta_start, theta_end, Tf=2.0, N=100, method=3
    )

## Performance-Optimized Methods

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    Performance-Optimized Methods
    ----------------------------

### joint_trajectory() with Adaptive Execution

The optimized joint_trajectory() method automatically selects the best execution strategy:

    def optimized_trajectory_demo():
        """Demonstrate adaptive trajectory generation with performance monitoring."""

        # Test different problem sizes
        test_cases = [
            {"N": 50, "name": "Small (CPU preferred)"},
            {"N": 500, "name": "Medium (GPU beneficial)"},
            {"N": 5000, "name": "Large (GPU optimal)"}
        ]

        theta_start = np.zeros(6)
        theta_end = np.array([0.8, -0.5, 0.3, -0.2, 0.6, -0.4])

        for case in test_cases:
            print(f"\n=== {case['name']} ===")

            # Reset performance stats
            planner.reset_performance_stats()

            # Generate trajectory
            start_time = time.time()
            trajectory = planner.joint_trajectory(
                theta_start, theta_end, Tf=2.0, N=case['N'], method=5
            )
            elapsed = time.time() - start_time

            # Get performance statistics
            stats = planner.get_performance_stats()

            print(f"Points generated: {trajectory['positions'].shape}")
            print(f"Execution time: {elapsed:.4f}s")
            print(f"Used GPU: {stats['gpu_calls'] > 0}")
            print(f"GPU usage: {stats['gpu_usage_percent']:.1f}%")

            if stats['gpu_calls'] > 0:
                print(f"Avg GPU time: {stats['avg_gpu_time']:.4f}s")
            if stats['cpu_calls'] > 0:
                print(f"Avg CPU time: {stats['avg_cpu_time']:.4f}s")

        return trajectory

    # Run demonstration
    demo_trajectory = optimized_trajectory_demo()

### batch_joint_trajectory() for Multiple Trajectories

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    batch_joint_trajectory() for Multiple Trajectories
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Process multiple trajectories simultaneously with optimized batch kernels:

    def batch_trajectory_demo():
        """Demonstrate high-performance batch trajectory generation."""

        # Generate multiple start/end configurations
        batch_size = 20
        num_joints = 6

        # Random start and end configurations
        np.random.seed(42)  # For reproducible results
        thetastart_batch = np.random.uniform(-1.0, 1.0, (batch_size, num_joints))
        thetaend_batch = np.random.uniform(-1.0, 1.0, (batch_size, num_joints))

        print(f"Generating {batch_size} trajectories in batch...")

        # Reset stats for clean measurement
        planner.reset_performance_stats()

        # Generate batch trajectories
        start_time = time.time()
        batch_trajectories = planner.batch_joint_trajectory(
            thetastart_batch=thetastart_batch,
            thetaend_batch=thetaend_batch,
            Tf=3.0,
            N=200,
            method=5
        )
        batch_time = elapsed = time.time() - start_time

        print(f"Batch processing completed:")
        print(f"- Total time: {batch_time:.4f}s")
        print(f"- Time per trajectory: {batch_time/batch_size:.4f}s")
        print(f"- Output shape: {batch_trajectories['positions'].shape}")

        # Compare with sequential processing
        print(f"\nComparing with sequential processing...")
        planner.reset_performance_stats()

        start_time = time.time()
        sequential_trajectories = []
        for i in range(batch_size):
            traj = planner.joint_trajectory(
                thetastart_batch[i], thetaend_batch[i], Tf=3.0, N=200, method=5
            )
            sequential_trajectories.append(traj)
        sequential_time = time.time() - start_time

        speedup = sequential_time / batch_time
        print(f"- Sequential time: {sequential_time:.4f}s")
        print(f"- Batch speedup: {speedup:.2f}x")

        # Verify results are equivalent
        sequential_positions = np.array([t['positions'] for t in sequential_trajectories])
        max_diff = np.max(np.abs(batch_trajectories['positions'] - sequential_positions))
        print(f"- Max difference: {max_diff:.2e} (should be ~0)")

        return batch_trajectories, speedup

    # Run batch demonstration
    batch_trajs, speedup = batch_trajectory_demo()

## Advanced Performance Features

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    Advanced Performance Features
    ----------------------------

### Memory Pool Management

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    Memory Pool Management
    ~~~~~~~~~~~~~~~~~~~~~

Optimize memory allocation for better performance:

    def memory_optimization_demo():
        """Demonstrate memory pool optimization for sustained performance."""

        print("Memory Pool Optimization Demo")
        print("=" * 40)

        # Create planner with large memory pool
        large_pool_planner = OptimizedTrajectoryPlanning(
            serial_manipulator=robot,
            urdf_path="robot.urdf",
            dynamics=dynamics,
            joint_limits=joint_limits,
            memory_pool_size_mb=1024,  # 1GB memory pool
            enable_profiling=True
        )

        # Test sustained performance with many trajectories
        num_iterations = 50
        trajectory_sizes = [100, 500, 1000, 2000]

        print(f"Testing {num_iterations} iterations for each size...")

        for N in trajectory_sizes:
            print(f"\nTesting N={N}:")

            # Reset stats
            large_pool_planner.reset_performance_stats()

            times = []
            for i in range(num_iterations):
                # Generate random trajectory
                theta_start = np.random.uniform(-1, 1, 6)
                theta_end = np.random.uniform(-1, 1, 6)

                start_time = time.time()
                traj = large_pool_planner.joint_trajectory(
                    theta_start, theta_end, Tf=2.0, N=N, method=5
                )
                times.append(time.time() - start_time)

            # Analyze performance stability
            times = np.array(times)
            stats = large_pool_planner.get_performance_stats()

            print(f"  Mean time: {np.mean(times):.4f}s ± {np.std(times):.4f}s")
            print(f"  Min/Max: {np.min(times):.4f}s / {np.max(times):.4f}s")
            print(f"  GPU usage: {stats['gpu_usage_percent']:.1f}%")
            print(f"  Memory transfers: {stats['memory_transfers']}")
            print(f"  Kernel launches: {stats['kernel_launches']}")

        # Clean up memory pool
        large_pool_planner.cleanup_gpu_memory()

        return times

    # Run memory optimization demo
    memory_times = memory_optimization_demo()

### Performance Benchmarking

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    Performance Benchmarking
    ~~~~~~~~~~~~~~~~~~~~~~~

Built-in benchmarking capabilities for performance analysis:

    def comprehensive_benchmark():
        """Run comprehensive performance benchmarks."""

        print("Comprehensive Performance Benchmark")
        print("=" * 50)

        # Test 1: Built-in benchmark
        print("Running built-in benchmarks...")
        benchmark_results = planner.benchmark_performance()

        for test_name, result in benchmark_results.items():
            print(f"\n{test_name} Test:")
            print(f"  Problem size: {result['N']} × {result['joints']}")
            print(f"  Total time: {result['total_time']:.4f}s")
            print(f"  Used GPU: {result['used_gpu']}")
            print(f"  Output shape: {result['trajectory_shape']}")

            if 'stats' in result:
                stats = result['stats']
                print(f"  GPU calls: {stats['gpu_calls']}")
                print(f"  CPU calls: {stats['cpu_calls']}")

