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We present a versatile nonlinear model predictive control (NMPC) formulationfor quadrupedal locomotion. Our formulation jointly optimizes a base trajectoryand a set of footholds over a finite time horizon based on simplified dynamicsmodels. We leverage second-order sensitivity analysis and a sparse Gauss-Newton(SGN) method to solve the resulting optimal control problems. We furtherdescribe our ongoing effort to verify our approach through simulation andhardware experiments. Finally, we extend our locomotion framework to deal withchallenging tasks that comprise gap crossing, movement on stepping stones, andmulti-robot control.

Nonlinear Model Predictive Control for Quadrupedal Locomotion Using Second-Order Sensitivity Analysis