High absolute accuracy is an essential prerequisite for a humanoid robot to autonomously and robustly perform manipulation tasks while avoiding obstacles. We present for the first time a kinematic model for a humanoid upper body incorporating joint and transversal elasticities. These elasticities lead to significant deformations due to the robot's own weight, and the resulting model is implicitly defined via a torque equilibrium. We successfully calibrate this model for DLR's humanoid Agile Justin, including all Denavit-Hartenberg parameters and elasticities. The calibration is formulated as a combined least-squares problem with priors and based on measurements of the end effector positions of both arms via an external tracking system. The absolute position error is massively reduced from 21mm to 3.1mm on average in the whole workspace. Using this complex and implicit kinematic model in motion planning is challenging. We show that for optimization-based path planning, integrating the iterative solution of the implicit model into the optimization loop leads to an elegant and highly efficient solution. For mildly elastic robots like Agile Justin, there is no performance impact, and even for a simulated highly flexible robot with 20 times higher elasticities, the runtime increases by only 30%.

翻译：高绝对精度是仿人机器人自主鲁棒执行操作任务并避开障碍物的关键前提。我们首次提出了一个融合关节与横向弹性的仿人上半身运动学模型。机器人自重导致的弹性形变显著，该模型通过力矩平衡隐式定义。我们成功标定了DLR仿人机器人Agile Justin的该模型，包括所有Denavit-Hartenberg参数及弹性参数。标定过程被构造为带先验的联合最小二乘问题，基于外部跟踪系统对双臂末端执行器位置的测量数据。整个工作空间中的绝对位置误差从21毫米大幅降低至3.1毫米平均误差。在运动规划中运用这一复杂隐式运动学模型颇具挑战性。我们证明：在基于优化的路径规划中，将隐式模型的迭代求解集成至优化循环内可产生优雅且高效的解决方案。对于Agile Justin这类低弹性机器人，该方法无性能影响；即便在弹性系数高出20倍的模拟高柔性机器人中，运行时间仅增加30%。