Approximating Global Contact-Implicit MPC via Sampling and Local Complementarity

TL;DR

The paper tackles real-time global optimization for contact-rich manipulation by coupling a global, contact-free sampling stage with a local, contact-rich CI-MPC based on LCS. It introduces a bilevel framework where end-effector locations are globally sampled to seed a local C3-based controller, enabling real-time, dexterous manipulation despite the locality of traditional CI-MPC. Key contributions include the separation of modes, parallel sample evaluation with $\text{C3Cost}$, hysteresis-driven switching, and a practical implementation on a Franka Panda that demonstrates improved precision and safety relative to a non-local baselines in simulation and hardware. This approach advances practical, generalizable manipulation by leveraging global exploration to augment local, reliable contact-implicit control, with potential impact on home and industrial robotics.

Abstract

To achieve general-purpose dexterous manipulation, robots must rapidly devise and execute contact-rich behaviors. Existing model-based controllers are incapable of globally optimizing in real-time over the exponential number of possible contact sequences. Instead, recent progress in contact-implicit control has leveraged simpler models that, while still hybrid, make local approximations. However, the use of local models inherently limits the controller to only exploit nearby interactions, potentially requiring intervention to richly explore the space of possible contacts. We present a novel approach which leverages the strengths of local complementarity-based control in combination with low-dimensional, but global, sampling of possible end-effector locations. Our key insight is to consider a contact-free stage preceding a contact-rich stage at every control loop. Our algorithm, in parallel, samples end effector locations to which the contact-free stage can move the robot, then considers the cost predicted by contact-rich MPC local to each sampled location. The result is a globally-informed, contact-implicit controller capable of real-time dexterous manipulation. We demonstrate our controller on precise, non-prehensile manipulation of non-convex objects using a Franka Panda arm. Project page: https://approximating-global-ci-mpc.github.io

Figures (9)

• Figure 1: Our real-time CI-MPC combines a global, explorative contact-free stage with a local contact-rich stage. At every control loop, our algorithm chooses contact-rich actions to make goal progress, or contact-free actions to pursue more amenable starting locations for future contact-rich actions.
• Figure 2: Left: A spherical end effector approaches a spherical object on a flat table. Loosely speaking, the LCS approximates object geometry as a set of hyperplanes coincident with and tangent to their witness points with respect to other geometries of interest. The hyperplane for ground-object contact is in red, while the robot-object contact hyperplane is in blue. Each initial condition has its associated MPC cost. In this example, the rightmost sample's LCS approximation allows the robot to most effectively foresee progressing the object toward the goal and correspondingly has the lowest sample cost. Right: These LCS approximations are well-defined even for more complicated geometries, only requiring witness points between the object and other collision geometry.
• Figure 3: The algorithm for one control loop of our sampling-based contact-implicit controller. The third step that solves a local contact-implicit MPC problem for each sample can be parallelized, since each plan is independent. In this example, the top sample's CI-MPC plan makes little progress to the object goal, and thus is associated with high cost. The second sample's CI-MPC plan shows more progress, and thus is lower cost.
• Figure 4: We demonstrate our controller on two manipulation examples: 3D pose goals with a jack (left), and 2D planar pose goals with a T (right). The inset renderings in the bottom corners depict a view of the object's goal pose relative to the current pose estimate.
• Figure 5: Illustration of contact points considered for the jack object.