Modular method simplifies closed-chain robot motion calculations
Modular Kinematic Reduction of Closed-Chain Mechanisms Using Path Assembly and Defect Homotopy
Robotics
Summary
Robots with closed loops in their arms are tricky to model because some parts move together in complicated ways. The authors created a new method that breaks down these loops into simpler pieces, making calculations easier and faster. Their approach uses math to measure differences along paths and fixes errors smoothly. Tests showed their method is very accurate and much quicker than older techniques. This could help design and control complex robotic arms more efficiently.
What this means in practice
- •For robotics engineers: Integrate modular closure resolution to improve accuracy and speed when modeling and controlling robots with closed-loop mechanisms.
- •For mechanical design teams: Use the framework to verify and simulate complex multi-path closed mechanisms during design phases to ensure feasible motion without heavy computation.
Authors
Mohammad Dastranj, Jouni Mattila
Abstract
Closed kinematic chains complicate modular modeling by coupling active and passive coordinates through nonlinear closure constraints. This paper presents a Path-Assembled Closure Differential Mapping (PACDM) framework for modular closure resolution and kinematic reduction. Each closure element compares two ordered transformation paths with common endpoints, with their mismatch expressed through the logarithm on SE(3) and the corresponding Jacobian assembled from local transformation derivatives. Multi-path modules are constructed from a minimal set of pairwise closure elements, while rank-revealing analysis selects locally independent scalar constraints. A defect homotopy recovers closure-consistent passive coordinates from approximate estimates along a feasible and regular continuation path. At regular configurations, implicit differentiation yields the local active-to-passive differential mapping, which is subsequently used in a predictor-corrector continuation procedure for prescribed motion. The framework is evaluated on a seven-degree-of-freedom heavy-duty manipulator containing two-path and three-path closed-chain modules. Comparison with Simscape Multibody yields trajectory root-mean-square errors below 8.5 x 10^-10 rad, while predictor-corrector continuation is approximately 45.8 times faster than applying defect homotopy at every trajectory sample.