Switched control barrier functions-based safe docking control strategy for a planar floating platform

Abstract

In this article, we present and experimentally validate a safe docking control strategy designed for an experimental planar floating platform, called the Slider. Three degrees-of-freedom (DOF) platforms like the Slider are used extensively in space industry and academia to emulate micro-gravity conditions on Earth, for validating in-plane Guidance, Navigation and Control (GNC) algorithms. The Slider uses an air cushion (induced by air bearings) to levitate on a smooth flat table, thus emulating the in-plane zero-gravity motion of a spacecraft in orbit. The proposed docking control strategy is applicable in the in-plane approach and docking phases of space docking missions, and is based on the Control Barrier Functions (CBF) approach, where a safe set (a Cardioid), capturing the clearance and direction-of-approach constraints, is rendered positively forward invariant. To enable precise and safe docking in the presence of unmodeled dynamics, disturbances induced by the tether and drifts induced by the non-flat floating surface, we present a switching strategy among the zero and positive level sets of a Cardioid function. In the approach phase, the positive contour of the Cardioid function smoothly steers the Slider platform into the neighborhood of a deadlock point, which is designed to be at a safe distance from the docking port. In the neighborhood of the deadlock point, Slider corrects its proximity and heading until its configuration is well-suited to enter the docking phase. The docking maneuver is initiated by the CBF switching mechanism (positive to zero contour), which expands the safe zone to include the final docking configuration. We present an analysis of the Quadratic program defining the CBF filter, and identify two deadlock points (an asymptotically stable point in the vicinity of the docking port and an unstable point diametrically opposite on the CBF boundary). Both the approach and docking phases are validated through experimentation on the Slider platform, in the presence of tether-induced disturbances and drifts induced by the non-ideal floating surface. In the docking phase, the CBF switching condition effectively handles experimental non-idealities and recovers the slider platform from unsafe configurations. The proposed docking strategy caters to the in-plane (3DOF) approach and docking phases of real space docking missions and is scalable to three-dimensional 6DOF operations, in conjunction with controllers that stabilize the attitude and the out-of-plane degree-of-freedom. Link to the video of experimental demonstration: https://youtu.be/eBiWvnKtG7U?si=QFPD-vm11wydyZSd.