Quadratic Programs for High Relative Degree Spatial Constraints and Spatiotemporal Specifications with Spacecraft Applications

This paper presents a new methodology for ensuring forward invariance of sublevel sets of high relative degree functions, and convergence of the state to these sets. We introduce the notion of the boundary layer of a set defined by multiple constraints, and develop polynomially-derived trajectory constraints as means to enforce set invariance by redirecting trajectories that enter this boundary layer. This strategy is then extended to achieve convergence to and invariance of goal sets that are specified using Signal Temporal Logic. A quadratic program computes control inputs online that yield trajectories that achieve high level objectives specified by these sets, such as obstacle avoidance and target observation. We present a case study utilizing this controller for a spacecraft position and attitude control problem requiring observation of targets on the surface of a small body.