Morgan Baldwin

Model Predictive Control for Spacecraft Rendezvous and Docking: Strategies for Handling Constraints and Case Studies

This paper presents a strategy and case studies of spacecraft relative motion guidance and control based on the application of linear quadratic model predictive control (MPC) with dynamically reconfigurable constraints. The controller is designed to transition between the MPC guidance during a spacecraft rendezvous phase and MPC guidance during a spacecraft docking phase, with each phase having distinct requirements, constraints, and sampling rates. Obstacle avoidance is considered in the rendezvous phase, while a line-of-sight cone constraint, bandwidth constraints on the spacecraft attitude control system, and exhaust plume direction constraints are addressed during the docking phase. The MPC controller is demonstrated in simulation studies using a nonlinear model of spacecraft orbital motion. The implementation uses estimates of spacecraft states derived from relative angle and range measurements, and is robust to estimator dynamics and measurement noise.

Model Predictive Control of three dimensional spacecraft relative motion

This paper further develops an approach for spacecraft relative motion control based on the application of linear quadratic Model Predictive Control (MPC) with dynamically reconfigurable constraints. Previous results for maneuvers confined to the orbital plane are extended to three dimensional maneuvers with three dimensional Line-of-Sight (LoS) constraint handling. The MPC controller is designed to prescribe Δv impulsive velocity changes rather than piecewise constant thrust profiles. The ability to transition between MPC guidance in the spacecraft rendezvous phase and MPC guidance in the spacecraft docking phase, with requirements, constraints, and sampling rates specific to each phase, is demonstrated. Bandwidth constraints of the spacecraft attitude control system and exhaust plume direction constraints are also addressed. The MPC controller is validated on the full nonlinear model of spacecraft orbital motion and augmented with an Extended Kalman Filter (EKF) to estimate spacecraft states based on relative angles and relative range measurements.

Model Predictive Control Guidance with Extended Command Governor Inner-Loop Flight Control for Hypersonic Vehicles

The paper describes a control system for hypersonic vehicles that consists of an outerloop guidance layer and an inner-loop flight control layer. For the outer-loop, a Model Predictive Control approach is pursued to prescribe the desired bank angle and flight path angle commands so that the vehicle can follow the way points and avoid exclusion zones during its flight. For the inner-loop, a combination of a Linear Quadratic state feedback control and an Extended Command Governor to handle pointwise-in-time state and control constraints is proposed. Simulation results are presented for an implementation of the proposed approach that includes the outer-loop MPC bank angle/flight path angle control and the inner-loop controller that tracks the desired angle-of-attack and enforces the constraints.

Safe Positively Invariant Sets for Spacecraft Obstacle Avoidance

This paper presents an obstacle avoidance method for spacecraft relative motion control. In this approach, a connectivity graph is constructed for a set of relative frame points, which form a virtual net centered around a nominal orbital position. The connectivity between points in the virtual net is determined based on the use of safe positively invariant sets for guaranteed collision free maneuvering. A graph search algorithm is then applied to find a maneuver that avoids specified obstacles and adheres to specified thrust limits. As compared to conventional open-loop trajectory optimization, this approach enables the handling of bounded disturbances, which can represent the effects of perturbing forces and model uncertainty, while rigorously guaranteeing that nonconvex and possibly time-varying obstacle avoidance constraints are satisfied. Details for handling a single stationary obstacle, multiple stationary obstacles, moving obstacles, and bounded disturbances are reported and illustrated with simula...

