The small size, high dexterity, and intrinsic compliance of continuum robots (CRs) make them well suited for constrained environments. Solving the inverse kinematics (IK), that is finding robot joint configurations that satisfy desired position or pose queries, is a fundamental challenge in motion planning, control, and calibration for any robot structure. For CRs, the need to avoid obstacles in tightly confined workspaces greatly complicates the search for feasible IK solutions. Without an accurate initialization or multiple re-starts, existing algorithms often fail to find a solution. We present CIDGIKc (Convex Iteration for Distance-Geometric Inverse Kinematics for Continuum Robots), an algorithm that solves these nonconvex feasibility problems with a sequence of semidefinite programs whose objectives are designed to encourage low-rank minimizers. CIDGIKc is enabled by a novel distance-geometric parameterization of constant curvature segment geometry for CRs with extensible segments. The resulting IK formulation involves only quadratic expressions and can efficiently incorporate a large number of collision avoidance constraints. Our experimental results demonstrate >98% solve success rates within complex, highly cluttered environments which existing algorithms cannot account for.

翻译：连续体机器人因其尺寸小、灵活度高且具有内在柔顺性，非常适用于受限环境。求解逆运动学问题——即找到满足期望位置或姿态查询的机器人关节构型——是任何机器人结构在运动规划、控制与标定中的基本挑战。对于连续体机器人而言，在高度受限的工作空间中避免障碍物极大地增加了寻优可行逆运动学解的复杂性。现有算法在缺乏精确初始化或多次重启的情况下，常无法找到可行解。我们提出CIDGIKc（连续体机器人的距离几何逆运动学凸迭代算法），该算法通过一系列半定规划来解决这些非凸可行性问题，其目标函数旨在鼓励低秩极小化。CIDGIKc基于一种新颖的距离几何参数化方法，对具有可伸缩段的连续体机器人常曲率段几何进行建模。由此得到的逆运动学公式仅包含二次表达式，并能高效融入大量避碰约束。实验结果表明，在现有算法无法处理的复杂高拥挤环境中，CIDGIKc的求解成功率超过98%。