Real-Time Acceleration-Continuous Path-Constrained Trajectory Planning With Built-In Tradeoff Between Cruise and Time-Optimal Motions

Abstract

In this article, a novel real-time acceleration-continuous path-constrained trajectory planning algorithm is proposed with an appealing built-in tradeoff mechanism between the cruise motion and time-optimal motion. Different from existing approaches, the proposed approach smoothens time-optimal trajectories with bang-bang input structures to generate acceleration-continuous trajectories while preserving the completeness property. More importantly, a novel built-in tradeoff mechanism is proposed and embedded into the trajectory planning framework so that the proportion of the cruise motion and time-optimal motion can be flexibly adjusted by changing a user-specified functional parameter. Thus, the user can easily apply the trajectory planning algorithm for various tasks with different requirements on motion efficiency and cruise proportion. Moreover, it is shown that feasible trajectories are computed more quickly than optimal trajectories. Rigorous mathematical analysis and proofs are presented for those aforementioned theoretical results. Comparative simulations and experimental results on an omnidirectional wheeled mobile robot demonstrate that flexible tunings between the cruise and time-optimal motions can be achieved in a higher computational efficiency manner by the proposed algorithm. Note to Practitioners —This article is motivated by the time-optimal and smooth motion planning problem for mobile robots along given paths. Existing approaches generally use the piecewise polynomial interpolations to smoothen and adjust feasible trajectories. This article proposes a novel path-constrained trajectory planning approach, which preserves properties of completeness and a high-efficient tradeoff mechanism between the optimal and cruise motions when achieving a globally optimal and acceleration-continuous trajectory. Comparative experimental results with other methods show the effectiveness of the proposed approach. In future research, we will attempt to integrate the proposed approach with typical path planning methods to achieve a complete and high-efficient motion planning framework.