A robust linear MPC approach to online generation of 3D biped walking motion

A crucial part in biped walking motion generation is to ensure dynamic feasibility, which takes the form of a nonlinear constraint in the general case. Our proposition is to bound the nonlinear part of the dynamic feasibility constraint between some properly chosen extreme values. Making sure that this constraint is satisfied for the extreme values guarantees its satisfaction for all possible values in between. This follows a classical approach from robust nonlinear control theory, which is to consider a nonlinear dynamical system as a specific selection of a time-invariant Linear Differential Inclusion. As a result, dynamic feasibility can be imposed by using only linear constraints, which can be included in an efficient linear MPC scheme, to generate 3D walking motions online. Our simulation results show two major achievements: 1) walking motions over uneven ground such as stairs can be generated online, with guaranteed kinematic and dynamic feasibility, 2) walking on flat ground is significantly improved, with a 3D motion of the CoM closely resembling the one observed in humans.