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Stable gait generation is a crucial problem for legged robot locomotion asthis impacts other critical performance factors such as, e.g. mobility over anuneven terrain and power consumption. Gait generation stability results fromthe efficient control of the interaction between the legged robot's body andthe environment where it moves. Here, we study how this can be achieved by acombination of model-predictive and predictive reinforcement learningcontrollers. Model-predictive control (MPC) is a well-established method thatdoes not utilize any online learning (except for some adaptive variations) asit provides a convenient interface for state constraints management.Reinforcement learning (RL), in contrast, relies on adaptation based on pureexperience. In its bare-bone variants, RL is not always suitable for robots dueto their high complexity and expensive simulation/experimentation. In thiswork, we combine both control methods to address the quadrupedal robot stablegate generation problem. The hybrid approach that we develop and apply uses acost roll-out algorithm with a tail cost in the form of a Q-function modeled bya neural network; this allows to alleviate the computational complexity, whichgrows exponentially with the prediction horizon in a purely MPC approach. Wedemonstrate that our RL gait controller achieves stable locomotion at shorthorizons, where a nominal MP controller fails. Further, our controller iscapable of live operation, meaning that it does not require previous training.Our results suggest that the hybridization of MPC with RL, as presented here,is beneficial to achieve a good balance between online control capabilities andcomputational complexity.

Combining model-predictive control and predictive reinforcement learning for stable quadrupedal robot locomotion