Time-optimal Reorientation Research Articles

Time-Optimal Spacecraft Reorientation for the Observation of Multiple Asteroids

Abstract To observe multiple asteroids in a short time, the time-optimal reorientation is investigated here for the rest-to-rest reorientation of a generic rigid spacecraft. First, the problem is formulated and solved using the hp-adaptive pseudospectral method. It is found that there exist not merely bang-bang but also singular solutions for the problem. Then, the bang-bang and singular solutions are discussed by various cases. The results reveal that the optimal solution is essentially a balance between the larger torque, the shorter angular path and the less moment of inertia. For bang-bang solutions, the total number of switches varies with the reorientation angle and the moment of inertia. The number of switches is usually 5 or 6 and does not exceed 8. For singular solutions, either one and two controls singular are possible. The singular optimal solution is probably optimal for the slender rod-like spacecraft. Finally, an analytical estimation method is proposed for determining the range of the optimal time. The results of the simulations indicate that the proposed method is real-time and highly accurate. All formulas of this paper are derived in canonical units and therefore apply to any rigid spacecraft.

Algorithm of the Time-Optimal Reorientation of an Axially Symmetric Spacecraft in the Class of Conical Motions

The problem of the time-optimal turn of a spacecraft as a rigid body with one axis of symmetry and bounded control function in absolute value is considered in the quaternion statement. For simplifying problem (concerning dynamic Euler equations), we change the variables reducing the original optimal turn problem of axially symmetric spacecraft to the problem of optimal turn of the rigid body with spherical mass distribution including one new scalar equation. Using the Pontryagin maximum principle, a new analytical solution of this problem in the class of conical motions is obtained. Algorithm of the optimal turn of a spacecraft is given. An explicit expression for the constant in magnitude optimal angular velocity vector of a spacecraft is found. The motion trajectory of a spacecraft is a regular precession. The conditions for the initial and terminal values of a spacecraft angular velocity vector are formulated. These conditions make it possible to solve the problem analytically in the class of conical motions. The initial and the terminal vectors of spacecraft angular velocity must be on the conical surface generated by arbitrary given constant conditions of the problem. The numerical example is presented. The example contain optimal reorientation of the Space Shuttle in the class of conical motions.

Particle Swarm Optimization for Time-Optimal Spacecraft Reorientation with Keep-Out Cones

This paper deals with the problem of spacecraft time-optimal reorientation maneuvers under boundaries and path constraints. The minimum time solution with keep-out constraints is proposed using the particle swarm optimization technique. A novel method based on the evolution of the kinematics and the successive obtainment of the control law is presented and named as inverse dynamics particle swarm optimization. It is established that the computation of the minimum time maneuver with the proposed technique leads to near-optimal solutions, which fully satisfy all the boundaries and path constraints.

Time-optimal reorientation of the rigid spacecraft using a pseudospectral method integrated homotopic approach

This paper proposes a robust algorithm for time-optimal rigid spacecraft reorientation trajectory generation. Based on the Pontryagin's maximum principle, the first-order necessary optimality conditions are derived. These optimality conditions are numerically satisfied by adopting a pseudospectral method integrated homotopic approach to solve the associated shooting functions. First, the energy-optimal reorientation solution is obtained using the Radau pseudospectral method, which has a spectral convergence speed and can give a precise estimation of the initial costates used to start the homotopic approach. Then, a modified homotopy scheme is given to deform the associated energy-optimal solution to the desired time-optimal solution continuously. Finally, for the inertially symmetric spacecraft reorientation problem, the newly found time-optimal solutions are presented. The performance of the algorithm is illustrated by simulating a general asymmetric rigid spacecraft time-optimal reorientation problem. Copyright © 2014 John Wiley & Sons, Ltd.

Maximum-likelihood estimation optimizer for constrained, time-optimal satellite reorientation

The Covariance Matrix Adaptation-Evolutionary Strategy (CMA-ES) method provides a high-quality estimate of the control solution for an unconstrained satellite reorientation problem, and rapid, useful guesses needed for high-fidelity methods that can solve time-optimal reorientation problems with multiple path constraints. The CMA-ES algorithm offers two significant advantages over heuristic methods such as Particle Swarm or Bacteria Foraging Optimisation: it builds an approximation to the covariance matrix for the cost function, and uses that to determine a direction of maximum likelihood for the search, reducing the chance of stagnation; and it achieves second-order, quasi-Newton convergence behaviour.

