We present a general approach for controlling robotic systems that make and break contact with their environments: linear contact-implicit model-predictive control (LCI-MPC). Our use of differentiable contact dynamics provides a natural extension of linear model-predictive control to contact-rich settings. The policy leverages precomputed linearizations about a reference state or trajectory while contact modes, encoded via complementarity constraints, are explicitly retained, resulting in policies that can be efficiently evaluated while maintaining robustness to changes in contact timings. In many cases, the algorithm is even capable of generating entirely new contact sequences. To enable real-time performance, we devise a custom structure-exploiting linear solver for the contact dynamics. We demonstrate that the policy can respond to disturbances by discovering and exploiting new contact modes and is robust to model mismatch and unmodeled environments for a collection of simulated robotic systems, including: pushbot, hopper, quadruped, and biped.
In this paper, we consider sorting for the broad class of micromachines (also known as microswimmers, microrobots, micropropellers, etc.) propelled by rotating magnetic fields. We present a control policy that capitalizes on the variation in magnetic properties between otherwise-homogeneous micromachines to enable the sorting of a select fraction of a group from the remainder and prescribe its net relative movement, using a uniform magnetic field that is applied equally to all micromachines. The method enables us to accomplish this sorting task using open-loop control, without relying on a structured environment or localization information of individual micromachines. With our method, the control time to perform the sort is invariant to the number of micromachines. The method is verified through simulations and scaled experiments. Finally, we include an extended discussion about the limitations of the method and open questions related to its practical application.
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