MR-MPCC: Model Predictive Contouring Control for Robotic Manipulator Tracking under Moving Reference Frames

Tactile sensing plays a key role in robotic manipulation, particularly in tasks like surface inspection. Successful execution requires maintaining contact while accurately tracking object contours. In this work, we propose a Vision-Based Tactile Model Predictive Control (VBT-MPC) framework for robotic contour following using a Vision-Based Tactile Sensor (VBTS) mounted in an eye-in-hand configuration. The proposed controller operates directly in contour features space, thereby avoiding the need for separate pose-estimation modules or complex force-control architectures. We further compare our VBT-MPC with visual-servoing strategies adapted to tactile features, and evaluate contour tracking on objects with diverse geometries and materials in both simulation and real-world experiments.

Sampling-based model predictive control methods, such as Model Predictive Path Integral (MPPI), offer derivative-free optimization and robustness in complex robotic systems. However, standard MPPI relies on cost-based soft penalties that cannot guarantee hard-constraint satisfaction, severely limiting its applicability to highly constrained tasks such as closed-chain manipulation. To address this, we propose Manifold-Constrained MPPI (MC-MPPI), a real-time sampling-based control framework that regulates nonlinear equality constraints while preserving the computational advantages of MPPI. The key idea is to decouple the constrained optimal control problem into latent-space planning and execution-level correction. At the planning stage, a Variational Autoencoder (VAE) learns a low-dimensional latent representation of the constraint manifold, enabling MPPI to efficiently generate near-feasible candidate trajectories without per-sample modification. Since this reference enables accurate linearization of the equality constraints, an execution-level Quadratic Programming (QP) controller resolves the residual manifold mismatch in a single solve rather than through iterative projection. Experiments on a 14-DoF closed-chain dual-arm system in both simulation and real-world settings demonstrate 100 Hz planning and 500 Hz execution, equality-residual regulation in static and dynamic environments, and a 95% success rate over 40 randomized hardware trials. Supplementary videos and implementation details are available at https://rcilab.github.io/mcmppi.

Model Predictive Path Integral (MPPI) control is widely used in manipulation for its gradient-free, parallel handling of non-convex costs. Manipulation tasks, however, often impose constraints that hold throughout the motion: a closed kinematic chain that two grasping arms keep exactly, or joint limits and obstacle clearances that are never crossed. MPPI handles such constraints only through the cost, as soft penalties that hold approximately and fail under a strong task cost. To address this, we propose Projection-Retraction MPPI (PR-MPPI), which enforces the constraints inside the sampled dynamics. At every rollout step, the sampled velocity is projected to satisfy both constraint types: the equality restricts it to a subspace, and each inequality to a half-space within that subspace, so inequality handling never breaks the equality. This projection, however, satisfies the constraints only to first order, and a finite step leaves a small drift off the equality. Therefore, we retract the returned command back onto the constraint to numerical tolerance and independent of task weighting. We validate PR-MPPI on 14-DoF dual-arm systems. In simulation, the returned commands satisfy the closed-chain equality to numerical tolerance through a joint-limit stress test and randomized obstacle avoidance. On real hardware, the arms of a Unitree H1-2 humanoid reactively avoid a moving obstacle. Code and experiment videos are available at https://rcilab.github.io/prmppi.