This paper discusses translation and attitude control in spacecraft rendezvous and soft docking. The target spacecraft orbit can be either circular or elliptic. The high fidelity model for this problem is intrinsically a nonlinear system but can be viewed as a linear time varying system (LTV). Therefore, a model predictive control (MPC) based design is proposed to deal with the time-varying feature of the problem. A robust pole assignment method is used in the MPC-based design because of the following merits and/or considerations: (a) no overshoot of the relative position and attitude between the target and the chaser to achieve soft docking by placing all closed-loop poles in the negative real axis of the complex plan, which avoids oscillation of the relative position and attitude, in particular, in the final stage, (b) fast on-line computation, (c) modeling error tolerance, and (d) disturbance rejection. We will discuss these considerations and merits, and use a design simulation to demonstrate that the desired performance is indeed achieved.
This paper presents a time-constrained model predictive control strategy for the 6 degree-of-freedom (6DOF) autonomous rendezvous and docking problem between a controllable "deputy" spacecraft and an uncontrollable "chief" spacecraft. The control strategy accounts for computational time constraints due to limited onboard processing speed. The translational dynamics model is derived from the Clohessy-Wiltshire equations and the angular dynamics are modeled on gas jet actuation about the deputy's center of mass. Simulation results are shown to achieve the docking configuration under computationa…
Multi-rendezvous spacecraft trajectory optimization problems are notoriously difficult to solve. For this reason, the design space is usually pruned by using heuristics and past experience. As an alternative, the current research explores some properties of $ΔV$ matrices which provide the minimum $ΔV$ values for a transfer between two celestial bodies for various times of departure and transfer duration values. These can assist in solving multi-rendezvous problems in an automated way. The paper focuses on the problem of, given a set of candidate objects, how to find the sequence of $N$ objects…
In this paper we present a fast method based on successive convexification for generating fuel-optimized spacecraft rendezvous trajectories in the presence of mixed-integer constraints. A recently developed paradigm of state-triggered constraints allows to efficiently embed a subset of discrete decision constraints into the continuous optimization framework of successive convexification. As a result, we are able to solve difficult trajectory optimization problems at interactive speeds, as opposed to a mixed-integer programming approach that would require significantly more solution time and co…
This paper presents a strategy for control of a spacecraft docking with a non-maneuvering target in the presence of safety constraints and bounded disturbances. The presence of disturbances prevents convergence to a unique docking state, so in our formulation, docking is defined as occurring within a set constructed using prescribed tolerances. Safety is ensured via application of Robust Control Barrier Functions to render a designated safe set forward invariant for any allowable disturbance. However, this safety strategy necessarily presumes a worst-case disturbance, and thus restricts trajec…
Missions to rendezvous with or capture an asteroid present significant interest both from a geophysical and safety point of view. They are key to the understanding of our solar system are as well stepping stones for interplanetary human flight. In this paper, we focus on a rendezvous mission with \RH, an asteroid classified as a Temporarily Captured Orbiter (TCO). TCOs form a new population of near Earth objects presenting many advantages toward that goal. Prior to the mission, we consider the spacecraft hibernating on a Halo orbit around the Earth-Moon's $L_2$ libration point. The objective i…
As the number of uncontrollable objects in low earth orbit is rising, the thread of collisions and thus the breakdown of working satellites becomes worth analyzing. Consequently, projects on removing objects from the important orbits are taken into account by the international space associations. This paper is about the modelling and optimal path planning of a docking maneuver to an uncontrollable tumbling target. After deriving the system dynamics, we introduce boundary conditions to ensure a safe and realizable maneuver and a general Bolza type cost functional to incorporate different optimi…
This paper presents a computationally efficient optimization algorithm for solving nonconvex optimal control problems that involve discrete logic constraints. Traditional solution methods for these constraints require binary variables and mixed-integer programming, which is prohibitively slow and computationally expensive. This paper targets a fast solution that is capable of real-time implementation onboard spacecraft. To do so, a novel algorithm is developed that blends sequential convex programming and numerical continuation into a single iterative solution process. Inside the algorithm, di…
Language-Conditioned Safe Trajectory Generation for Spacecraft Rendezvous
Department of Aeronautics and Astronautics, 496 Lomita Mall（航空航天系，496号Lomita Mall）；Department of Mechanical Engineering, 440 Escondido Mall Building 530（机械工程系，440号Escondido Mall Building 530）
Geometric Conditions for Lossless Convexification in Linear Optimal Control with Discrete-Valued Inputs: Real-Time Implementation for Spacecraft Rendezvous
This paper shows how to find lower bounds on, and sometimes solve globally, a large class of nonlinear optimal control problems with impulsive controls using semi-definite programming (SDP). This is done by relaxing an optimal control problem into a measure differential problem. The manipulation of the measures by their moments reduces the problem to a convergent series of standard linear matrix inequality (LMI) relaxations. After providing numerous academic examples, we apply the method to the impulsive rendezvous of two orbiting spacecrafts. As the method provides lower bounds on the global …
A novel trajectory design methodology is proposed in the current work to minimize the state uncertainty in the crucial mission of spacecraft rendezvous. The trajectory is shaped under constraints utilizing a multiple-impulse approach. State uncertainty is characterized in terms of covariance, and the impulse time as the only affective parameter in uncertainty propagation is selected to minimize the trace of the covariance matrix. Further, the impulse location is also adopted as the other design parameter to satisfy various translational constraints of the space mission. Efficiency and viabilit…
In this paper we consider the fuel-optimal rendezvous between a satellite and a spacecraft in a central force field with a drag force that is linear in the velocity. In this general setting we linearize the equations of motion of the spacecraft and show that they can be reduced effectively, in the case of a linear drag, to one second order linear differential equation. We then specialize to the case of inverse square laws. Under certain simplifying assumptions a state-transition matrix can be found in terms of integrals. The work can then be placed in the context of various control models that…
This paper presents a convex approach to the optimization of a cooperative rendezvous, that is, the problem of two distant spacecraft that simultaneously operate to get closer. Convex programming guarantees convergence towards the optimal solution in a limited, short, time by using highly efficient numerical algorithms. A combination of lossless and successive convexification techniques is adopted to handle the nonconvexities of the original problem. Specifically, a convenient change of variables and a constraint relaxation are performed, while a successive linearization of the equations of mo…
Recent studies of optimization methods and GNC of spacecraft near small bodies focusing on descent, landing, rendezvous, etc., with key safety constraints such as line-of-sight conic zones and soft landings have shown promising results; this paper considers descent missions to an asteroid surface with a constraint that consists of an onboard camera and asteroid surface markers while using a stochastic convex MPC law. An undermodeled asteroid gravity and spacecraft technology inspired measurement model is established to develop the constraint. Then a computationally light stochastic Linear Quad…
Neural-Rendezvous: Provably Robust Guidance and Control to Encounter Interstellar Objects
Jet Propulsion Laboratory（喷气推进实验室）；California Institute of Technology（加州理工学院）；National Aeronautics and Space Administration（美国国家航空航天局）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Learning Safety-Guaranteed, Non-Greedy Control Barrier Functions Using Reinforcement Learning
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Australian Centre for Robotics, The University of Sydney（悉尼大学澳大利亚机器人中心）；University of Auckland（奥克兰大学）
