Model Predictive Control for Legged Robots

Optimal planning is essential when it comes to autonomy in legged locomotion. In the last few decades, different optim- ization techniques have been presented to design a legged lo- comotion framework, such as Trajectory Optimization (TO) and Model Predictive Control (MPC). The choice of a dy- namic model utilized while synthesizing these planners plays a pivotal role because the chosen model defines the accuracy of the planning and also becomes a deciding factor for the computational cost of these techniques. In the first part of this thesis, we propose a closed-loop validation procedure for the Single Rigid Body Dynamics (SRBD) model and its vari- ants used for optimal planning. Thereafter, we introduce a Linear Time-Varying (LTV) based TO for legged locomotion, followed by the simulation results and discussion on its lim- itations in re-planning. Re-planning in legged locomotion is crucial to track the de- sired user velocity while adapting to the terrain and reject- ing external disturbances. In the second part of this thesis, we propose and test in experiments a real-time Nonlinear Model Predictive Control (NMPC) tailored to a legged robot to achieve dynamic locomotion on various terrains. We in- troduce a novel mobility-based criterion to define an NMPC cost that enhances the locomotion of quadruped robots while maximizing leg mobility and improving adaptation to the ter- rain features. The NMPC is based on the Real-Time Iteration (RTI) scheme that allows us to re-plan online at 25 Hz with a prediction horizon of 2 seconds. In simulations, the NMPC is tested to traverse a set of pallets of different sizes, walk into a V-shaped chimney, and locomote over rough terrain. In real experiments, we demonstrate the effectiveness of our NMPC with the mobility feature that allowed IIT’s 87 kg quadruped robot HyQ to achieve an omni-directional walk on flat terrain, traverse a static pallet, and adapt to a repositioned pallet dur- ing a walk.In the final part of this thesis, we present the extension of the NMPC with other dynamic gaits, i.e., trot and pace. We also introduce an Optimization-Based Reference Gener- ator (ORG) that computes dynamically feasible trajectories for the state and control input based on the Linear Inver- ted Pendulum (LIP) model-based optimization and Quad- ratic Programming (QP) based mapping. These feasible tra- jectories are passed to the NMPC to cope with the disturb- ances while following the user-defined trajectories with the dynamic gaits. We show the effectiveness of this two-stage optimization scheme in simulations and experiments per- formed on the AlienGo robot to trot in a straight line and to recover from the external disturbances while trotting. We also compare the performance of the two-stage scheme with respect to a traditional heuristic reference generator in an ex- periment.