PR-MPPI gives dual-arm robots exact constraint control on 14-DoF systems

Seulchan Lee, Leesai Park, Minhyeong Kang, and Sanghyun Kim have introduced Projection-Retraction MPPI (PR-MPPI), a new control framework for robot manipulators that enforces motion constraints exactly rather than approximately. Classical Model Predictive Path Integral (MPPI) control is popular in manipulation because it handles non-convex costs without gradient information and parallelizes well. However, MPPI incorporates constraints like joint limits, obstacle clearances, and closed kinematic chains only as soft penalties in the cost function. Those penalties hold approximately and often fail when the task cost is strong, leading to constraint violation or drift. PR-MPPI solves this by injecting constraint enforcement directly into the sampled dynamics: on every rollout step, sampled velocities are projected so equality constraints restrict the command to a linear subspace, and inequality constraints restrict it to half-spaces within that same subspace. This structure means inequality handling can never break the equality constraint. Because projection is only first-order accurate, a retraction step then corrects residual drift, returning the command onto the constraint manifold to numerical tolerance and independent of task weighting.

The team validated PR-MPPI on 14-DoF dual-arm systems in simulation. The returned commands maintained a closed-chain equality to numerical tolerance through both a joint-limit stress test and randomized obstacle avoidance. On real hardware, the arms of a Unitree H1-2 humanoid reactively avoided a moving obstacle. PR-MPPI retains MPPI's gradient-free, parallelizable approach to non-convex costs while making constraint satisfaction a structural property of the rollout rather than a tuning compromise. It is published as arXiv:2608.07573, with code and experiment videos released alongside the paper. For roboticists, PR-MPPI opens a practical path toward safer model-predictive control in contact-rich and bimanual manipulation, where exact closed-chain constraints are critical for carrying objects, assembly, and human-robot interaction.