Minimum-Time Energy-Optimal Path Following Control for a Wheeled Mobile Robot subject to Velocity Constraints using Linear Programming

This paper focuses on developing a path planning algorithm for a wheeled mobile robot with actuator constraints. The proposed motion planning approach is divided into two stages: path planning, followed by path following. In the path planning stage, the problem is formulated in a path coordinate frame and solved using an optimal control framework. The Bernstein basis function weighted benchmark minimum energy cost function is used to achieve the rest-to-rest motion. In the path-following stage, the optimal controls from the first stage are discretized and posed as a Linear programming problem to determine the time scaling to satisfy the actuator limits. Control in the path frame is transformed into time domain while satisfying the velocity constraints. The Pioneer3-DX test platform is used to validate the control method experimentally. Multiple trials are conducted to statistically validate the proposed approach.