Comparison of predictive controllers for locomotion and balance recovery of quadruped robots

Abstract

As locomotion decisions must be taken by considering the future, most existing quadruped controllers are based on a model predictive controller (MPC) with a reduced model of the dynamics to generate the motion and a wholebody controller to execute it. Yet the simplifying assumptions of the MPC are often chosen ad-hoc or by intuition. In this article, we focus on a set of MPCs and analyze the effect of chosen model reductions on the behavior of the robot. Based on existing formulations, we present additional controllers to better understand the influence of model reductions on the controller capabilities. Finally, we propose a robust predictive controller capable of optimizing the foot placements, gait period, centerof-mass trajectory and ground reaction forces. The behavior of these controllers is statistically evaluated in simulation. This empirical study aims to assess the relative importance of the components of the optimal control problem (variables, costs, dynamics) to be able to take reasoned decisions instead of arbitrarily emphasizing or neglecting some of them. We also provide a qualitative study in simulation and on the real robot Solo-12.

Improved Control Scheme for the Solo Quadruped and Experimental Comparison of Model Predictive Controllers

“…Estimates of the base height, orientation, linear and angular velocities come from a cascade of two complementary filters that combine forward kinematics and inertial measurement unit (IMU) data [19]. While the general control architecture is kept the same, efforts have been made to improve the nominal behavior in terms of stability and robustness so that it makes possible to pursue the work started in [20] where several MPC variants were compared in simulation only. Formerly, base oscillations during motion hampered realworld deployments by impacting the consistency of desired contact forces and footsteps locations over a gait period.…”

“…A common choice is to use a centroidal model of the quadruped, with various levels of reduction. In our previous work [17], [20], pitch and roll velocities were supposed small so that I ω + ω × (Iω) ≈ I ω. The trajectory of the center of mass p was assumed to perfectly follow its reference p ⋆ .…”

“…To study the relevance of these reductions and understand their influence on the controller capabilities, they were progressively lifted and evaluated in simulation [20].…”

“…In practice, with a small margin for µ, this approximation works well and no slipping occurs. For the last variant, contrary to [20] which applied a quadratic cost on the distance between r i and r ⋆ i , so that the optimization was done around the heuristic locations, here only the distance between the foot location and the shoulder is penalized to be completely heuristic-free. This cost ℓ r,i can be seen as a form of regularization so that, on average, contacts are centered on the shoulders projection, as it is done using Raibert's heuristic.…”

“…Out of the prototyping phase, all control blocks were converted from Python to C++ for computational efficiency, except for the main loop which calls them. MPCs were implemented using Crocoddyl [24] as in [20]. The QP problem was solved with OSQP [25].…”