        # Test 2: Implementation comparison
        print(f"\n" + "=" * 50)
        print("Comparing CPU vs GPU implementations...")

        comparison_results = compare_implementations(
            serial_manipulator=robot,
            urdf_path="robot.urdf",
            dynamics=dynamics,
            joint_limits=joint_limits,
            test_params={"N": 2000, "Tf": 3.0, "method": 5}
        )

        print("\nCPU Implementation:")
        cpu_result = comparison_results['cpu']
        print(f"  Time: {cpu_result['time']:.4f}s")
        print(f"  Shape: {cpu_result['result_shape']}")

        gpu_result = comparison_results.get('gpu', {})
        if gpu_result.get('available', True):
            print("\nGPU Implementation:")
            print(f"  Time: {gpu_result['time']:.4f}s")
            print(f"  Shape: {gpu_result['result_shape']}")
            print(f"  Speedup: {gpu_result['speedup']:.2f}x")

            if 'accuracy' in comparison_results:
                acc = comparison_results['accuracy']
                print("\nAccuracy Comparison:")
                print(f"  Max position diff: {acc['max_pos_diff']:.2e}")
                print(f"  Max velocity diff: {acc['max_vel_diff']:.2e}")
                print(f"  Max acceleration diff: {acc['max_acc_diff']:.2e}")
        else:
            print("\nGPU Implementation: Not available")

        return benchmark_results, comparison_results

    # Run comprehensive benchmark
    bench_results, comp_results = comprehensive_benchmark()

## Optimized Dynamics Integration

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    Optimized Dynamics Integration
    -----------------------------

### Enhanced inverse_dynamics_trajectory()

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    Enhanced inverse_dynamics_trajectory()
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

GPU-accelerated dynamics computation with optimized memory management:

    def optimized_dynamics_demo():
        """Demonstrate optimized dynamics computation with performance analysis."""

        # Generate a complex trajectory
        theta_start = np.array([0.1, 0.2, -0.3, 0.1, 0.5, -0.2])
        theta_end = np.array([0.8, -0.4, 0.6, -0.3, 0.2, 0.7])

        # Large trajectory for performance testing
        N = 2000  # 2000 points
        Tf = 5.0  # 5 seconds

        print("Generating large trajectory for dynamics analysis...")
        trajectory = planner.joint_trajectory(
            theta_start, theta_end, Tf=Tf, N=N, method=5
        )

        print(f"Trajectory generated: {trajectory['positions'].shape}")

        # Test dynamics computation performance
        print("\nComputing inverse dynamics...")
        planner.reset_performance_stats()

        start_time = time.time()
        torques = planner.inverse_dynamics_trajectory(
            trajectory['positions'],
            trajectory['velocities'],
            trajectory['accelerations'],
            gravity_vector=[0, 0, -9.81],
            Ftip=[0, 0, 0, 0, 0, 0]
        )
        dynamics_time = time.time() - start_time

        print(f"Dynamics computation completed:")
        print(f"- Time: {dynamics_time:.4f}s")
        print(f"- Rate: {N/dynamics_time:.1f} points/second")
        print(f"- Torque shape: {torques.shape}")

        # Analyze torque statistics
        max_torques = np.max(np.abs(torques), axis=0)
        mean_torques = np.mean(np.abs(torques), axis=0)

        print(f"\nTorque Analysis:")
        for i, (max_t, mean_t) in enumerate(zip(max_torques, mean_torques)):
            limit = planner.torque_limits[i, 1]
            usage = max_t / limit * 100
            print(f"  Joint {i+1}: Max {max_t:.1f} N⋅m ({usage:.1f}% of limit), Mean {mean_t:.1f} N⋅m")

        # Get performance stats
        stats = planner.get_performance_stats()
        print(f"\nPerformance Stats:")
        print(f"- GPU usage: {stats['gpu_usage_percent']:.1f}%")
        print(f"- Kernel launches: {stats['kernel_launches']}")
        print(f"- Memory transfers: {stats['memory_transfers']}")

        return torques, dynamics_time

    # Run optimized dynamics demo
    demo_torques, demo_time = optimized_dynamics_demo()

### Enhanced forward_dynamics_trajectory()

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    Enhanced forward_dynamics_trajectory()
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Optimized forward dynamics simulation with adaptive execution:

    def optimized_forward_dynamics_demo():
        """Demonstrate optimized forward dynamics simulation."""

        # Initial conditions
        theta_initial = np.array([0.1, 0.2, -0.1, 0.0, 0.3, 0.0])
        theta_dot_initial = np.zeros(6)

        # Define control sequence - sinusoidal torques
        N_steps = 1000
        dt = 0.01
        time_steps = np.arange(N_steps) * dt

        # Generate realistic control torques
        tau_matrix = np.zeros((N_steps, 6))
        for i in range(6):
            frequency = 0.5 + i * 0.2  # Different frequency for each joint
            amplitude = 2.0 + i * 0.5   # Different amplitude for each joint
            tau_matrix[:, i] = amplitude * np.sin(2 * np.pi * frequency * time_steps)

        # External forces (varying)
        Ftip_matrix = np.zeros((N_steps, 6))
        Ftip_matrix[:, 2] = 10.0 * np.sin(2 * np.pi * 0.2 * time_steps)  # Vertical force

        print("Running optimized forward dynamics simulation...")
        print(f"Steps: {N_steps}, dt: {dt}s, Total time: {N_steps*dt}s")

        # Reset performance tracking
        planner.reset_performance_stats()

        # Run simulation
        start_time = time.time()
        sim_result = planner.forward_dynamics_trajectory(
            thetalist=theta_initial,
            dthetalist=theta_dot_initial,
            taumat=tau_matrix,
            g=[0, 0, -9.81],
            Ftipmat=Ftip_matrix,
            dt=dt,
            intRes=1
        )
        simulation_time = time.time() - start_time

        print(f"Simulation completed:")
        print(f"- Computation time: {simulation_time:.4f}s")
        print(f"- Real-time factor: {(N_steps*dt)/simulation_time:.1f}x")
        print(f"- Position shape: {sim_result['positions'].shape}")

        # Analyze results
        final_positions = sim_result['positions'][-1]
        max_velocities = np.max(np.abs(sim_result['velocities']), axis=0)
        max_accelerations = np.max(np.abs(sim_result['accelerations']), axis=0)

        print(f"\nSimulation Analysis:")
        print(f"Final positions: {np.degrees(final_positions).round(1)} deg")
        print(f"Max velocities: {max_velocities.round(2)} rad/s")
        print(f"Max accelerations: {max_accelerations.round(2)} rad/s²")

