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Dave Lattanzi’s Arm Planning Algorithms

This document provides an overview of arm planning algorithms, implemented using Python, Pygame, and Numpy. It extends the skeleton code of LT, utilizing inverse Jacobian configurations and the "phantom" linkage method for effective path planning. Key features include the utilization of Rapidly-exploring Random Trees (RRT) for navigation through obstacles. The main program initializes configurations, executes inverse and forward kinematics to find paths, and animates the arm movement. Future upgrades are discussed to improve path planning and collision checks.

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Dave Lattanzi’s Arm Planning Algorithms

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  1. Dave Lattanzi’s Arm Planning Algorithms

  2. Overview • Used Python, Pygame, and Numpy • Extended LT’s skeleton code • Configurations found using inverse jacobian • “Phantom” linkage method • Path planning using RRT • Implicit map vs explicit map

  3. Main Program Pseudocode Initialize(xyz_goal, obstacles, arm_params) Until effector_location == xyz_goal: new_config = iKinematics(xyz_goal) effector_location= fKinematics(new_config) startTree(startConfig) endTree(goalConfig) Until arm.intersection = True: RRTExtend(startTree,randomConfig) RRTExtend(endTree,randomConfig) BuildPath() AnimatePath()

  4. Inverse Kinematics iKinematics(arm, goalxyz): J = getJacobian(arm) InverseJ = pseudoinverse(J) Δxyz = β(goalxyz – arm.locationxyz) ΔΘ = InverseJ * Δxyz new_config = arm.config + ΔΘ return new_config

  5. Forward Kinematics fKinematics(arm, goal_config): T[i] = Transform(arm.joint[i], goal_config) for i = 1:DOF: arm.joints[i] = arm.T[i] * arm.joints[i] return

  6. RRTExtend RRTExtend(tree, randomConfig): nearestConfig = nearest(tree) Δ = (randomConfig – nearestConfig) / norm (randomConfig – nearestConfig) Until nearestConfig == randomConfig: nearestConfig = nearestConfig + Δ checkIntersections() checkCollisions()

  7. Planning Demo: 2 Obstacles

  8. Planning Demo: 4 Obstacles

  9. Issues and Future Upgrades • Restrict RRT to allowable halfspace • Refine dummy linkage method (damping?) • Optimize searches • Figure out tranpose/inverse issue

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