On the Efficiency of the SST Planner to Find Time Optimal Trajectories Among Obstacles With a DDR Under Second Order Dynamics

Abstract

In this work, we study a sampling based motion planner able to deal with a kinodynamic problem. We want to move a robot from an initial state to a final one, along the minimum cost trajectory in an environment with obstacles. In particular, we study the effect of using extremal controls as the inputs for two sampling-based algorithms, namely, the Stable Sparse Rapidly Exploring Random Tree (SST), and the asymptotically optimal planner SST*, in terms of the speed at which such methods converge and the resulting cost of a given stable trajectory. To exemplify our analysis and demonstrate the usefulness of the present study, we elaborate on the case of finding time optimal trajectories among obstacles for a differential drive robot (DDR) considering second-order dynamics. To further show the generality of the approach, we also present an experimental study comparing the use of extremal controls against the use of the entire range of controls, for other four systems. We found that utilizing extremal controls improves the convergence of the addressed algorithms.