        # Check joint limit compliance
        positions = sim_result['positions']
        limit_violations = 0
        for i in range(6):
            min_pos = np.min(positions[:, i])
            max_pos = np.max(positions[:, i])
            if min_pos < planner.joint_limits[i, 0] or max_pos > planner.joint_limits[i, 1]:
                limit_violations += 1
                print(f"  Joint {i+1}: LIMIT VIOLATION ({np.degrees([min_pos, max_pos]).round(1)} deg)")

        if limit_violations == 0:
            print("  All joints stayed within limits ✓")

        # Performance stats
        stats = planner.get_performance_stats()
        print(f"\nPerformance Stats:")
        print(f"- Used GPU: {stats['gpu_calls'] > 0}")
        print(f"- Execution strategy: {'GPU' if stats['gpu_calls'] > 0 else 'CPU'}")

        return sim_result, simulation_time

    # Run forward dynamics demonstration
    sim_results, sim_time = optimized_forward_dynamics_demo()

## Optimized Cartesian Trajectories

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    Optimized Cartesian Trajectories
    -------------------------------

### Enhanced cartesian_trajectory()

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    Enhanced cartesian_trajectory()
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

GPU-accelerated Cartesian trajectory generation with adaptive execution:

    def optimized_cartesian_demo():
        """Demonstrate optimized Cartesian trajectory generation."""

        # Define complex Cartesian trajectory
        X_start = np.eye(4)
        X_start[:3, 3] = [0.3, 0.2, 0.5]  # Start position

        # End pose with significant rotation and translation
        X_end = np.eye(4)
        X_end[:3, 3] = [0.6, -0.3, 0.3]   # End position

        # 90-degree rotation about Z-axis
        angle = np.pi/2
        X_end[:3, :3] = np.array([
            [np.cos(angle), -np.sin(angle), 0],
            [np.sin(angle),  np.cos(angle), 0],
            [0,              0,             1]
        ])

        # Test different trajectory sizes
        test_sizes = [100, 500, 2000, 5000]

        print("Optimized Cartesian Trajectory Generation")
        print("=" * 45)

        for N in test_sizes:
            print(f"\nTesting N={N} points:")

            # Reset performance stats
            planner.reset_performance_stats()

            # Generate trajectory
            start_time = time.time()
            cart_traj = planner.cartesian_trajectory(
                X_start, X_end, Tf=3.0, N=N, method=5
            )
            elapsed = time.time() - start_time

            # Analyze results
            positions = cart_traj['positions']
            velocities = cart_traj['velocities']
            accelerations = cart_traj['accelerations']
            orientations = cart_traj['orientations']

            # Calculate path metrics
            path_length = np.sum(np.linalg.norm(np.diff(positions, axis=0), axis=1))
            max_velocity = np.max(np.linalg.norm(velocities, axis=1))
            max_acceleration = np.max(np.linalg.norm(accelerations, axis=1))

            # Performance stats
            stats = planner.get_performance_stats()
            used_gpu = stats['gpu_calls'] > 0

            print(f"  Time: {elapsed:.4f}s ({'GPU' if used_gpu else 'CPU'})")
            print(f"  Path length: {path_length:.3f}m")
            print(f"  Max velocity: {max_velocity:.3f}m/s")
            print(f"  Max acceleration: {max_acceleration:.3f}m/s²")
            print(f"  Shapes: pos{positions.shape}, vel{velocities.shape}, acc{accelerations.shape}")

            # Verify start and end points
            start_error = np.linalg.norm(positions[0] - X_start[:3, 3])
            end_error = np.linalg.norm(positions[-1] - X_end[:3, 3])
            print(f"  Start/End errors: {start_error:.2e}, {end_error:.2e}")

        # Return the largest trajectory for visualization
        final_traj = planner.cartesian_trajectory(X_start, X_end, Tf=3.0, N=1000, method=5)

        return final_traj

    # Run Cartesian trajectory demonstration
    cartesian_demo = optimized_cartesian_demo()

## Real-World Application Examples

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    Real-World Application Examples
    ------------------------------

### High-Performance Pick-and-Place

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    High-Performance Pick-and-Place
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Optimized trajectory planning for industrial pick-and-place operations:

    def optimized_pick_and_place():
        """Demonstrate optimized pick-and-place trajectory planning."""

        print("Optimized Pick-and-Place Trajectory Planning")
        print("=" * 50)

        # Define task parameters
        pick_location = np.array([0.4, 0.3, 0.2])
        place_location = np.array([0.6, -0.2, 0.25])
        approach_height = 0.1  # 10cm above objects

        # Calculate waypoint poses
        home_pose = np.eye(4)
        home_pose[:3, 3] = [0.5, 0.0, 0.4]

        pick_approach = np.eye(4)
        pick_approach[:3, 3] = pick_location + np.array([0, 0, approach_height])

        pick_pose = np.eye(4)
        pick_pose[:3, 3] = pick_location

        place_approach = np.eye(4)
        place_approach[:3, 3] = place_location + np.array([0, 0, approach_height])

        place_pose = np.eye(4)
        place_pose[:3, 3] = place_location

        # Convert to joint space using inverse kinematics
        waypoint_poses = [home_pose, pick_approach, pick_pose, pick_approach,
                         place_approach, place_pose, place_approach, home_pose]
        waypoint_joints = []

        current_joints = np.zeros(6)  # Start from home

        print("Converting Cartesian waypoints to joint space...")
        for i, pose in enumerate(waypoint_poses):
            try:
                joints, success, _ = planner.serial_manipulator.iterative_inverse_kinematics(
                    pose, current_joints, max_iterations=200
                )
                if success:
                    waypoint_joints.append(joints)
                    current_joints = joints
                    print(f"  Waypoint {i+1}: ✓")
                else:
                    print(f"  Waypoint {i+1}: Failed IK, using approximation")
                    waypoint_joints.append(current_joints)
            except Exception as e:
                print(f"  Waypoint {i+1}: Error {e}")
                waypoint_joints.append(current_joints)

        # Define segment durations (optimized for speed)
        segment_durations = [1.5, 0.8, 0.5, 1.0, 2.0, 0.5, 0.8, 1.5]  # seconds
        segment_names = [
            "Move to pick approach",
            "Approach object",
            "Pick up",
            "Lift object",
            "Move to place approach",
            "Lower to place",
            "Place object",
            "Return home"
        ]

        # Generate optimized batch trajectory
        print(f"\nGenerating {len(segment_names)} trajectory segments...")

        # Prepare batch data
        batch_starts = waypoint_joints[:-1]
        batch_ends = waypoint_joints[1:]
        batch_size = len(batch_starts)

        # Use different point densities for different segments
        points_per_segment = [75, 40, 25, 50, 100, 25, 40, 75]

        all_segments = []
        total_computation_time = 0

        for i, (start, end, duration, points, name) in enumerate(
            zip(batch_starts, batch_ends, segment_durations, points_per_segment, segment_names)
        ):
            print(f"  {i+1}. {name} ({duration}s, {points} points)")

            planner.reset_performance_stats()
            start_time = time.time()

            segment = planner.joint_trajectory(
                start, end, Tf=duration, N=points, method=5
            )

            segment_time = time.time() - start_time
            total_computation_time += segment_time

            stats = planner.get_performance_stats()
            used_gpu = stats['gpu_calls'] > 0

            print(f"     Time: {segment_time:.3f}s ({'GPU' if used_gpu else 'CPU'})")

            all_segments.append({
                'name': name,
                'duration': duration,
                'trajectory': segment,
                'computation_time': segment_time,
                'used_gpu': used_gpu
            })

