Verified motion planner eliminates robot joint-limit violations with 100% success rate

A team of researchers from Carnegie Mellon University and Mitsubishi Electric Research Laboratories has introduced a novel approach to task-space motion planning that ensures robotic manipulators never violate their joint-angle limits. Reactive planners like Bug2 move in fixed Cartesian steps but become dangerous near kinematic singularities—small Cartesian moves can demand huge joint changes. Clipping those joints to their limits causes tracking drift and mission failure.

The new method, called SOS-verified planning, computes at each step the largest Cartesian hyperrectangle that is certifiably reachable under given joint displacement bounds. It uses a second-order polynomial approximation of the inverse kinematics combined with the S-procedure to formulate a small semidefinite program. Solving that program (or an equivalent bisection exploiting quadratic structure) yields a certified step size in sub-millisecond time. Integrated with Bug2, the planner adapts step size to local kinematic conditioning.

In statistical evaluation across 94 adversarial scenarios spanning six joint-limit settings, the SOS-verified planner achieved zero joint-limit violations and 100% goal-reaching. In contrast, standard Bug2 violated joint limits in 6–11% of steps and failed to reach the goal in up to 18% of scenarios. The method is computationally lightweight and ready for real-time robotic control.