Maneuverability Ellipsoid for Analyzing Sampling Space of Model Predictive Path-Integral Control for 4WIDS Robot Navigation

Four-wheel independent drive and steering (4WIDS) robot possesses high maneuverability, with exploiting its stemming 8-DoF (Degrees of Freedom) control inputs, for navigation itself in complex, obstacle-rich environments. In such scenarios, Model Predictive Path Integral (MPPI) control, a sampling-based approach to model predictive control, has emerged as a powerful technique. While MPPI can effec- tively handle nonlinear dynamics and non-differentiable cost functions, it confronts the fundamental challenge of curse of dimensionality, where the number of required samples grows exponentially with the dimension of the control space. Although dimensionality reduction of the control space is a known coun- termeasure for suppressing the computational burden of MPPI, a systematic analysis for rationally designing the reduced space remains as an open issue. This research therefore addresses this issue by first proposing a novel metric, Maneuverability Ellipsoid of the 4WIDS, to quantify the robot’s maneuvering capability with regard to the multiple DoFs of the robot control inputs. Based on this ellipsoid, we numerically analyze a sampling method for selecting variables that contribute higher maneu- verability in the MPPI framework. The robot maneuverability index is also proposed that is quantified by the size and shape of the manipulability ellipsoid. Through simulations, we demonstrate that this index significantly correlates with the success rate of robot navigation.