Safer Gap: Safe Navigation of Planar Nonholonomic Robots With a Gap-Based Local Planner

Abstract

This paper extends the gap-based navigation technique <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Potential Gap</i> with safety guarantees at the local planning level for a kinematic planar nonholonomic robot model, leading to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Safer Gap</i>. It relies on a subset of navigable free space from the robot to a gap, denoted the keyhole region. The region is defined by the union of the largest collision-free disc centered on the robot and a collision-free trapezoidal region directed through the gap. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Safer Gap</i> first generates Bézier-based collision-free paths within the keyhole regions. The keyhole region of the top scoring path is encoded by a shallow neural network-based zeroing barrier function (ZBF) synthesized in real-time. Nonlinear Model Predictive Control (NMPC) with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Keyhole ZBF</i> constraints and output tracking of the Bézier path, synthesizes a safe kinematically feasible trajectory. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Potential Gap</i> projection operator serves as a last action to enforce safety if the NMPC optimization fails to converge to a solution within the prescribed time. Simulation and experimental validation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Safer Gap</i> confirm its collision-free navigation properties.