Humanoid robot trajectory generator for safe haptic arm control via arm wrench limitation, trajectory compensation and reactive stepping

Abstract

An optimal trajectory planner for humanoid robots with a haptically controlled arm is proposed. This trajectory planner simultaneously plans time-varying arm wrench constraints, foot step positions, and a Center-of-Mass (COM) trajectory. This system has the useful characteristic of ensuring that the robot does not fall when the human operator commands an excessively large arm wrench and in the long term the resultant arm wrench approaches the desired arm wrench via a combination of changes in the foot positions and the COM position. This is accomplished via a Model Predictive Controller with a Quadratic Programming-based trajectory optimizer that calculates a time series of arm wrench constraints, foot positions and, a COM trajectory that optimizes the criteria of minimizing the tracking error of the desired foot positions and the desired arm wrench. A simulation and experiments demonstrate the validity of the proposed algorithm.

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

“…However, the ZMP constraints have been numerically verified to be non-positivesemidefinite 4 . Thus the ZMP constraints are non convex and as a result the QCQP is non-convex [21].…”

“…Regardless, as will be shown in the experiment section, simply using SQP to solve this QCQP problem can produce practically useful results. 4 In particular, P i,w in (15) was identified to be a hollow symmetric matrix Algorithm 1 Variable COM height trajectory generator…”

“…In this work the model predictive control (MPC) approach from [3] was used to formulate the trajectory planning problem of the feet as well as the COM in all three dimensions. MPC is very attractive because it can be used to generate an optimal motion plan while incorporating a variety of constraints such as ZMP, foot overstretch, foot collision, COM position&velocity and arm force constraints [4]. However, different from [3] this work modeled the ZMP constraints as quadratic constraints instead of linear constraints because doing so allows the COM vertical state to be included.…”