Algorithms for Robot Dynamics and Trajectory Planning

Robot dynamics and trajectory planning constitute core technologies in industrial robot control. For 6-DOF serial robots like the classic PUMA560, algorithm implementation typically involves the following key components:

Kinematic Calculations Forward Kinematics: Compute end-effector position and orientation from joint angles using coordinate transformation matrices based on DH parameters, typically implemented through matrix multiplication of sequential transformations. Inverse Kinematics: Solve joint angles from target end-effector pose using geometric methods or numerical iteration algorithms, requiring handling of multiple solutions and singularity issues through techniques like pseudo-inverse Jacobian.

Dynamics Analysis Forward Dynamics: Calculate robot motion states from joint forces/torques, commonly used for simulation verification through numerical integration of dynamic equations. Inverse Dynamics: Compute required joint torques from desired motion trajectories using core algorithms like recursive Newton-Euler formulation or Lagrangian dynamics, involving iterative calculations of forces and moments along the kinematic chain.

Trajectory Planning Users can specify target points via GUI, with the program automatically generating smooth joint-space or Cartesian-space trajectories using interpolation methods like cubic polynomials, S-curves, or B-splines to avoid instantaneous acceleration discontinuities through constraint-based optimization. Animation functions visually demonstrate robot movement processes, assisting in verification of obstacle avoidance and workspace reachability through real-time kinematic updates.

The MATLAB program's modular design supports secondary development, where modifying DH parameters or dynamic parameters (mass, inertia) can adapt the system to other serial robot models, providing a rapid verification platform for algorithm research or engineering applications through configurable parameter files and reusable function modules.