Online Trajectory Deformation and Tracking for Self-entanglement-free Differential-Driven Robots

This paper introduces an optimisation-based trajectory deformation and tracking algorithm for tethered differential-driven mobile robots. The motivation of this work is to generate self-entanglement-free (SEF) commands for a tethered differential-driven robot to track a path. Whilst existing path planners have been capable of generating SEF paths for tethered differential-driven robots lacking an omni-directional tether retracting mechanism, no trajectory planner can handle the unavoidable movement errors that cause robot pose deviate from the pre-defined path. The trajectory deformation and tracking is challenging because the admissible heading direction of the robot is highly constrained by the SEF constraint. As a result, even with an SEF path, the robot still encounters self-entanglement issues during execution.This paper fills this gap by formulating the trajectory deforming and tracking (TDT) problem of a tethered robot into a multi-objective optimisation framework. Explicit consideration of the constraint of the relative angle between the tether stretching direction and the robot’s heading direction to be admissible during its movement is provided in this framework. The proposed algorithm repeatedly deforms the pre-defined path for easier tracking, whilst generating a suitable velocity profile for robot execution. Compared to directly applying the commonly used untethered trajectory deformation and tracking algorithm into tethered cases, the proposed algorithm demonstrates improved performance in terms of minimising the risk of self-entanglement and maximising robot safety. These are validated in both simulated and real scenarios. An open-sourcesourcing implementation has also been provided for the benefit of the robotics community.