Optimisation-based Quasi Algebraic Controller for trajectory-tracking of a Class of Affine Systems with Constrained Controls

Controlling the locomotion of autonomous legged robots necessitates sophisticated techniques to address system constraints, imposing significant computational demands that hinder embedded implementation.This paper proposes a novel trajectory-tracking approach for a class of affine systems with constrained controls, tailored specifically for autonomous navigation.Leveraging an algebraic strategy initially designed for trajectory-tracking in unmanned wheeled vehicles, our methodology reformulates the approach into a streamlined optimisation problem.This reformulation ensures resulting controls adhere to the robot's actuator limits and accelerations, facilitating smoother, more energy-efficient manoeuvres.The theoretical stability of the proposed controller is established, and empirical validation is conducted through field experiments.Comparative analysis against a nonlinear model predictive controller (iNMPC) with integral mode demonstrates comparable performance, with significantly reduced computational overhead.Specifically, our controller achieves results akin to an iNMPC with a control horizon of 1 (s), sampled every 0.05 (s), showcasing its efficiency in autonomous legged robot navigation.