Title: A Parametric MPC Approach to Balancing the Cost of Abstraction for Differential-Drive Mobile Robots,
Abstract: When designing control strategies for differential-drive mobile robots, one
standard tool is the consideration of a point at a fixed distance along a line
orthogonal to the wheel axis instead of the full pose of the vehicle. This
abstraction supports replacing the non-holonomic, three-state unicycle model
with a much simpler two-state single-integrator model (i.e., a
velocity-controlled point). Yet this transformation comes at a performance
cost, through the robot's precision and maneuverability. This work contains
derivations for expressions of these precision and maneuverability costs in
terms of the transformation's parameters. Furthermore, these costs show that
only selecting the parameter once over the course of an application may cause
an undue loss of precision. Model Predictive Control (MPC) represents one such
method to ameliorate this condition. However, MPC typically realizes a control
signal, rather than a parameter, so this work also proposes a Parametric Model
Predictive Control (PMPC) method for parameter and sampling horizon
optimization. Experimental results are presented that demonstrate the effects
of the parameterization on the deployment of algorithms developed for the
single-integrator model on actual differential-drive mobile robots.