Optimal Rendezvous Trajectory Research Articles

Singular optimal control for rendezvous problem for cooperative vehicle control

In this paper an unmanned aerial vehicle works cooperatively with a unmanned ground vehicle to aid in the automatic control of the ground vehicle. One challenge is when the aerial vehicle has to urgently rendezvous with the ground vehicle. An optimal control problem is formulated for such a case, the key contribution is the singular optimal control rendezvous problem formulation. Illustrative results are utilised to demonstrate this key formulation of singular optimal control solution as well as the optimal rendezvous trajectory analysis.

Concurrent base-arm control of space manipulators with optimal rendezvous trajectory

This paper proposes a control method for space manipulators, involving concurrent operation of an optimal and a coordinated controller. The optimal controller moves center of mass of the base spacecraft to a desired position along an optimal rendezvous trajectory for minimizing the energy. The optimal control problem is solved through Calculus of Variations, using saturation functions to represent the physical limitations in thrust forces. The coordinated controller drives the arm end-effector to a desired pose (for rendezvousing with the target), as well as making the base attitude follow a desired profile. It also generates augmented reactive moments on the base spacecraft to ensure controlling its attitude when the base actuators reach their limits. Simulations of a realistic space manipulator model demonstrate the performance of the proposed concurrent control method.

Optimal rendezvous trajectory between Sample Return Orbiter and Orbiting Sample Container in a Mars Sample Return mission

A trajectory optimization problem is examined to determine the most fuel-efficient rendezvous trajectory between spacecrafts in different orbits. To explore the whole range of feasible solutions, the wait time and the total time of flight are treated as free parameters while the initial and transfer orbits are not restricted to a particular one. To improve the accuracy of the numerical computation, the Kepler's time of flight equation is posed in terms of universal variables while the Lagrange coefficients are employed to obtain three-dimensional orbit information. The optimal rendezvous trajectory is then obtained enforcing the determined necessary conditions to be satisfied given only the initial state vectors of the involved spacecrafts. Two optimal rendezvous trajectories between a Sample Return Orbiter (SRO) and an Orbiting Sample Container (OS) are computed in the context of a future Mars Sample Return mission to demonstrate the reliability of the proposed solution. Finally, orbital perturbations due to the real shape of planet Mars and the solar radiation pressure are taken into account to determine the additional energy required to compensate these perturbations while performing the rendezvous manoeuvre.

Convex relaxation for optimal rendezvous of unmanned aerial and ground vehicles

In this paper, we present an optimal rendezvous approach that facilitates the coordination of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs). Of particular interest is the problem of UAV-UGV rendezvous for autonomous aerial refueling, which is an important capability for the future use of UAVs. The main contribution of this work is the development of a promising method for the generation of optimal rendezvous trajectories in real time using convex optimization. First, the UAV-UGV rendezvous problem is formulated as a nonconvex optimal control problem using an error dynamic model, where the state and control variables are highly coupled. Then, great effort is devoted to reducing the nonconvexity and coupling of the dynamics through change of variables. Based on a lossless convexification technique, a sequential convex programming algorithm is designed and the solution is obtained by solving a sequence of convex optimization problems. Theoretical proof is provided to demonstrate the exactness of convexification. Furthermore, a simple line search technique is introduced to handle the model error resulting from the linear approximations and to improve the convergence of the designed successive process. Simulation results of two refueling rendezvous situations validate that the proposed method is capable of converging to the solutions within a second, which shows great potential for real-time applications.

