The general inverse kinematics (IK) problem of a manipulator, namely that of acquiring the self-motion manifold (SMM) of all admissible joint angles for a desired end-effector pose, plays a vital role in robotics modeling, planning and control. To efficiently solve the generalized IK, this paper proposes an interval branch-and-bound-based approach, which is augmented with a fast numerical IK-solver-enabled search heuristics. In comparison to independent solutions generated by sampling based methods, our approach generates patches of neighboring solutions to provide richer information of the inherent geometry of the SMM for optimal planning and other applications. It can also be utilized in an anytime fashion to obtain solutions with sub-optimal resolution for applications within a limited period. The performance of our approach is verified by numerical experiments on both non-redundant and redundant manipulators.

翻译：机械臂的通用逆运动学（IK）问题，即获取期望末端执行器姿态下所有可行关节角度的自运动流形（SMM），在机器人建模、规划与控制中具有至关重要的作用。为高效求解广义逆运动学，本文提出一种基于区间分支定界的方法，并辅以快速数值逆运动学求解器支持的搜索启发式策略。与基于采样的方法生成的独立解相比，本方法生成邻域解块，可为最优规划及其他应用提供SMM内在几何结构的更丰富信息。该方法还可采用任意时间模式运行，在有限时间内获得具有次优分辨率的解。通过在非冗余与冗余机械臂上的数值实验验证了所提方法的性能。