Robust Approximate Constraint-Following Control Design Based on Udwadia–Kalaba Theory and Experimental Verification for Collaborative Robots With Inequality Constraints and Uncertainties

Abstract

A robust approximate constraint-following control (RACC) approach is proposed in this article for collaborative robots with inequality constraints. The trajectory-following control and boundary control of the robot are investigated. First, an explicit constraint equation for the collaborative robot system is established based on the Udwadia–Kalaba (U-K) theory. Second, due to the monotone unbounded property of the tangent function, a special function is constructed to transform the joint output angles of the constrained robot into unconstrained state variables, and a new form of the robot constraint equation is obtained. Through this transformation, the joint motion of the robot will always be confined to specified angles and follow the desired trajectory. The constraint equation ensures the safety of the robot at the algorithmic level and innovatively solves the control problem of the equality and inequality of the robot's motion. According to theoretical analysis, the control approach can deal with uncertainty and satisfy both uniform boundedness (UB) and uniform ultimate boundedness (UUB) requirements. Finally, based on the rapid controller prototype CSPACE and a two-degree-of-freedom collaborative robot platform, experimental verification is carried out. Numerical simulation and experimental results demonstrate that the proposed RACC approach with state transformation exhibits significant advantages in trajectory tracking performance and safety for collaborative robots.