        # Combine all segments
        print(f"\nCombining trajectory segments...")
        combined_positions = []
        combined_velocities = []
        combined_accelerations = []

        for i, segment in enumerate(all_segments):
            traj = segment['trajectory']
            if i == 0:
                # Include all points for first segment
                combined_positions.extend(traj['positions'])
                combined_velocities.extend(traj['velocities'])
                combined_accelerations.extend(traj['accelerations'])
            else:
                # Skip first point to avoid duplication
                combined_positions.extend(traj['positions'][1:])
                combined_velocities.extend(traj['velocities'][1:])
                combined_accelerations.extend(traj['accelerations'][1:])

        # Convert to arrays
        combined_trajectory = {
            'positions': np.array(combined_positions),
            'velocities': np.array(combined_velocities),
            'accelerations': np.array(combined_accelerations)
        }

        total_duration = sum(segment_durations)
        total_points = combined_trajectory['positions'].shape[0]

        print(f"\nPick-and-Place Trajectory Generated:")
        print(f"- Total duration: {total_duration:.1f}s")
        print(f"- Total points: {total_points}")
        print(f"- Computation time: {total_computation_time:.3f}s")
        print(f"- Real-time factor: {total_duration/total_computation_time:.1f}x")

        # Analyze trajectory for safety and performance
        print(f"\nTrajectory Analysis:")

        # Check joint limits compliance
        positions = combined_trajectory['positions']
        velocities = combined_trajectory['velocities']
        accelerations = combined_trajectory['accelerations']

        for i in range(6):
            joint_range = [np.min(positions[:, i]), np.max(positions[:, i])]
            limit_range = planner.joint_limits[i]

            if joint_range[0] < limit_range[0] or joint_range[1] > limit_range[1]:
                print(f"  Joint {i+1}: ⚠️ NEAR LIMITS {np.degrees(joint_range).round(1)}° "
                      f"(limits: {np.degrees(limit_range).round(1)}°)")
            else:
                margin = min(joint_range[0] - limit_range[0], limit_range[1] - joint_range[1])
                print(f"  Joint {i+1}: ✓ Safe margin: {np.degrees(margin).round(1)}°")

        # Velocity and acceleration analysis
        max_vel = np.max(np.abs(velocities), axis=0)
        max_acc = np.max(np.abs(accelerations), axis=0)

        print(f"\nMotion Analysis:")
        print(f"  Max velocities: {max_vel.round(3)} rad/s")
        print(f"  Max accelerations: {max_acc.round(3)} rad/s²")

        return combined_trajectory, all_segments

    # Run optimized pick-and-place demonstration
    pick_place_traj, segments = optimized_pick_and_place()

### Multi-Robot Trajectory Coordination

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    Multi-Robot Trajectory Coordination
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Optimized trajectory planning for multiple robots with collision avoidance:

    def multi_robot_coordination():
        """Demonstrate optimized multi-robot trajectory coordination."""

        print("Multi-Robot Trajectory Coordination")
        print("=" * 40)

        # Simulate 4 robots working in shared workspace
        num_robots = 4
        robot_configs = []

        # Different start/end configurations for each robot
        for i in range(num_robots):
            start_config = np.random.uniform(-0.5, 0.5, 6) + i * 0.1
            end_config = np.random.uniform(-0.5, 0.5, 6) - i * 0.1
            robot_configs.append((start_config, end_config))

        print(f"Planning trajectories for {num_robots} robots...")

        # Method 1: Sequential planning (traditional)
        print(f"\n1. Sequential Planning:")
        start_time = time.time()
        sequential_trajectories = []

        for i, (start, end) in enumerate(robot_configs):
            traj = planner.joint_trajectory(start, end, Tf=3.0, N=150, method=5)
            sequential_trajectories.append(traj)
            print(f"   Robot {i+1}: {traj['positions'].shape}")

        sequential_time = time.time() - start_time
        print(f"   Total time: {sequential_time:.4f}s")

        # Method 2: Batch planning (optimized)
        print(f"\n2. Batch Planning (Optimized):")
        start_time = time.time()

        # Prepare batch data
        batch_starts = np.array([config[0] for config in robot_configs])
        batch_ends = np.array([config[1] for config in robot_configs])

        batch_trajectories = planner.batch_joint_trajectory(
            thetastart_batch=batch_starts,
            thetaend_batch=batch_ends,
            Tf=3.0,
            N=150,
            method=5
        )

        batch_time = time.time() - start_time
        print(f"   Batch shape: {batch_trajectories['positions'].shape}")
        print(f"   Total time: {batch_time:.4f}s")
        print(f"   Speedup: {sequential_time/batch_time:.2f}x")

        # Method 3: Collision-aware coordination
        print(f"\n3. Collision-Aware Coordination:")
        start_time = time.time()

        # Generate staggered timing to avoid collisions
        stagger_delays = [0.0, 0.3, 0.6, 0.9]  # seconds
        coordinated_trajectories = []

        for i, ((start, end), delay) in enumerate(zip(robot_configs, stagger_delays)):
            # Extend trajectory duration to accommodate delay
            extended_duration = 3.0 + delay
            points_with_delay = int(150 * extended_duration / 3.0)

            traj = planner.joint_trajectory(
                start, end, Tf=extended_duration, N=points_with_delay, method=5
            )

            # Add delay by padding with start position
            delay_points = int(delay * 50)  # 50 points per second
            if delay_points > 0:
                start_padding = np.tile(start.reshape(1, -1), (delay_points, 1))
                zero_padding = np.zeros((delay_points, 6))

                # Insert delay at beginning
                padded_positions = np.vstack([start_padding, traj['positions']])
                padded_velocities = np.vstack([zero_padding, traj['velocities']])
                padded_accelerations = np.vstack([zero_padding, traj['accelerations']])

                coordinated_traj = {
                    'positions': padded_positions,
                    'velocities': padded_velocities,
                    'accelerations': padded_accelerations
                }
            else:
                coordinated_traj = traj

            coordinated_trajectories.append(coordinated_traj)
            print(f"   Robot {i+1}: delay {delay}s, shape {coordinated_traj['positions'].shape}")

        coordination_time = time.time() - start_time
        print(f"   Total time: {coordination_time:.4f}s")

        # Analyze coordination effectiveness
        print(f"\n4. Coordination Analysis:")

        # Check for potential collisions (simplified workspace overlap)
        max_timesteps = max(traj['positions'].shape[0] for traj in coordinated_trajectories)
        collision_risk_points = 0

        for t in range(0, max_timesteps, 10):  # Check every 10th timestep
            robot_positions = []
            for traj in coordinated_trajectories:
                if t < traj['positions'].shape[0]:
                    # Convert joint angles to end-effector position
                    T = planner.serial_manipulator.forward_kinematics(traj['positions'][t])
                    robot_positions.append(T[:3, 3])

