Convex Iteration for Distance-Geometric Inverse Kinematics

Inverse kinematics (IK) is the problem of finding robot joint configurations that satisfy constraints on position or pose one more end-effectors. For robots with redundant degrees freedom, there often an infinite, nonconvex set solutions. The IK further complicated when collision avoidance are imposed by obstacles in workspace. In general, closed-form expressions yielding feasible do not exist, motivating use numerical solution methods. However, these approaches rely local optimization problems, requiring accurate initialization numerous re-initializations to converge a valid solution. this work, we first formulate inverse complex workspace as convex feasibility whose low-rank points provide exact We then present \texttt{CIDGIK} (Convex Iteration for Distance-Geometric Kinematics), algorithm solves sequence semidefinite programs objectives designed encourage minimizers. Our formulation elegantly unifies configuration space and robot: intrinsic geometry obstacle both expressed simple linear matrix equations inequalities. experimental results variety popular manipulator models demonstrate faster convergence than conventional nonlinear optimization-based approach, especially environments many obstacles.