Nullspace Structure in Model Predictive Control
This work addresses robotic task planning by leveraging redundancies in MPC, but it appears incremental as it builds on existing MPC frameworks with specific computational enhancements.
The paper tackles the problem of planning redundancy in Model Predictive Control (MPC) by presenting a nullspace structure with quadratic cost and linear dynamics, exploiting low-rank precision matrices for hierarchical task planning and treating nullspace computation as a fusion problem using a product of Gaussian experts.
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.