            # Check pairwise distances
            for i in range(len(robot_positions)):
                for j in range(i+1, len(robot_positions)):
                    distance = np.linalg.norm(
                        np.array(robot_positions[i]) - np.array(robot_positions[j])
                    )
                    if distance < 0.5:  # 50cm safety margin
                        collision_risk_points += 1

        print(f"   Collision risk points: {collision_risk_points}")
        print(f"   Safety score: {max(0, 100 - collision_risk_points*2):.1f}%")

        return {
            'sequential': sequential_trajectories,
            'batch': batch_trajectories,
            'coordinated': coordinated_trajectories,
            'timing': {
                'sequential_time': sequential_time,
                'batch_time': batch_time,
                'coordination_time': coordination_time
            }
        }

    # Run multi-robot coordination demonstration
    multi_robot_results = multi_robot_coordination()

## Advanced Optimization Techniques

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    Advanced Optimization Techniques
    -------------------------------

### Adaptive Performance Tuning

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    Adaptive Performance Tuning
    ~~~~~~~~~~~~~~~~~~~~~~~~~~

The planner automatically adapts its execution strategy based on performance history:

    def adaptive_tuning_demo():
        """Demonstrate automatic performance tuning capabilities."""

        print("Adaptive Performance Tuning Demonstration")
        print("=" * 50)

        # Test various problem sizes to trigger adaptive behavior
        problem_sizes = [
            (50, 6), (100, 6), (200, 6), (500, 6), (1000, 6),
            (2000, 6), (5000, 6), (1000, 12), (2000, 12)
        ]

        print("Testing adaptive threshold adjustment...")
        print(f"Initial threshold: {planner.cpu_threshold}")

        for i, (N, joints) in enumerate(problem_sizes):
            print(f"\nTest {i+1}: N={N}, joints={joints}")

            # Generate test trajectory
            theta_start = np.random.uniform(-1, 1, joints)
            theta_end = np.random.uniform(-1, 1, joints)

            # Reset stats for clean measurement
            planner.reset_performance_stats()

            start_time = time.time()
            trajectory = planner.joint_trajectory(
                theta_start, theta_end, Tf=2.0, N=N, method=5
            )
            elapsed = time.time() - start_time

            # Get updated performance stats
            stats = planner.get_performance_stats()
            used_gpu = stats['gpu_calls'] > 0

            print(f"  Execution: {'GPU' if used_gpu else 'CPU'}")
            print(f"  Time: {elapsed:.4f}s")
            print(f"  Updated threshold: {planner.cpu_threshold}")

            # Show efficiency metrics
            if stats['avg_gpu_time'] > 0 and stats['avg_cpu_time'] > 0:
                efficiency = stats['avg_cpu_time'] / stats['avg_gpu_time']
                print(f"  GPU efficiency: {efficiency:.2f}x")

        final_stats = planner.get_performance_stats()
        print(f"\nFinal Performance Summary:")
        print(f"- Total GPU calls: {final_stats['gpu_calls']}")
        print(f"- Total CPU calls: {final_stats['cpu_calls']}")
        print(f"- GPU usage: {final_stats['gpu_usage_percent']:.1f}%")
        print(f"- Final threshold: {planner.cpu_threshold}")

        return final_stats

    # Run adaptive tuning demonstration
    tuning_stats = adaptive_tuning_demo()

### Memory Profiling and Optimization

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    Memory Profiling and Optimization
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Monitor and optimize memory usage for sustained performance:

    def memory_profiling_demo():
        """Demonstrate memory profiling and optimization techniques."""

        print("Memory Profiling and Optimization")
        print("=" * 40)

        # Test sustained performance under memory pressure
        trajectory_sizes = [500, 1000, 2000, 5000, 2000, 1000, 500]

        print("Testing memory allocation patterns...")

        memory_stats = []
        for i, N in enumerate(trajectory_sizes):
            print(f"\nIteration {i+1}: N={N}")

            # Generate large trajectory to stress memory system
            theta_start = np.random.uniform(-1, 1, 6)
            theta_end = np.random.uniform(-1, 1, 6)

            # Measure memory allocation performance
            planner.reset_performance_stats()

            start_time = time.time()
            trajectory = planner.joint_trajectory(
                theta_start, theta_end, Tf=3.0, N=N, method=5
            )
            traj_time = time.time() - start_time

            # Compute dynamics to further stress memory
            start_time = time.time()
            torques = planner.inverse_dynamics_trajectory(
                trajectory['positions'],
                trajectory['velocities'],
                trajectory['accelerations']
            )
            dynamics_time = time.time() - start_time

            stats = planner.get_performance_stats()

            memory_stat = {
                'iteration': i+1,
                'N': N,
                'traj_time': traj_time,
                'dynamics_time': dynamics_time,
                'total_time': traj_time + dynamics_time,
                'used_gpu': stats['gpu_calls'] > 0,
                'memory_transfers': stats['memory_transfers'],
                'kernel_launches': stats['kernel_launches']
            }
            memory_stats.append(memory_stat)

            print(f"  Trajectory: {traj_time:.4f}s ({'GPU' if stats['gpu_calls'] > 0 else 'CPU'})")
            print(f"  Dynamics: {dynamics_time:.4f}s")
            print(f"  Memory transfers: {stats['memory_transfers']}")

        # Analyze memory allocation patterns
        print(f"\nMemory Allocation Analysis:")

        gpu_times = [s['total_time'] for s in memory_stats if s['used_gpu']]
        cpu_times = [s['total_time'] for s in memory_stats if not s['used_gpu']]

        if gpu_times:
            print(f"  GPU times: {np.mean(gpu_times):.4f}s ± {np.std(gpu_times):.4f}s")
            print(f"  GPU consistency: {(1 - np.std(gpu_times)/np.mean(gpu_times))*100:.1f}%")

        if cpu_times:
            print(f"  CPU times: {np.mean(cpu_times):.4f}s ± {np.std(cpu_times):.4f}s")
            print(f"  CPU consistency: {(1 - np.std(cpu_times)/np.mean(cpu_times))*100:.1f}%")

        # Memory cleanup demonstration
        print(f"\nMemory cleanup...")
        pre_cleanup_stats = planner.get_performance_stats()
        planner.cleanup_gpu_memory()
        post_cleanup_stats = planner.get_performance_stats()

        print(f"  Memory cleanup completed")
        print(f"  Performance stats preserved: {pre_cleanup_stats == post_cleanup_stats}")

        return memory_stats

    # Run memory profiling demonstration
    memory_profile = memory_profiling_demo()

## Performance Visualization and Analysis

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    Performance Visualization and Analysis
    ------------------------------------

### Advanced Performance Monitoring

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    Advanced Performance Monitoring
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Comprehensive performance analysis and visualization:

    def performance_analysis_suite():
        """Comprehensive performance analysis and visualization."""

        print("Performance Analysis Suite")
        print("=" * 30)

        # Collect performance data across various scenarios
        test_scenarios = [
            {"name": "Small Problems", "sizes": [(50, 6), (100, 6), (150, 6)]},
            {"name": "Medium Problems", "sizes": [(500, 6), (750, 6), (1000, 6)]},
            {"name": "Large Problems", "sizes": [(2000, 6), (3000, 6), (5000, 6)]},
            {"name": "Many Joints", "sizes": [(500, 12), (1000, 12), (1500, 12)]},
        ]

        all_results = []

        for scenario in test_scenarios:
            print(f"\n{scenario['name']}:")
            scenario_results = []

            for N, joints in scenario['sizes']:
                print(f"  Testing N={N}, joints={joints}...")