Rendezvous Path Planning for Multiple Autonomous Marine Vehicles

In this paper, a distributed shell-space decomposition (DSSD) scheme is proposed for rendezvous trajectory planning of multiple autonomous marine vehicles (AMVs); this category of vehicle includes both autonomous underwater vehicles and autonomous surface vessels. The DSSD extends the concept of shell-space decomposition (SSD) by generating multiple sets of shells radiating out from the starting position of each vehicle to the rendezvous destination, enabling each vehicle to generate its trajectory within its own SSD subset. This scheme is combined with an optimized mass-center rendezvous-point selection scheme, together with a B-spline-based quantum particle swarm optimization technique to find optimal rendezvous trajectories for multiple AMVs with minimal travel time and simultaneous time of arrival for all the participating vehicles. The path planner identifies the optimal rendezvous location and generates the corresponding rendezvous trajectories based on the capabilities of each vehicle and the dynamics of the ocean environment. Simulation results show that the proposed DSSD method, combined with a novel optimized mass-center rendezvous-point selection scheme, is able to find trajectories for multiple AMVs that ensure that they reach their common destination simultaneously and with optimized time/energy consumption. A set of representative Monte Carlo simulations were run to analyze the performance of these path planners for multiple AMVs rendezvous. The results demonstrate the inherent robustness and superiority of the proposed planner based on the combined DSSD method and optimized mass-center rendezvous-point selection scheme, in comparison with other techniques.

Optimal Rendezvous Trajectory for Unmanned Aerial-Ground Vehicles

Fixed-wing unmanned aerial vehicles (UAVs) can be an essential tool for low-cost aerial surveillance and mapping applications in remote regions. There is, however, a key limitation, which is the fact that low-cost UAVs have limited fuel capacity and, hence, require periodic refueling to accomplish a mission. Moreover, the usual mechanism of commanding the UAV to return to a stationary base station for refueling can result in the fuel wastage and inefficient mission operation time. Alternatively, one strategy could be the use of an unmanned ground vehicle (UGV) as a mobile refueling unit, where the UAV will rendezvous with the UGV for refueling. In order to accurately perform this task in the presence of wind disturbances, we need to determine an optimal trajectory in three-dimensional taking UAV and UGV dynamics and kinematics into account. In this paper, we propose an optimal control formulation to generate a tunable UAV trajectory for rendezvous on a moving UGV that also addresses the possibility of the presence of wind disturbances. By a suitable choice of the value of an aggressiveness index that we introduce in our problem setting, we are able to control the UAV rendezvous behavior. Several numerical results are presented to illustrate the reliability and effectiveness of our approach.

Model predictive control for autonomous rendezvous and docking with a tumbling target

In this paper, we investigate the application of model predictive control (MPC) strategy for controlling a chaser spacecraft to dock with a tumbling target in space. The CW-based model is used to predict the proximity trajectory, while a receding prediction horizon is employed to complete the specific docking manipulation in finite time, and a 2-norm cost index about control input is used to minimize the fuel consumption of the chaser during docking. To ensure the implementation of the docking procedure, several engineering constraints such as control input saturation, collision avoidance, velocity constraint, and dock-enabling condition are considered simultaneously. A time-varying linear inequality constraint is used rather than the original quadratic constraint, to achieve the collision-avoidance requirement. Therefore, the constrained optimal rendezvous trajectory in the case of such a MPC framework can be obtained by solving a quadratic program subject to linear constraints. To verify the feasibility of the proposed MPC strategy, four AR&D scenarios are simulated. The simulation results show that MPC strategy can be an effective approach to achieve rendezvous and proximity maneuvering between a chaser spacecraft and a tumbling target while satisfying various constraints, and provide robustness to disturbances.

Robust Planning of Nonlinear Rendezvous with Uncertainty

Practical uncertainties are not considered by optimal rendezvous trajectory designs proposed in many current studies. In this study, a robust optimization method for on-ground rendezvous trajectory design is proposed by considering the uncertainties and orbital replanning process. Two robust performance indices related to the final rendezvous errors and the total velocity increment are first defined, then a multi-objective optimization model (including the minimum and minimum rendezvous errors) is formulated. The unscented transformation method is used to efficiently compute the robust indices in optimization process, and a multi-objective, nondominated sorting genetic algorithm is employed to obtain a Pareto-optimal solution set. It is shown that the proposed approach can be used to design a rendezvous trajectory with the and final rendezvous errors that are both robust against uncertainties. Furthermore, the proposed approach can identify the most preferable design space in which specific solutions for practical application of rendezvous control are selected.

