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A novel mechanism to derive self-entanglement-free (SEF) path for tethereddifferential-driven robots is proposed in this work. The problem is tailored tothe deployment of tethered differential-driven robots in situations where anomni-directional tether re-tractor is not available. This is frequentlyencountered when it is impractical to concurrently equip an omni-directionaltether retracting mechanism with other geometrically intricate devices, such asa manipulator, which is notably relevant in applications like disasterrecovery, spatial exploration, etc. Without specific attention to the spatialrelation between the shape of the tether and the pose of the mobile unit, theissue of self-entanglement arises when the robot moves, resulting in unsaferobot movements and the risk of damaging the tether. In this paper, the SEFconstraint is first formulated as the boundedness of a relative angle functionwhich characterises the angular difference between the tether stretchingdirection and the robot's heading direction. Then, a constrainedsearching-based path planning algorithm is proposed which produces a path thatis sub-optimal whilst ensuring the avoidance of tether self-entanglement.Finally, the algorithmic efficiency of the proposed path planner is furtherenhanced by proving the conditioned sparsity of the primitive path validitychecking module. The effectiveness of the proposed algorithm is assessedthrough case studies, comparing its performance against untethereddifferential-driven planners in challenging planning scenarios. A comparativeanalysis is further conducted between the normal node expansion module and theimproved node expansion module which incorporates sparse waypoint validitychecking. Real-world tests are also conducted to validate the algorithm'sperformance. An open-source implementation has also made available for thebenefit of the robotics community.

Sparse Waypoint Validity Checking for Self-Entanglement-Free Tethered Path Planning