The hybrid nature of multi-contact robotic systems, due to making and breaking contact with the environment, creates significant challenges for high-quality control. Existing model-based methods typically rely on either good prior knowledge of the multi-contact model or require significant offline model tuning effort, thus resulting in low adaptability and robustness. In this paper, we propose a real-time adaptive multi-contact model predictive control framework,  which enables online adaption of the hybrid multi-contact model and continuous improvement of the control performance for contact-rich tasks. This framework includes an adaption module, which continuously learns a residual of the hybrid model to minimize the gap between the prior model and reality, and a real-time multi-contact MPC controller. We demonstrated the effectiveness of the framework in synthetic examples,  and applied it on hardware to solve contact-rich manipulation tasks, where a robot uses its end-effector to roll different unknown objects on a table to track given paths. The hardware experiments show that with a rough prior model, the multi-contact MPC controller adapts itself on-the-fly with an adaption rate around 20 Hz and successfully manipulates previously unknown objects with non-smooth surface geometries.

We consider solving model predictive control (MPC) problems subject to multi-contact hybrid dynamics, which can be locally represented as a Linear Complementarity System (LCS). In previous works [1], we present Consensus Complementarity Control (C3) that tackles the non-convex MPC problem at real-time rates. However, accurate multi-contact models are hard to get due to factors like geometry and friction coefficient, which pose challenges to the model-based approach such as C3. Therefore, we aim to achieve online model learning for adaptive MPC. Utilizing our previous works on offline LCS learning [2], we introduce a variant of the implicit loss function that was proposed. Our focus is on learning both the hybrid boundary and the contact dynamics, represented as a residual term in the complementarity part of the LCS formulation.

An example that demonstrates the principle of our approach is a classical cart-pole underactuated system that has been augmented with two soft walls. The model has a wrong estimate of the distance to the wall, leading to the contact model predicting both situations: contact and no contact, as well as the presence or absence of actual contact events during those situations. We highlight that our approach is capable of adapting even when there are no actual contact events. As shown in the above figure, a “contact event” refers to a situation where actual physical contact is occurring, while “contact prediction” pertains to instances where the model anticipates contact, potentially inaccurately. Our method can produce meaningful gradients, even when there is no actual contact event (yellow region). The only scenario in which a zero gradient is produced is when the model and data both agree that there is no contact (white region).

This work was supported by the National Science Foundation under Grants No. FRR-2238480, EFRI-1935294, and Toyota Research Institute.