A novel mechanism to derive self-entanglement-free (SEF) path for tethered differential-driven robots is proposed in this work. The problem is tailored to the deployment of tethered differential-driven robots in situations where an omni-directional tether re-tractor is not available. This is frequently encountered when it is impractical to concurrently equip an omni-directional tether retracting mechanism with other geometrically intricate devices, such as a manipulator, which is notably relevant in applications like disaster recovery, spatial exploration, etc. Without specific attention to the spatial relation between the shape of the tether and the pose of the mobile unit, the issue of self-entanglement arises when the robot moves, resulting in unsafe robot movements and the risk of damaging the tether. In this paper, the SEF constraint is first formulated as the boundedness of a relative angle function which characterises the angular difference between the tether stretching direction and the robot's heading direction. Then, a constrained searching-based path planning algorithm is proposed which produces a path that is sub-optimal whilst ensuring the avoidance of tether self-entanglement. Finally, the algorithmic efficiency of the proposed path planner is further enhanced by proving the conditioned sparsity of the primitive path validity checking module. The effectiveness of the proposed algorithm is assessed through case studies, comparing its performance against untethered differential-driven planners in challenging planning scenarios. A comparative analysis is further conducted between the normal node expansion module and the improved node expansion module which incorporates sparse waypoint validity checking. Real-world tests are also conducted to validate the algorithm's performance. An open-source implementation has also made available for the benefit of the robotics community.

翻译：本文提出了一种新颖的机制，用于生成绳系差分驱动机器人的无自缠绕路径。该问题专门针对无法使用全向绳缆收缩器的情况下的绳系差分驱动机器人部署场景。当将全向绳缆收缩机构与其它几何结构复杂的装置（如机械臂）同时部署不可行时，这种情况经常出现，尤其是在灾害救援、空间探索等应用中尤为突出。若不关注绳缆形状与移动单元位姿之间的空间关系，机器人在运动过程中会产生自缠绕问题，导致不安全运动行为并存在损坏绳缆的风险。本文首先将无自缠绕约束表述为表征绳缆拉伸方向与机器人航向方向之间角度差的相对角度函数的有界性条件。随后，提出一种基于约束搜索的路径规划算法，该算法在确保避免绳缆自缠绕的同时生成次优路径。最后，通过证明原始路径有效性检查模块的条件化稀疏性，进一步提升了所提路径规划器的算法效率。通过挑战性规划场景中的案例研究，将该算法与无绳系差分驱动规划器进行性能对比，并进一步对普通节点扩展模块与集成稀疏航点有效性检查的改进节点扩展模块开展比较分析。同时开展真实环境实验验证算法性能。为促进机器人社区发展，相关开源实现也已公开。