A follow-up article on the MPC-Net Algorithm was just released:

Imitation Learning from MPC for Quadrupedal Multi-Gait Control.
Alexander Reske, Jan Carius, Yuntao Ma, Farbod Farshidian, Marco Hutter
IEEE International Conference on Robotics and Automation (ICRA), 2021

Here is the abstract of the publication:

We present a learning algorithm for training a single policy that imitates multiple gaits of a walking robot. To achieve this, we use and extend MPC-Net, which is an Imitation Learning approach guided by Model Predictive Control (MPC). The strategy of MPC-Net differs from many other approaches since its objective is to minimize the control Hamiltonian, which derives from the principle of optimality. To represent the policies, we employ a mixture-of-experts network (MEN) and observe that the performance of a policy improves if each expert of a MEN specializes in controlling exactly one mode of a hybrid system, such as a walking robot. We introduce new loss functions for single- and multi-gait policies to achieve this kind of expert selection behavior. Moreover, we benchmark our algorithm against Behavioral Cloning and the original MPC implementation on various rough terrain scenarios. We validate our approach on hardware and show that a single learned policy can replace its teacher to control multiple gaits.

A preprint of the paper is available below.

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This work was supported by the Swiss National Science Foundation (SNSF) through project 166232, 188596, the National Centre of Competence in Research Robotics (NCCR Robotics), and the European Union’s Horizon 2020 (grant agreement No.852044). Moreover, this work has been conducted as part of ANYmal Research, a community to advance legged robotics.