Robust motion planning for non-holonomic robots with planar geometric constraints

We present a motion planning algorithm for cases where geometry of the robot cannot be neglected and where its dynamics are governed by non-holonomic constraints. While the two problems are classically treated separately, orientation of the robot strongly affects its possible motions both from the obstacle avoidance and from kinodynamic constraints perspective. We adopt an abstraction based approach ensuring asymptotic completeness. To handle the complex dynamics, a data driven approach is presented to construct a library of feedback motion primitives that guarantee a bounded error in following arbitrarily long trajectories. The library is constructed along local abstractions of the dynamics that enables addition of new motion primitives through abstraction refinement. Both the robot and the obstacles are represented as a union of circles, which allows arbitrarily precise approximation of complex geometries. To handle the geometrical constraints, we represent over- and under-approximations of the three-dimensional collision space as a finite set of two-dimensional "slices" corresponding to different intervals of the robot's orientation space. Starting from a coarse slicing, we use the collision space over-approximation to find a valid path and the under-approximation to check for potential path non-existence. If none of the attempts are conclusive, the abstraction is refined. The algorithm is applied for motion planning and control of a rover with slipping without its prior modelling.QC 20220517