In this paper we propose a hybrid control strategy to solve the problem of rendezvous, proximity operations, and docking of an autonomous spacecraft in 3D. Due to the different constraints and tasks to perform, a hybrid systems approach is implemented to solve the problem in three phases: 1) rendezvous; 2) rendezvous with smaller relative distance; 3) docking phase; and 4) docked phase; with range and angle measurements. In this approach, we implement a supervisor that robustly coordinates the individual controllers to accomplish the whole mission. We also present the designs of these individual controllers that solve the appropriate control problems for the individual phases. Numerical results for both the nominal and perturbed case validate the hybrid control strategy for the spacecraft close-proximity mission.

A hybrid feedback control scheme is proposed for stabilization of rigid body dynamics (pose and velocities) using unit dual quaternions, in which the dual quaternions and veloc- ities are used for feedback. It is well-known that rigid body attitude control is subject to topological constraints which often result in discontinuous control to avoid the unwinding phenomenon. In contrast, the hybrid scheme allows the controlled system to be robust in the presence of uncertainties, which would otherwise cause chattering about the point of discontinuous control while also ensuring acceptable closed-loop response characteristics. The stability of the closed-loop system is guaranteed through a Lyapunov analysis and the use of invariance principles for hybrid systems. Simulation results for a rigid body model are presented to illustrate the performance of the proposed hybrid dual quaternion feedback control scheme.

Motivated by real-world applications with intermittent sensor data, an extended Kalman filter is formulated as a hybrid system and constructive conditions on its parameters guaranteeing an asymptotic stability property are provided. The dynamical properties of the estimation error are first characterized infinitesimally so to yield bounds on the rate of convergence and overshoot that depend on the parameters. By recasting the problem as the stabilization of a compact set, robustness properties of the proposed algorithm in the presence of disturbances in the system dynamics as well as measurement noise in the output are established. The proposed strategy is applied to spacecraft relative motion control with position-only measurements.

We consider the problem of rendezvous, proximity operations, and docking of an autonomous spacecraft. The problem can be conveniently divided into four phases: 1) rendezvous with angles-only measurements; 2) rendezvous with range measurements; 3) docking phase; and 4) docked phase. Due to the different constraints, available measurements, and tasks to perform on each phase, we study this problem using a hybrid systems approach, in which the system has different modes of operation for which a suitable controller is to be designed. Following this approach, we characterize the family of individual controllers and the required properties they should induce to the closed-loop system to solve the problem within each phase of operation. Furthermore, we propose a supervisor that robustly coordinates the individual controllers so as to provide a solution to the problem. Due to the stringent mission requirements, the solution requires hybrid controllers that induce convergence, invariance, or asymptotic stability properties, which can be designed using recent techniques in the literature of hybrid systems. In addition, we outline specific controller designs that appropriately solve the control problems for individual phases and validate them numerically.1

A hybrid control methodology is presented for autonomous rendezvous, proximity operations and docking of a pair of spacecraft. For the theoretical development of the control algorithms, the dynamics of the spacecraft are modeled using the Clohessy-Wiltshire-Hill equations, which result in a linear system of relative motion equations. Only in-plane motion is considered, resulting in a two-dimensional system, and the control input is the acceleration vector of the active spacecraft, constrained by a maximum thrust value. Individual controllers are designed for different phases of the of approach and transitions are governed by a hybrid supervising algorithm. The hybrid control algorithm is implemented both in MATLAB, using a simplified dynamic model, as well as in actual spacecraft flight code and tested in a high-fidelity spacecraft simulation test environment.