CIDGIKc: Distance-Geometric Inverse Kinematics for Continuum Robots

TL;DR

CIDGIKc is a novel distance-geometric inverse kinematics algorithm for continuum robots that efficiently finds feasible configurations in cluttered environments, outperforming existing methods.

Contribution

The paper introduces CIDGIKc, a new algorithm using semidefinite programming and a distance-geometric parameterization for solving IK in continuum robots with collision avoidance.

Findings

Achieves over 98% success rate in complex environments

Efficiently incorporates collision avoidance constraints

Outperforms existing IK algorithms in cluttered scenarios

Abstract

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.