Nullspace Structure in Model Predictive Control

TL;DR

This paper explores the nullspace structure in Model Predictive Control (MPC) to leverage redundancy for hierarchical task planning, using low-rank precision matrices and Gaussian fusion methods, demonstrated through robotics examples.

Contribution

It introduces a novel nullspace analysis in MPC with quadratic cost and linear dynamics, enabling hierarchical planning via Gaussian expert fusion.

Findings

Nullspace computation can be formulated as a Gaussian fusion problem.

Exploits low-rank structure of precision matrices for efficient planning.

Validated with robotics simulations and point mass examples.

Abstract

Robotic tasks can be accomplished by exploiting different forms of redundancies. This work focuses on planning redundancy within Model Predictive Control (MPC) in which several paths can be considered within the MPC time horizon. We present the nullspace structure in MPC with a quadratic approximation of the cost and a linearization of the dynamics. We exploit the low rank structure of the precision matrices used in MPC (encapsulating spatiotemporal information) to perform hierarchical task planning, and show how nullspace computation can be treated as a fusion problem (computed with a product of Gaussian experts). We illustrate the approach using proof-of-concept examples with point mass objects and simulated robotics applications.