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 to rendezvous with that minimizes the total $ΔV$ required. Transfers are considered as single algebraic objects corresponding to $ΔV$ matrices, which allow intuitive concatenation via a generalized summation. Waiting times, both due to mission requirements and prospects for cheaper and faster future transfers, are also incorporated in the $ΔV$ matrices. A transcription of the problem as a shortest path search on a graph can utilize a range of available efficient shortest path solvers. Given an efficient $ΔV$ matrix estimator, the new paradigm proposed here is believed to offer an alternative to the pruning techniques currently used.
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 …
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…
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…
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…
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 …
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…
A deep-space exploration mission with low-thrust propulsion to rendezvous with multiple asteroids is investigated. Indirect methods, based on the optimal control theory, are implemented to optimize the fuel consumption. The application of indirect methods for optimizing low-thrust trajectories between two asteroids is briefly given. An effective method is proposed to provide initial guesses for transfers between close near-circular near-coplanar orbits. The conditions for optimality of a multi-asteroid rendezvous mission are determined. The intuitive method of splitting the trajectories into s…
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）
Spacecraft relative motion planning is concerned with the design and execution of maneuvers relative to a nominal target. These types of maneuvers are frequently utilized in missions such as rendezvous and docking, satellite inspection and formation flight where exclusion zones representing spacecraft or other obstacles must be avoided. The presence of these exclusion zones leads to non-linear and non-convex constraints which must be satisfied. In this paper, a novel approach to spacecraft relative motion planning with obstacle avoidance and thrust constraints is developed. This approach is ba…
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）
This paper extends the optimal covariance steering problem for linear stochastic systems subject to chance constraints to account for optimal risk allocation. Previous works have assumed a uniform risk allocation to cast the optimal control problem as a semi-definite program (SDP), which can be solved efficiently using standard SDP solvers. We adopt an Iterative Risk Allocation (IRA) formalism, which uses a two-stage approach to solve the optimal risk allocation problem for covariance steering. The upper-stage of IRA optimizes the risk, which is proved to be a convex problem, while the lower-s…
One of the fundamental problems in spacecraft trajectory design is finding the optimal transfer trajectory that minimizes the propellant consumption and transfer time simultaneously. We formulate this as a multi-objective optimal control (MOC) problem that involves optimizing over the initial or final state, subject to state constraints. Drawing on recent developments in reachability analysis subject to state constraints, we show that the proposed MOC problem can be stated as an optimization problem subject to a constraint that involves the sub-level set of the viscosity solution of a quasi-va…