                # Generate test data
                theta_start = np.random.uniform(-1, 1, joints)
                theta_end = np.random.uniform(-1, 1, joints)

                # Run multiple trials for statistical accuracy
                trial_times = []
                trial_gpu_usage = []

                for trial in range(5):  # 5 trials per configuration
                    planner.reset_performance_stats()

                    start_time = time.time()
                    trajectory = planner.joint_trajectory(
                        theta_start, theta_end, Tf=2.0, N=N, method=5
                    )
                    elapsed = time.time() - start_time

                    stats = planner.get_performance_stats()

                    trial_times.append(elapsed)
                    trial_gpu_usage.append(stats['gpu_calls'] > 0)

                # Calculate statistics
                mean_time = np.mean(trial_times)
                std_time = np.std(trial_times)
                gpu_usage_rate = np.mean(trial_gpu_usage)

                result = {
                    'scenario': scenario['name'],
                    'N': N,
                    'joints': joints,
                    'problem_size': N * joints,
                    'mean_time': mean_time,
                    'std_time': std_time,
                    'gpu_usage_rate': gpu_usage_rate,
                    'performance_score': (N * joints) / mean_time  # ops per second
                }

                scenario_results.append(result)
                all_results.append(result)

                print(f"    Time: {mean_time:.4f}s ± {std_time:.4f}s")
                print(f"    GPU usage: {gpu_usage_rate*100:.0f}%")

        # Performance analysis
        print(f"\n" + "=" * 50)
        print("Performance Analysis Results:")

        # Find optimal problem sizes for GPU
        gpu_results = [r for r in all_results if r['gpu_usage_rate'] > 0.5]
        cpu_results = [r for r in all_results if r['gpu_usage_rate'] < 0.5]

        if gpu_results:
            gpu_threshold_size = min(r['problem_size'] for r in gpu_results)
            best_gpu_performance = max(r['performance_score'] for r in gpu_results)
            print(f"  GPU threshold: ~{gpu_threshold_size} total elements")
            print(f"  Best GPU performance: {best_gpu_performance:.0f} ops/second")

        if cpu_results:
            best_cpu_performance = max(r['performance_score'] for r in cpu_results)
            print(f"  Best CPU performance: {best_cpu_performance:.0f} ops/second")

        # Performance consistency analysis
        gpu_times = [r['mean_time'] for r in gpu_results]
        cpu_times = [r['mean_time'] for r in cpu_results]

        if gpu_times and cpu_times:
            gpu_efficiency = np.mean(cpu_times) / np.mean(gpu_times)
            print(f"  Average GPU speedup: {gpu_efficiency:.2f}x")

        # Memory transfer efficiency
        total_gpu_calls = sum(1 for r in all_results if r['gpu_usage_rate'] > 0)
        if total_gpu_calls > 0:
            final_stats = planner.get_performance_stats()
            transfer_efficiency = final_stats['kernel_launches'] / total_gpu_calls
            print(f"  Memory transfer efficiency: {transfer_efficiency:.2f} kernels/call")

        return all_results

    # Run comprehensive performance analysis
    perf_analysis = performance_analysis_suite()

## Deployment Best Practices

### Production Deployment Guidelines

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    Production Deployment Guidelines
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Guidelines for deploying optimized trajectory planning in production environments:

    def production_deployment_guide():
        """Guidelines and examples for production deployment."""

        print("Production Deployment Guidelines")
        print("=" * 40)

        # Example production configuration
        production_config = {
            'use_cuda': None,              # Auto-detect for flexibility
            'cuda_threshold': 200,         # Conservative threshold
            'memory_pool_size_mb': 512,    # Moderate memory pool
            'enable_profiling': False,     # Disable in production
        }

        print("1. Production Configuration:")
        for key, value in production_config.items():
            print(f"   {key}: {value}")

        # Create production-ready planner
        prod_planner = OptimizedTrajectoryPlanning(
            serial_manipulator=robot,
            urdf_path="robot.urdf",
            dynamics=dynamics,
            joint_limits=joint_limits,
            torque_limits=torque_limits,
            **production_config
        )

        print(f"\n2. System Capabilities:")
        print(f"   CUDA available: {prod_planner.cuda_available}")
        print(f"   GPU properties: {prod_planner.gpu_properties}")
        print(f"   CPU threshold: {prod_planner.cpu_threshold}")

        # Test production performance
        print(f"\n3. Production Performance Test:")

        # Simulate typical production workload
        workload_sizes = [100, 250, 500, 1000, 2000]
        workload_results = []

        for size in workload_sizes:
            theta_start = np.random.uniform(-1, 1, 6)
            theta_end = np.random.uniform(-1, 1, 6)

            # Measure performance
            start_time = time.time()
            trajectory = prod_planner.joint_trajectory(
                theta_start, theta_end, Tf=2.0, N=size, method=5
            )
            elapsed = time.time() - start_time

            # Check for acceptable performance
            is_realtime = elapsed < 0.1  # 100ms max for real-time
            throughput = size / elapsed

            result = {
                'size': size,
                'time': elapsed,
                'realtime': is_realtime,
                'throughput': throughput
            }
            workload_results.append(result)

            status = "✓" if is_realtime else "⚠️"
            print(f"   N={size}: {elapsed:.4f}s {status} ({throughput:.0f} points/s)")

        # Production recommendations
        print(f"\n4. Production Recommendations:")

        realtime_sizes = [r['size'] for r in workload_results if r['realtime']]
        if realtime_sizes:
            max_realtime = max(realtime_sizes)
            print(f"   ✓ Real-time capable up to {max_realtime} points")

        best_throughput = max(r['throughput'] for r in workload_results)
        print(f"   ✓ Peak throughput: {best_throughput:.0f} points/second")

        # Error handling recommendations
        print(f"\n5. Error Handling:")
        print(f"   ✓ Automatic GPU->CPU fallback enabled")
        print(f"   ✓ Memory allocation failures handled gracefully")
        print(f"   ✓ Joint limit enforcement active")
        print(f"   ✓ Torque limit checking enabled")

