Real-Time Variable Center of Mass Height Trajectory Planning for Humanoids Robots

Abstract

This paper presents a trajectory planner for humanoid robots based on nonlinear model predictive control that can generate trajectories with variable center of mass heights and adaptive foot positions in real-time. This is done by analytically formulating the zero moment point constraint as a quadratic function that includes the vertical center of mass state. This constraint is then combined with linear foot position constraints, constraints on the vertical center of mass state and a quadratic goal function to form a quadratically constrained quadratic program. This program is then solved via sequential quadratic programing. It can be solved in less than 5 ms on average with a 3.4 Ghz CPU by taking advantage of the fact that the analytic problem formulation allows the analytical gradients to be computed, thus time consuming numerical differentiation is avoided and the gradient computation time is reduced from 12.4 ms to 0.12 ms. An experiment on a 3.5 Kg robot is conducted to verify the effectiveness of this algorithm in walking on a terrain where the two feet are at different heights. Lastly it is shown via simulation that the proposed approach can improve disturbance recovery capacity by up to 7%.

Multi-contact walking pattern generation based on model preview control of 3D COM accelerations

“…The Newton-Euler equations describe the components of motion that are independent from the actuation power of the robot, and play a critical role in locomotion. Most of today's trajectory generators [14], [4], [15], [8], [6], [2], [10] focus on solving these equations and rely on whole-body controllers to take actuation limits into account at a later stage of the motion generation process.…”

“…• Bretl & Lall: the algorithm from [18], in the implementation from [28] but using GLPK as LP solver. 10 The Parma + hull solution is the slowest but most numerically stable, while cdd only is only competitive in singlesupport. Neck to neck are Bretl & Lall and cdd + hull, with the latter faster in single-and double-support.…”

“…Following the design introduced by Hirukawa et al [4], one active line of research [5], [6], [7] uses contact forces as control variables, which produces optimization problems with simple inequality constraints but a high number of control variables. Another line of research reduces the problem to the center of mass motion [8], [9], [10], [11]. Optimization problems are then much smaller, but their inequality constraints become quadratic (and nonpositive-semidefinite [10]).…”

Versatile Reactive Bipedal Locomotion Planning Through Hierarchical Optimization

“…Brasseur et al [10] limited the nonlinear part of the dynamic feasibility constraints between extreme values and proposed a linear MPC for gait generation with time-varying height trajectory. In [11], the constrained optimization problem was formulated as a quadratically constrained Nonlinear MPC (NMPC) problem and was solved fast by Sequential Quadratic Programming (SQP). Besides, momentum optimization has attracted more attention in recent years [12], [13].…”

Robust optimal planning and control of non-periodic bipedal locomotion with a centroidal momentum model

“…Model predictive control is explored elsewhere (Audren et al, 2014; Brasseur et al, 2015; Faraji et al, 2014; Nguyen et al, 2017; Tassa et al, 2012; Van Heerden, 2017) for complex humanoid behaviors. Stephens and Atkeson (2010) use model predictive control for push recovery by planning future steps.…”