Introducing Force Feedback in Model Predictive Control

Abstract

In the literature about model predictive control (MPC), contact forces are planned rather than controlled. In this paper, we propose a novel paradigm to incorporate effort measurements into a predictive controller, hence allowing to control them by direct measurement feedback. We first demonstrate why the classical optimal control formulation, based on position and velocity state feedback, cannot handle direct feedback on force information. Following previous approaches in force control, we then propose to augment the classical formulations with a model of the robot actuation, which naturally allows to generate online trajectories that adapt to sensed position, velocity and torques. We propose a complete implementation of this idea on the upper part of a real humanoid robot, and show through hardware experiments that this new formulation incorporating effort feedback outperforms classical MPC in challenging tasks where physical interaction with the environment is crucial.

Non-Prehensile Object Transportation via Model Predictive Non-Sliding Manipulation Control

“…Several recent papers have focused instead on the problem of executing robotic manipulation and, in general, interaction tasks using model predictive control (MPC). To date, the common trend is to integrate contact forces tracking as an objective and feedback their measure in the controller [8]. For instance, a whole-body MPC for dynamically stabilizing a mobile manipulator while executing end-effector pose tracking tasks while skillfully planning for end-effector contact forces is devised in [27].…”

“…In addition, to guarantee a continuous execution of the task, we consider the rate-of-change of the joint torques as output of our controller (in literature, this is referred to as jerk control [7]) which, once integrated over time, returns the overall input of our robotic system. This procedure makes the obtained joint torque profile (and thus the system accelerations) continuous and allows integrating force signals stemming from the interaction as feedback into the controller [8]. We derive and incorporate the combined system (manipulator and object) dynamical model and its related constraints into a nonlinear model predictive control (NMPC) problem [9].…”

On the Derivation of the Contact Dynamics in Arbitrary Frames: Application to Polishing with Talos

“…We use the force feedback MPC formulated in [11], which solves the following Optimal Control Problem (OCP) min w(.),z(. )…”

“…In the literature, several contact models have been used in MPC. The rigid contact dynamics implemented in Pinocchio [10] is utilized for instance in [11]- [13]. In our previous work [11] the target force was expressed in a local frame whose alignment with the surface normal was part of the task.…”

“…The rigid contact dynamics implemented in Pinocchio [10] is utilized for instance in [11]- [13]. In our previous work [11] the target force was expressed in a local frame whose alignment with the surface normal was part of the task. In [12], [13] contact force constraints are expressed in a surface-aligned frame but the contact forces are optimized as control variables and not explicitly tracked.…”