Spacecraft constrained attitude control using positively invariant constraint admissible sets on SO(3) × ℝ 3

This paper presents a constrained attitude control approach for performing spacecraft reorientation maneuvers that maintain specified body vectors within inclusion zones and out of exclusion zones, while respecting control authority limits. The controller uses a supervisory switching strategy with an inner-loop Lyapunov SO(3)-based controller and an outer-loop set-point guidance. A virtual net of orientation equilibria covering SO(3) is introduced, and positively invariant constraint admissible sets on SO(3) × ℝ3 of the inner loop controller are constructed to determine if equilibria are connected by a feasible trajectory. Optimization procedures to maximize the size of the positively-invariant sets are discussed. Graph search is used in the outer-loop to compute the set-point sequence leading from an initial orientation to a final orientation that rigorously enforces constraints. The proposed methodology reduces the search space of possible attitude maneuver solutions, and has computational and implementation simplicity. Numerical simulation results are reported to illustrate the performance of the proposed constrained attitude control methodology.

Optimal Deorbit Guidance

can be hundreds of seconds apart from that of the impulsive solution), duration of the burn, and thrust direction duringtheburn.Inthispaperthe deorbitguidanceproblem isformulatedasanoptimalcontrolproblemwith finitetime burn structure. Several sets of general targeting conditions are derived to be met at the entry interface. Numerical solutions are obtained by employing a fast multiburn shooting algorithm. The solution contains the coast times before and after a burn, duration of the burn, and thrust-direction profile during the burn. This study investigates both single- and two-burn deorbit maneuvers, and demonstrates how each works in different mission scenarios.

Hypersonic glider guidance using Model Predictive Control

A Model Predictive Control (MPC) approach to hypersonic glider flight management is proposed. Given the capability of MPC to handle constraints, it is promising for application to a hypersonic glider with path constraints. With this approach, the glider navigates through defined way points while avoiding exclusion zones. The minimum-time formulation of MPC is employed. The gliders capability to perform the maneuvers is demonstrated using simulations.

Finite-horizon controllability and reachability for deterministic and stochastic linear control systems with convex constraints

This paper presents a method for rapidly generating controllability and reachability sets for constrained finite horizon Linear Time Varying (LTV) control systems by using convex optimization techniques. Set generation is accomplished by first solving a Semi-Definite Programming (SDP) problem and then solving a series of Second Order Cone Programming (SOCP) problems. Recent advances in convex optimization solvers have made it possible to find the solutions to these problems very quickly. From a geometric stand-point, we first find the largest volume symmetric simplex that fits within the constrained control problem, then grow new simplices out of the faces of the original simplex. This process is repeated until the growing polytope converges to the constraint boundaries of the actual set. Additionally, a method for incorporating stochastic constraints and uncertainties into the deterministic framework is developed by posing the stochastic constraints as chance-constrained constraints. Finally, the controllability set for a two-vehicle Low Earth Orbit (LEO) rendezvous problem with stochastic uncertainties is generated using the new algorithm.

Forward-integration Riccati-based feedback control for spacecraft rendezvous maneuvers on elliptic orbits

We apply the forward-integrating Riccati-based feedback controller, which has been developed in our previous work for stabilization of time-varying systems, to a maneuvering spacecraft in an elliptic orbit around the Earth. We simulate rendezvous maneuvers on Molniya and Tundra orbits. We demonstrate that the controller performs well under thrust constraints, in the case where the spacecraft can thrust in only the orbital tangential direction, in the case where the thrusters may operate only intermittently due to faults or power availability, with thrust direction errors, and, finally, in an output feedback configuration where only relative position measurements are available.

Computing reach-avoid sets for space vehicle docking under continuous thrust

We compute the reach-avoid set for space vehicle rendezvous and docking under continuous thrust. We model the space vehicle dynamics through the Clohessy-Wiltshire-Hill (CWH) equations, resulting in a switched hybrid system with affine, time-invariant dynamics. We exploit a closed-form solution to the CWH equations to analytically determine evolution of the boundary of the reach-avoid set, then modify the cost function of the reach-avoid variational equations to identify minimum thrust trajectories. Our contribution is two-fold: 1) the set of states from which there exists a maneuver (irrespective of the cost) that will allow a spacecraft to reach a target while remaining within a line-of-sight cone, and 2) a minimum-thrust cost that allows quick assessment, for points that lie within the reach-avoid set, of minimum fuel trajectories.