Optimal planning approaches with multiple impulses for rendezvous based on hybrid genetic algorithm and control method

In this article, we focus on safe and effective completion of a rendezvous and docking task by looking at planning approaches and control with fuel-optimal rendezvous for a target spacecraft running on a near-circular reference orbit. A variety of existent practical path constraints are considered, including the constraints of field of view, impulses, and passive safety. A rendezvous approach is calculated by using a hybrid genetic algorithm with those constraints. Furthermore, a control method of trajectory tracking is adopted to overcome the external disturbances. Based on Clohessy–Wiltshire equations, we first construct the mathematical model of optimal planning approaches of multiple impulses with path constraints. Second, we introduce the principle of hybrid genetic algorithm with both stronger global searching ability and local searching ability. We additionally explain the application of this algorithm in the problem of trajectory planning. Then, we give three-impulse simulation examples to acquire an optimal rendezvous trajectory with the path constraints presented in this article. The effectiveness and applicability of the tracking control method are verified with the optimal trajectory above as control objective through the numerical simulation.

Robust optimization of nonlinear impulsive rendezvous with uncertainty

The optimal rendezvous trajectory designs in many current research efforts do not incorporate the practical uncertainties into the closed loop of the design. A robust optimization design method for a nonlinear rendezvous trajectory with uncertainty is proposed in this paper. One performance index related to the variances of the terminal state error is termed the robustness performance index, and a two-objective optimization model (including the minimum characteristic velocity and the minimum robustness performance index) is formulated on the basis of the Lambert algorithm. A multi-objective, non-dominated sorting genetic algorithm is employed to obtain the Pareto optimal solution set. It is shown that the proposed approach can be used to quickly obtain several inherent principles of the rendezvous trajectory by taking practical errors into account. Furthermore, this approach can identify the most preferable design space in which a specific solution for the actual application of the rendezvous control should be chosen.

Optimal Rendezvous Trajectories of a Controlled Spacecraft and a Tumbling Object

This paper formulates and solves the problem of minimum-time and minimum-energy optimal trajectories of rendezvous of a powered chaser and a passive tumbling target, in a circular orbit. Both translational and rotational dynamics are considered. In particular, ending conditions are imposed of matching the positions and velocities of two points of interest onboard the vehicles. A collision-avoidance condition is imposed as well. The optimal control problems are analytically formulated through the use of the Pontryagin minimum principle. The problems are then solved numerically, by using a direct collocation method based on the Gauss pseudospectral approach. Finally, the obtained solutions are verified through the minimum principle, solved by a shooting method. The simulation results show that the pseudospectral solver provides solutions very close to the optimal ones, except in the case of presence of singular arcs when it may not provide a feasible solution. The computational time needed by the pseudospectral solver is a small fraction of the one needed by the indirect approach, but it is still considerably too large to allow for its use in real-time onboard guidance.

Deflection of Earth-Crossing Asteroids/Comets Using Rendezvous Spacecraft and Laser Ablation

Space missions are presented to deflect four fictitious Earth impacting objects by using an advanced magnetoplasma spacecraft designed to deliver a laser ablation payload. The laser energy required to provide sufficient change in velocity is estimated for one long-period comet and three asteroids, and an optimal rendezvous trajectory is provided for each threat scenario. The end-to-end simulations provide an overall concept for solving the deflection problem. These analyses illustrate that the optimal deflection strategy is highly dependent on the size and the orbital elements of the impacting object, as well as the amount of warning time. A rendezvous spacecraft with a multi-megawatt laser ablation payload could be available by the year 2050. This approach could provide a capable and robust orbit modification approach for altering the orbits of Earthcrossing objects with relatively small size or long warning time. Significant technological advances, multiple spacecraft, or alternative deflection techniques are required for a feasible scenario to protect the Earth from an impacting celestial body with large size and short warning time.