Rigid-body dynamics derivatives improve modeling of closed-chain systems
Adapting Rigid-Body Dynamics Derivatives for Constraint Embedding Closed-Chain Models
Robotics
Summary
Calculating how robots move and respond often involves understanding their joints and how they connect. The authors worked on improving methods that calculate changes in robot movement, especially for robots with loops in their joints (closed chains). They extended earlier methods to handle more complex joint types that appear when these loops are modeled with certain constraints. Their improvements allow for more accurate and efficient simulation and control of these robots, especially when motors and extra moving parts are included.
What this means in practice
- •For robotics control engineers: Enable more precise dynamics computations for robots with closed-chain actuators to improve model-predictive control accuracy.
- •For simulation software developers: Incorporate adapted derivative algorithms into differentiable physics simulators to better handle constraint-embedded robot models.
- •For industrial automation technicians: Improve modeling of robotic arms with embedded motor rotors for more accurate maintenance diagnostics.$Commercial implications: This advancement enables development of more accurate diagnostic tools for robotic arms used in industry.
Authors
Daniel J. Volpi, Patrick M. Wensing
Abstract
This paper extends an existing algorithm for the first-order derivatives of rigid-body dynamics to the case of closed-chain kinematic systems modeled using constraint embed- ding. Many standard dynamics algorithms apply to both open- chain and constraint-embedded models, but existing efficient derivative methods assume joint velocity effects are locally config- uration invariant. We remove this assumption and derive adapted algorithms that extend dynamics derivatives to more general joint types, including those arising in constraint-embedded closed- chain models. Our results compare conventional pin-joint robot models with more complete actuation models that capture local closed chains. We show that the additional terms introduced by these generalizations have low computational impact when mod- eling actuation kinematics alone, but can incur higher cost when additional rigid bodies, such as motor rotors, are included in the actuation chain, or when considering non-local loops. Overall, these results enable more accurate dynamics computations for constraint-embedded actuation submechanisms to be adopted in model-predictive control and differentiable simulation.