- 3-DOF Planar Cable-Driven Robot
- 4 Antagonistic Driving Cables
- Dynamic Mass Matrix & Jacobian
- Real-Time MATLAB Animation
ROBOTICS DYNAMICS / CABLE-DRIVEN PARALLEL ROBOTS
Multibody Kinematics, Dynamics, and Antagonistic Cable Tension Control
Cable-robot-R implements a complete simulation and control architecture for a 3-DOF planar cable-driven parallel robot (CDPR). Actuated by four antagonistic cables mounted on a 2.0 m × 2.0 m frame, the system models inverse kinematics, configuration-dependent mass matrices, positive tension distribution, and continuous trajectory tracking in MATLAB.
Analytical kinematics & Jacobian formulation
Computes closed-form inverse kinematics (invKIN.m) and joint angle configurations (TETA.m) for target end-effector coordinates. The geometric Jacobian (jak.m) maps joint angular velocities to platform Cartesian velocities while evaluating kinematic manipulability.
Lagrangian dynamics & inertia matrix
Derives the non-linear equations of motion using rigid-body Lagrange mechanics. Calculates the state-dependent mass matrix M(q) (Mass_matrix.m) across distributed link masses (m1=6 kg, m2=4 kg, m3=1 kg) and rotational inertias Ji = (mi·li²)/3.
Antagonistic cable force allocation
Solves positive cable tension feasibility constraints (cables.m). Because cables cannot push, the four tension vectors are continuously optimized to ensure positive tension bounds are preserved throughout high-acceleration maneuvers.
Trajectory control & ODE simulation pipeline
Implements closed-loop PD control with dynamic feedforward compensation (controle.m). Integrates continuous state equations forward in time using MATLAB ODE solvers (RRode.m), backed by automated unit benchmarks (TestControle.m) and real-time animation (Rrobot2024.m).
System Specifications & Dynamic Parameters
- Manipulator Geometry
- 3 articulated planar links: l₁=0.5 m, l₂=0.5 m, l₃=0.3 m (Platform r=0.25 m)
- Mass Distribution
- Link masses: m₁=6.0 kg, m₂=4.0 kg, m₃=1.0 kg (Total moving mass: 11.0 kg)
- Actuation System
- 4 antagonistic cables anchored to a rigid 2.0 m × 2.0 m perimeter frame
- Control Law
- PD feedback control with dynamic mass-matrix feedforward compensation
- ODE Integrator
- Adaptive numerical ODE time-stepping in MATLAB (RRode.m, Rrobot2024.m)
- Verification Suite
- Automated control testbench (TestControle.m) and trajectory diagnostics
Significance for Advanced Robotics & Automation
Demonstrates rigorous mathematical modeling and tension optimization essential for large-scale cable-suspended robotics, high-speed pick-and-place manipulators, and aerospace wind tunnel test systems.