In teleoperation, the human operator typically controls only the end-effector pose, which often leads to self-collisions of the manipulator and collisions with environmental obstacles, since joints and links are not controlled individually. A common strategy to mitigate this issue is to enhance the operator's input using optimal-control-based trajectory planning. As derivative-based solvers require differentiable constraints, existing approaches either approximate robots and obstacles with spheres, reducing geometric accuracy, or approximate derivatives, degrading convergence and increasing computation times. We address these limitations by adapting a recent formulation of differentiable collision-avoidance constraints, based on duality in convex optimization, to the teleoperation setting. The robot is approximated with capsules and the environment with polytopes. We compare the resulting trajectory planning method against state-of-the-art techniques in simulation with varying numbers of obstacles and evaluate it on a UR5e manipulator in a real-world teleoperation test. Results show that our approach achieves lower computation times while enabling more accurate obstacle modeling, leading to smoother and collision-free end-effector teleoperation.

翻译：在遥操作中，操作员通常仅控制末端执行器的位姿，由于关节和连杆未被单独控制，这常导致机械臂自碰撞及与环境障碍物的碰撞。缓解此问题的常见策略是通过基于最优控制的轨迹规划来增强操作员输入。由于基于导数的求解器需要可微约束，现有方法要么用球体近似机器人和障碍物（降低几何精度），要么近似导数（导致收敛性下降并增加计算时间）。我们通过将基于凸优化对偶性的可微避碰约束最新公式适配至遥操作场景，解决了上述局限。机器人采用胶囊体建模，环境采用多面体建模。我们通过不同数量障碍物的仿真实验，将所提轨迹规划方法与前沿技术进行对比，并在UR5e机械臂的真实遥操作测试中评估其性能。结果表明，本方法在实现更低计算时间的同时，支持更精确的障碍物建模，从而实现了更平滑且无碰撞的末端执行器遥操作。