Time-optimal reorientation for rigid satellite with reaction wheels

This article introduces a time-optimal reorientation manoeuvre controller with saturation constraints on both reaction wheels’ torques and angular momentum. The proposed control scheme consists of two parts. The first part is an open-loop time-minimum reorientation trajectory generated by the Legendre pseudospectral method. Actuator dynamics, saturations on control torques and angular momentums of reaction wheels are taken into account in generating the open-loop optimal trajectory. The second part is a closed-loop tracking control law to track the optimised reference trajectory based on attitude error dynamics with reaction wheel dynamics. Numerical simulations show that reaction wheel dynamics play an important role in attitude manoeuvres. The proposed controller performs better for rest-to-rest reorientation manoeuvre than other existing methods.

First Flight Results on Time-Optimal Spacecraft Slews

This paper describes the design and flight implementation of time-optimal attitude maneuvers performed onboard NASA’s Transition Region and Coronal Explorer spacecraft. Minimum-time reorientation maneuvers have obvious applications for improving the agility of spacecraft systems, yet this type of capability has never before been demonstrated in flight due to the lack of reliable algorithms for generating practical optimal control solutions suitable for flight implementation. Constrained time-optimal maneuvering of a rigid body is studied first, in order to demonstrate the potential for enhancing the performance of the Transition Region and Coronal Explorer spacecraft. Issues related to the experimental flight implementation of time-optimal maneuvers onboard Transition Region and Coronal Explorer are discussed. A description of an optimal control problem that includes practical constraints such as the nonlinear reaction wheel torque-momentum envelope and rate gyro saturation limits is given. The problem is solved using the pseudospectral optimal control theory implemented in the MATLAB® software DIDO. Flight results, presented for a typical large-angle time-optimal reorientation maneuver, show that the maneuvers can be implemented without any modification of the existing spacecraft attitude control system. A clear improvement in spacecraft maneuver performance as compared with conventional eigenaxis maneuvering is demonstrated.

Time-Optimal Detumbling Control of Spacecraft

T HE problem of designing fast detumbling maneuvers for a spacecraft with restricted actuation torques arises inmany space applications. Satellites are often equipped with an attitude control system (ACS), which usually has two modes of operation: detumbling and stabilization. In detumbling mode, the ACS controller is responsible for dumping the initial angular velocity from when the satellite was in the idle mode; this situation occurs when the satellite is released from the launch vehicle or when power is so low that ACS has to be turned off to save power [1]. Only after this phase can the stabilization mode be activated to control the orientation of the satellite to align antennas toward the Earth. Reaction wheels are commonly used as the actuators of the ACSs. Satellites frequently need fast maneuvers [2], minimum time maneuvers, while the speed is restricted owing to a low level capacity of the actuators. Hence, planning optimal maneuvers is highly desired. Alternatively, spin-stabilized spacecraft allow simple attitude maneuvers without the need for complex control systems. The spacecraft can be spun up around its axisymmetric axis to stabilize the orientation of the vehicle axis through the gyroscopic effect. This method is also widely used to stabilize the final stage of a launch vehicle [3]. However, when a spacecraft is in the tumblingmotion, its angular velocity is not parallel to the axisymmetric axis. Therefore, the objective in deployment of a spin-stabilized spacecraft [4] is to bring the spacecraft form the tumblingmotion to the statewherein the spacecraft spins around a single axis. The detumbling or passivation of a satellite is also required before on-orbit servicing of the satellite or its retrieval [5]. For such a mission, an orbital maneuvering vehicle can be used to apply torques to the target satellite for removing any relative velocity [5,6]. Also, the vehicle can be equipped by an articulating arm with a grappling device on it that could be driven to capture a tumbling target satellite and then detumble it [7,8]. After capture of an uncontrolled tumbling satellite by a spacemanipulator, the satellite should be brought to rest in minimum time. Again, the restriction of the manipulator end effector to provide “braking torques” for the fast maneuvers motivates an optimal trajectory planning. Optimal detumbling ofmultibody systems has been considered for spacecraft possessing appendages, such as a robotic manipulator, with well-controlled motion relative to the spacecraft to achieve detumbling [9–13].However, because of the complexity of dynamics of space manipulators, only a numerical solution or intensive trialand-error procedures have been found for the optimization problem. The problem of time-optimal detumbling control of rigid spacecraft is formulated as a nonlinear programming and solved numerically by using an iterative procedure in [14], while nonoptimal control approaches have been reported in [15–17]. There also exists a fair amount of research done on the time-optimal reorientation control, rest to rest, of rigid spacecraft [18–20] and a survey, for example, can be found in [21]. This paper presents a closed-form solution for time-optimal detumbling control of a rigid spacecraft with the constraint on maintaining the Euclidean norm of the braking torques below a prescribed value. Thefinal angular rate can be specified as zero or any vector parallel to the eigenaxis. The optimal control theory and Pontryagin’s principle are applied to derive the optimal solution, which is not only easy to implement but also gives a great deal of insight. First, it will be shown that for our particular optimal control problem, the system costates and states are related by a nonlinear but static function. Subsequently, the optimal control law is explicitly derived in the form of a nonlinear state feedback. The magnitude of the system angular momentum is found to be linearly deceasing with time, leading to a simple expression for the terminal time needed for control implementation. Furthermore, the time-optimal controller is extended for the case of nonzero terminal velocity. To this end, the time-optimal control technique is applied to derive a nonlinear feedback control law which can drive a tumbling axisymmertic spacecraft to a final spin-stabilized state. Finally, the time-optimal detumbling technique is illustrated through numerical examples.