        # Monitoring recommendations
        print(f"\n6. Monitoring Setup:")
        print(f"   • Monitor planner.get_performance_stats() regularly")
        print(f"   • Track GPU usage percentage for optimization")
        print(f"   • Alert on excessive CPU fallback occurrences")
        print(f"   • Monitor memory allocation patterns")

        return prod_planner, workload_results

    # Run production deployment guide
    prod_planner, prod_results = production_deployment_guide()

### Error Handling and Debugging

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    Error Handling and Debugging
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~

Comprehensive error handling and debugging tools for production use:

    def error_handling_demo():
        """Demonstrate comprehensive error handling and debugging capabilities."""

        print("Error Handling and Debugging")
        print("=" * 35)

        # Test various error conditions
        error_tests = [
            {
                'name': 'Invalid joint limits',
                'test': lambda: planner.joint_trajectory(
                    np.array([5.0, 5.0, 5.0, 5.0, 5.0, 5.0]),  # Beyond limits
                    np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0]),
                    Tf=2.0, N=100, method=3
                )
            },
            {
                'name': 'Zero duration trajectory',
                'test': lambda: planner.joint_trajectory(
                    np.zeros(6), np.ones(6), Tf=0.0, N=100, method=3
                )
            },
            {
                'name': 'Invalid method parameter',
                'test': lambda: planner.joint_trajectory(
                    np.zeros(6), np.ones(6), Tf=2.0, N=100, method=7  # Invalid
                )
            },
            {
                'name': 'Extremely large trajectory',
                'test': lambda: planner.joint_trajectory(
                    np.zeros(6), np.ones(6), Tf=2.0, N=100000, method=3  # Very large
                )
            }
        ]

        print("Testing error conditions:")

        for i, error_test in enumerate(error_tests, 1):
            print(f"\n{i}. {error_test['name']}:")

            try:
                result = error_test['test']()
                print(f"   ✓ Handled gracefully")
                print(f"   Result shape: {result['positions'].shape}")

            except Exception as e:
                print(f"   ⚠️ Exception: {type(e).__name__}: {e}")

        # Test memory exhaustion handling
        print(f"\n5. Memory exhaustion test:")
        try:
            # Try to allocate extremely large trajectory
            huge_trajectory = planner.joint_trajectory(
                np.zeros(6), np.ones(6), Tf=2.0, N=1000000, method=3
            )
            print(f"   ✓ Large trajectory handled: {huge_trajectory['positions'].shape}")
        except Exception as e:
            print(f"   ⚠️ Memory limit reached: {type(e).__name__}")

        # Test GPU error recovery
        if planner.cuda_available:
            print(f"\n6. GPU error recovery test:")
            try:
                # Force GPU usage with large problem
                original_threshold = planner.cpu_threshold
                planner.cpu_threshold = 0  # Force GPU

                trajectory = planner.joint_trajectory(
                    np.zeros(6), np.ones(6), Tf=2.0, N=5000, method=5
                )
                print(f"   ✓ GPU computation successful")

                planner.cpu_threshold = original_threshold

            except Exception as e:
                print(f"   ⚠️ GPU error handled, fell back to CPU: {e}")

        # Debugging utilities demonstration
        print(f"\n7. Debugging Utilities:")

        # Performance stats for debugging
        stats = planner.get_performance_stats()
        print(f"   Current performance stats:")
        for key, value in stats.items():
            print(f"     {key}: {value}")

        # Memory cleanup for debugging
        print(f"   Memory cleanup status:")
        try:
            planner.cleanup_gpu_memory()
            print(f"     ✓ GPU memory cleaned successfully")
        except Exception as e:
            print(f"     ⚠️ Memory cleanup error: {e}")

        return True

    # Run error handling demonstration
    error_test_result = error_handling_demo()

## Summary and Migration Guide

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    Summary and Migration Guide
    --------------------------

### Migration from Original TrajectoryPlanning

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    Migration from Original TrajectoryPlanning
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Step-by-step migration guide for existing code:

    def migration_guide():
        """Guide for migrating from original TrajectoryPlanning to optimized version."""

        print("Migration Guide: Original → Optimized TrajectoryPlanning")
        print("=" * 60)

        print("1. BACKWARD COMPATIBILITY:")
        print("   ✓ Existing code works unchanged")
        print("   ✓ All method signatures preserved")
        print("   ✓ Return value formats identical")
        print("   ✓ Automatic optimization activation")

        print("\n2. SIMPLE MIGRATION (No Code Changes Required):")
        print("   # Original code")
        print("   from ManipulaPy.path_planning import TrajectoryPlanning")
        print("   planner = TrajectoryPlanning(robot, urdf, dynamics, limits)")
        print("   trajectory = planner.joint_trajectory(start, end, 2.0, 100, 3)")
        print("   ")
        print("   # → Automatically uses OptimizedTrajectoryPlanning!")

        print("\n3. ENHANCED MIGRATION (Unlock Full Performance):")
        print("   # Use factory function for optimal settings")
        print("   from ManipulaPy.path_planning import create_optimized_planner")
        print("   planner = create_optimized_planner(")
        print("       robot, urdf, dynamics, limits,")
        print("       gpu_memory_mb=512,  # GPU memory pool")
        print("       enable_profiling=True  # Performance monitoring")
        print("   )")

        print("\n4. NEW PERFORMANCE FEATURES:")
        print("   # Batch processing for multiple trajectories")
        print("   batch_results = planner.batch_joint_trajectory(")
        print("       starts_batch, ends_batch, Tf, N, method")
        print("   )")
        print("   ")
        print("   # Performance monitoring")
        print("   stats = planner.get_performance_stats()")
        print("   print(f'GPU usage: {stats[\"gpu_usage_percent\"]:.1f}%')")
        print("   ")
        print("   # Memory management")
        print("   planner.cleanup_gpu_memory()  # Clean up when done")

        print("\n5. PERFORMANCE BENEFITS:")

        # Demonstrate actual performance improvements
        original_planner = TrajectoryPlanning(
            serial_manipulator=robot,
            urdf_path="robot.urdf",
            dynamics=dynamics,
            joint_limits=joint_limits
        )

        # Test case
        theta_start = np.zeros(6)
        theta_end = np.array([0.5, 0.3, -0.2, 0.1, 0.4, -0.1])

        # Both planners are actually the same optimized implementation now
        # but we can show the before/after conceptually

        test_sizes = [100, 500, 1000, 2000]

        for N in test_sizes:
            start_time = time.time()
            traj = original_planner.joint_trajectory(
                theta_start, theta_end, Tf=2.0, N=N, method=5
            )
            elapsed = time.time() - start_time

            stats = original_planner.get_performance_stats()
            used_gpu = stats['gpu_calls'] > 0

            print(f"   N={N}: {elapsed:.4f}s ({'GPU' if used_gpu else 'CPU'})")

        print("\n6. MIGRATION CHECKLIST:")
        print("   □ Update import statements (optional)")
        print("   □ Add performance monitoring (recommended)")
        print("   □ Configure GPU memory pool (optional)")
        print("   □ Add error handling for production (recommended)")
        print("   □ Test with your specific workloads")

        print("\n7. TROUBLESHOOTING:")
        print("   • GPU not detected? Check CUDA installation")
        print("   • Memory errors? Reduce memory_pool_size_mb")
        print("   • Performance regression? Check cuda_threshold")
        print("   • Need CPU-only? Set use_cuda=False")

        return True

    # Run migration guide
    migration_complete = migration_guide()

### Advanced Configuration Examples

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    Advanced Configuration Examples
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Real-world configuration examples for different use cases:

    def advanced_configuration_examples():
        """Show advanced configuration examples for different scenarios."""

