UR16e Industrial Robot — Modeling, Planning, and Control

Kinematics, dynamics, collision detection, RRT+B-spline planning, time-optimal trajectory generation, and computed-torque/robust control with Simulink-URDF simulation.

This project focuses on the UR16e industrial manipulator, completing a full pipeline from kinematic and dynamic modeling, collision detection, path planning and smoothing, and time-optimal trajectory generation to controller design and simulation.
The system is validated by importing the SolidWorks assembly into MATLAB/Simulink through URDF, supporting a flexible manufacturing scenario involving pick-and-place and palletizing tasks.

1. Kinematic and Dynamic Modeling

  • Forward Kinematics (FK): Established using DH parameters for a 6-DOF joint chain; results verified with MATLAB’s Robotics Toolbox.
  • Inverse Kinematics (IK): Applied the Newton–Raphson iterative method (after testing the spherical-wrist approximation) to solve joint angles; consistent with toolbox results.
  • Inverse Dynamics (ID): Implemented the Newton–Euler recursive algorithm from end-effector to base to compute joint torques.
  • Forward Dynamics (FD): Derived (M(q)), (C(q,\dot q)), and (G(q)) via the Lagrangian formulation: [ M(q)\ddot q + C(q,\dot q)\dot q + G(q) = \tau ] enabling computation of joint accelerations consistent with the analytical model.

2. Collision Detection via Capsule Approximation

  • Link Modeling: Each link is approximated as a capsule (cylinder with hemispherical ends), while obstacles are enclosed by bounding spheres.
  • Environment Collision: Reduced to computing the minimum point–segment distance versus the sum of radii.
  • Self-Collision: Converted to segment–segment distance checks between link pairs. Four relative cases are defined for robust detection.
  • During motion planning, the detector is called online rather than pre-computing the entire free space.

3. Path Planning and Smoothing

  • Task Scenario: pick–place and palletizing operations in a flexible manufacturing cell.
  • RRT: Implemented in the joint space, adopting a goal-biasing strategy for faster convergence.
  • B-Spline Smoothing: Applied cubic B-spline interpolation (de Boor–Cox recursion and matrix form) to smooth RRT piecewise paths.

4. Time-Optimal Trajectory Generation

Under joint velocity, acceleration, and torque limits, the trajectory timing is optimized to minimize total execution time: [ \min \sum_k \Delta t_k ] A nonlinear time-scaling and re-parameterization ensure that all kinematic and dynamic constraints are satisfied.

5. Control Design and Robustness Evaluation

  • Computed-Torque Control (CTC): [ \tau = M(q)(\ddot q_d + K_p e + K_d \dot e) + C(q,\dot q)\dot q + G(q) ] achieving accurate tracking of the reference trajectory.
  • Robust Control: Added compensation for model uncertainties; stability guaranteed by Lyapunov conditions on (P,Q).
  • Disturbance Tests: Injected joint measurement noise, torque noise, and parameter perturbations in (M(q)) and (G(q)) to evaluate tracking stability.

6. System-Level Simulation (URDF → Simulink)

  • Defined coordinate frames via MDH/DH and exported URDF from SolidWorks.
  • Imported into Simulink using smimport, built the system diagram, and simulated the collision-free trajectory animation.

Tools

MATLAB / Simulink · Robotics System Toolbox · Custom geometric collision module (capsule–sphere) · RRT + B-spline · SolidWorks → URDF

Files