Universal Trajectory Optimization Framework for Differential Drive Robot Class (I)

Abstract

Differential drive robots are widely used in various scenarios thanks to their straightforward principle, from household service robots to disaster response field robots. The nonholonomic dynamics and possible lateral slip of these robots lead to difficulty in getting feasible and high-quality trajectories. Although there are several types of driving mechanisms for real-world applications, they all share a similar driving principle, which involves controlling the relative motion of independently actuated tracks or wheels to achieve both linear and angular movement. Therefore, a comprehensive trajectory optimization to compute trajectories efficiently for various kinds of differential drive robots is highly desirable. In this paper, we propose a universal trajectory optimization framework, enabling the generation of high-quality trajectories within a restricted computational timeframe for these robots. We introduce a novel trajectory representation based on polynomial parameterization of motion states or their integrals, such as angular and linear velocities, which inherently matches the robots' motion to the control principle. The trajectory optimization problem is formulated to minimize computation complexity while prioritizing safety and operational efficiency. We conduct extensive simulations and real-world testing in crowded environments with three kinds of differential drive robots to validate the effectiveness of our approach.