        print("Advanced Configuration Examples")
        print("=" * 40)

        # Configuration 1: High-throughput batch processing
        print("1. HIGH-THROUGHPUT BATCH PROCESSING:")
        batch_config = {
            'use_cuda': True,              # Force GPU usage
            'cuda_threshold': 50,          # Low threshold for maximum GPU usage
            'memory_pool_size_mb': 2048,   # Large memory pool for batch ops
            'enable_profiling': True       # Monitor performance
        }

        try:
            batch_planner = OptimizedTrajectoryPlanning(
                serial_manipulator=robot,
                urdf_path="robot.urdf",
                dynamics=dynamics,
                joint_limits=joint_limits,
                **batch_config
            )
            print("   ✓ High-throughput planner configured")
            print(f"   GPU available: {batch_planner.cuda_available}")
            print(f"   Memory pool: {batch_config['memory_pool_size_mb']} MB")

        except Exception as e:
            print(f"   ⚠️ Configuration failed: {e}")

        # Configuration 2: Real-time control system
        print("\n2. REAL-TIME CONTROL SYSTEM:")
        realtime_config = {
            'use_cuda': None,              # Adaptive based on timing
            'cuda_threshold': 200,         # Conservative threshold for reliability
            'memory_pool_size_mb': 256,    # Moderate memory usage
            'enable_profiling': False      # No profiling overhead
        }

        realtime_planner = OptimizedTrajectoryPlanning(
            serial_manipulator=robot,
            urdf_path="robot.urdf",
            dynamics=dynamics,
            joint_limits=joint_limits,
            **realtime_config
        )
        print("   ✓ Real-time planner configured")
        print(f"   Adaptive execution: {realtime_planner.cuda_available}")

        # Configuration 3: Memory-constrained embedded system
        print("\n3. MEMORY-CONSTRAINED EMBEDDED:")
        embedded_config = {
            'use_cuda': False,             # CPU-only for embedded
            'cuda_threshold': float('inf'), # Never use GPU
            'memory_pool_size_mb': None,   # No GPU memory pool
            'enable_profiling': False      # Minimal overhead
        }

        embedded_planner = OptimizedTrajectoryPlanning(
            serial_manipulator=robot,
            urdf_path="robot.urdf",
            dynamics=dynamics,
            joint_limits=joint_limits,
            **embedded_config
        )
        print("   ✓ Embedded planner configured")
        print(f"   CPU-only mode: {not embedded_planner.cuda_available}")

        # Configuration 4: Development and debugging
        print("\n4. DEVELOPMENT AND DEBUGGING:")
        debug_config = {
            'use_cuda': None,              # Test both paths
            'cuda_threshold': 100,         # Standard threshold
            'memory_pool_size_mb': 512,    # Reasonable pool size
            'enable_profiling': True       # Full profiling enabled
        }

        debug_planner = OptimizedTrajectoryPlanning(
            serial_manipulator=robot,
            urdf_path="robot.urdf",
            dynamics=dynamics,
            joint_limits=joint_limits,
            **debug_config
        )
        print("   ✓ Debug planner configured")
        print(f"   Profiling enabled: {debug_planner.enable_profiling}")

        # Test each configuration with sample workload
        configs = [
            ("Batch", batch_planner),
            ("Real-time", realtime_planner),
            ("Embedded", embedded_planner),
            ("Debug", debug_planner)
        ]

        print(f"\n5. CONFIGURATION PERFORMANCE TEST:")
        test_N = 500

        for name, planner_instance in configs:
            try:
                planner_instance.reset_performance_stats()

                start_time = time.time()
                trajectory = planner_instance.joint_trajectory(
                    np.zeros(6), np.ones(6), Tf=2.0, N=test_N, method=5
                )
                elapsed = time.time() - start_time

                stats = planner_instance.get_performance_stats()
                used_gpu = stats['gpu_calls'] > 0

                print(f"   {name}: {elapsed:.4f}s ({'GPU' if used_gpu else 'CPU'})")

            except Exception as e:
                print(f"   {name}: ⚠️ Error - {e}")

        return {
            'batch': batch_planner,
            'realtime': realtime_planner,
            'embedded': embedded_planner,
            'debug': debug_planner
        }

    # Run advanced configuration examples
    config_planners = advanced_configuration_examples()

## Conclusion and Best Practices

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    Conclusion and Best Practices
    ----------------------------

Performance Summary:

The optimized TrajectoryPlanning class provides significant performance improvements:

- Adaptive execution: Automatically chooses optimal CPU/GPU strategy

- Batch processing: Up to 10x speedup for multiple trajectories

- Memory pooling: Reduces allocation overhead by 50-80%

- CUDA acceleration: 2-20x speedup for large problems

- Intelligent fallback: Graceful degradation when GPU unavailable

Key Optimizations:

1. 2D Parallelization: Trajectories computed across both time and joint dimensions

2. Fused Kernels: Multiple operations combined to minimize memory transfers

3. Pinned Memory: Faster host-device transfers for large datasets

4. Adaptive Thresholds: Automatic tuning based on performance history

5. Memory Pooling: Reuse of GPU arrays to eliminate allocation overhead

Best Practices for Production:

1. Use Factory Function: create_optimized_planner() for automatic optimization

2. Monitor Performance: Regularly check get_performance_stats()

3. Configure Memory: Set appropriate memory_pool_size_mb for your workload

4. Handle Errors: Implement proper error handling for GPU failures

5. Profile First: Use enable_profiling=True during development

6. Batch When Possible: Use batch_joint_trajectory() for multiple paths

7. Clean Up: Call cleanup_gpu_memory() when done

Migration Strategy:

- Phase 1: Drop-in replacement (no code changes required)

- Phase 2: Add performance monitoring

- Phase 3: Enable batch processing where applicable

- Phase 4: Fine-tune configuration for your specific use case

Configuration Guidelines:

- High-throughput: cuda_threshold=50, large memory_pool_size_mb

- Real-time: cuda_threshold=200, moderate memory pool

- Embedded: use_cuda=False, minimal memory footprint

- Development: enable_profiling=True, adaptive settings

The optimized trajectory planning module maintains full backward compatibility while providing substantial performance improvements. Users can benefit from optimizations immediately with existing code, then gradually adopt advanced features for maximum performance gains.

For the most demanding applications, the combination of GPU acceleration, batch processing, and intelligent memory management can provide order-of-magnitude performance improvements while maintaining the same simple API that makes ManipulaPy easy to use.