Minimum-time reorientation of a two-degree-of-freedom gyroscope

The problem of time-optimal reorientation of the inner gimbal of a two-degree-of-freedom gimballed gyroscope mounted on a nonrotating base is considered. The states in the gyro model are the gimbals' angles (nutation is ignored). The model is nonlinear (not limited to small angles), state constrained, control limited, and double input, double output. A simple, explicit solution based on an intuitive observation is presented; it exploits the system's nonlinearity and channel coupling for attaining the minimum-tune goal. It is analytically shown, in detail, that the solution satisfies the Maximum Principle and fulfills a sufficient condition for optimality based on the Hamilton-Jacobi-Bellman equation.

Extremal vehicle reorientation maneuvers - Symmetries and group properties

The setting for this study is time-optimal reorientation maneuvers for a rigid-body. Analysis of the dynamic model reveals certain symmetries among solutions for a class of rest-to-rest maneuvers. An operator-theo retic approach is used to formalize the analysis and the set of operators is shown to form a commutative group. For extremal trajectories, a second group of transformatio ns is identified: these are mappings between the adjoint variables. The two groups are shown to be homomorphic. A particular subgroup of the adjoints maps is highlighted and used to generate several distinct extremal trajectories from a single known one. A number of extremal trajectories, shown graphically, supplement and illustrate the analytical considerations.

Time-optimal reorientation maneuvers for a combat aircraft

Results are presented from a study of time-optimal attitude reorientation maneuvering for an aircraft with thrust-vectoring capability. A detailed mathematical model for attitude motions of the aircraft is developed. First-order necessary conditions for optimality are applied and a family of extremal solutions obtained for two classes of reorientation maneuvers of practical interest. The thrust-vectoring power is varied parametrically, and thus an estimate of the reduction in maneuvering time due to the thrust-vectoring enhancement of the aircraft is obtained. ARIOUS analyses have shown that emerging trends in missile and radar technologies will have a profound effect on design requirements for air-superiority vehicles. It appears that, in close-in combat, vehicles with the ability to operate at extreme angles of attack will have a decided advantage.1'4 Designing such supermaneuverable aircraft is a complex and challenging task, and future design efforts may well lead to radically new concepts. At present, however, the preferred approach is to provide a form of thrust vectoring in which propulsive power is used to generate control moments.5'6 At high angles of attack a, especially in the post-stall region, the effectiveness of the aerodynamic control surfaces decreases rapidly with increase in a.. Thus, thrust-vectoring generated (propulsive) moments must be used to maintain control of the aircraft at high a. At low a the propulsive moments can supplement the aerodynamic control surfaces and thus increase the agility of the aircraft. In addition, thrust vectoring can be used for control of the aircraft in case of mechanical failure or malfunction of the aerodynamic control surfaces. Several research programs that focus on utilizing thrust-vectoring control are currently under way. Among these is the F/A-18 based High Angle-of-attack Research Vehicle (HARV) program.7 The flight mechanics issues can be divided into two areas: 1) analysis of changes in the velocity vector and 2) analysis of changes in the body attitude. This paper presents some results obtained in a study that focused on understanding the nature of aircraft minimum-time fuselage-reorientation maneuvering. In the study, data for the HARV were used. Accordingly, the numerical results correspond to this aircraft. However, the discussion and methodology in analyzing the results presented in the next sections are quite general. A mathematical model of the aircraft and the interacting environment (the aerodynamic forces and moments) is derived in Sec. II. The basic ideas and assumptions in the development of the mathematical model are discussed in detail. In Sec. Ill a class of optimal control problems of interest is formulated and a set of necessary conditions for optimality derived by using the Minimum Principle.8'10 This set of necessary conditions is cast into a numerical multipoint boundary-value problem (MPBVP). Subsequently, a homotopy method and the related procedure for solving the MPBVPs (and thus generat