Control and Simulation of Motion of Constrained Multibody Systems Based on Projection Matrix Formulation

TL;DR

This paper introduces a unified projection matrix approach for the dynamics and control of constrained multibody systems, enabling analysis and simulation even with redundant constraints and passive joints.

Contribution

It develops a novel projection-based dynamic formulation that handles redundant constraints and passive joints without changing control structure.

Findings

Simulation can proceed with redundant constraints or singular configurations.

The control scheme minimizes actuation force norm and is stable.

Analytical condition simplifies force control in decoupled systems.

Abstract

This paper presents a unified approach for inverse and direct dynamics of constrained multibody systems that can serve as a basis for analysis, simulation, and control. The main advantage of the formulation of the dynamic is that it does not require the constraint equations to be linearly independent. Thus, a simulation may proceed even in the presence of redundant constraints or singular configurations and a controller does not need to change its structure whenever the mechanical system changes its topology or number of degrees of freedom. A motion control scheme is proposed based on a projected inverse-dynamics scheme which proves to be stable and minimizes the weighted Euclidean norm of the actuation force. The projection-based control scheme is further developed for constrained systems, e.g. parallel manipulators, which have some joints with no actuators (passive joints). This is complemented by the development of constraint force control. A condition on the inertia matrix resulting in a decoupled mechanical system is analytically derived which simplifies the implementation of the force control.