Control variable parameterisation with penalty approach for hypersonic vehicle reentry optimisation

Ascent Trajectory Optimization of Launch Vehicles with Air-Breathing Propulsion

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.

Trajectory optimization for lunar rover performing vertical takeoff vertical landing maneuvers in the presence of terrain

The structure of the time-optimal control law for multiple robot arms cooperatively moving a common object along a specified path with the control torque constraints is addressed. The overall mechanical system is modeled by considering the arms as closed kinematic chains using the Lagrange formulation. This results in a reduced-order dynamic model of the multi-arm system. By parameterizing the resulting dynamic model along a given path, the original higher order optimal control problem with state constraints (path constraints) is transformed into a problem of a double integrator system with state-dependent control constraints that are determined by a linear programming approach. It is then shown that the number of saturated actuators on any finite time interval along the optimal trajectory is (1+3(D-1)(m-1)), where D=2 in 2-dimensional Cartesian space, D=3 in 3-dimensional space, and m is the number of robot arms in the system. The theoretical result is validated by a numerical example.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimal control of semi-batch reactors

This paper presents a systematic method for generating optimal helicopter flight trajectories in real time for cockpit display. Helicopter flights in the event of a single engine failure are critical, and display of optimal flight paths on-board is desirable. Due to the large number of states and constraints, however, numerical solutions on a mainframe computer can take a long tune. In this paper, optimal solutions are first obtained off-line using a ground computer. For a given set of initial helicopter states and flight parameters, optimal solutions are fitted by a Fourier series. The coefficients of the Fourier approximations are then interpolated as functions of initial flight states and parameters. The approximate optimal trajectories can be quickly generated on-board using the proposed method. Introduction Engine failure is a major safety issue for all helicopters, especially during takeoff and landing operations. Due to the complexity of the situation and the dependence of safety on many parameters, optimal flight trajectories can provide useful guidance for pilot operation. In particular, on-board display of optimal trajectories is desirable. This paper presents a method for generating optimal flight trajectories in real-tune that can be used for on-board display. Depending on its capability and performance during an engine failure, a transport helicopter can be certified as Category A or Category B. The Federal Aviation Administration (FAA) grants Category B certification to a single or multi-engine helicopter with gross weight less than 20,000 Ib and capable of landing safely in case of one or all engine failures. Category A certification, on the other hand, is granted to multi-engine helicopters with independent engine systems. Category A helicopters must be able to either land safely or continue flight in case of One Engine Inoperation (OEI). This makes Category A helicopters uniquely suited for remote places where emergency landing sites are not available. I Ph.D. Candidate, Center for Control Sciences, Member AIAA * Assistant Professor, Dept. of Aerospace Eng. and Mechanics, Member AIAA + Civil Rotorcraft Group Leader, Rotorcraft and Powered Lift Branch The decision to continue the flight or to land represents an energy management problem. It has been shown''' that this decision depends on initial conditions at the time of failure as well as flight parameters. Due to the numerous initial variables involved in this decision, a method to communicate all this information to the pilot instantaneously, at engine failure, is needed. This method must keep the emergency procedure simple and manageable. In particular, on-board cockpit display of optimal flight trajectories is useful. This requires a reliable real-tune solution of optimal trajectories, on board, with limited time, limited computing power, and limited memory available. If possible, an analytical solution of optimal trajectories is desirable. Unfortunately, this can only be achieved for systems of low order and where the equations of motion and the cost function are simple. Therefore, for a complex system, an open-loop numerical procedure becomes necessary. Research efforts were made to solve optimal control problems in real-time. Schultz et al. used calculus of variation and energy state method to generate optimal trajectories on-board for the National Aerospace Plane (NASP). In his study, the equations of motion of the NASP are less complex than those of the helicopter, and an interval of time of few minutes is allowed. Bryson used neighboring control theory to generate near-optimal solutions that could be used in real-time. This method is elegant but requires a large amount of memory to store the needed perturbation matrices. Also, it is valid on a relatively small neighborhood of the nominal trajectory. Perturbation methods and table lookups are often used if only few parameters are involved. In the current problem, the equations of motion of the helicopter are complex and too many path equality and inequality constraints are present. Also, limitations on tune, computing power, and memory available make all the above methods unsuitable for this problem. This paper proposes a technique of real-time optimal trajectory generation based on approximation and

Trajectory Optimization for Planetary Multi-Point Powered Landing

The objective of this paper is to investigate a reliable method to generate optimal ascent trajectory for hypersonic air-breathing vehicles. When solving optimal trajectories in endo-atmospheric flight, most of traditional indirect methods suffer from difficulties in finding an appropriate initial guess and getting a convergent solution for the two point boundary value problem (TPBVP). With improvements on on-board computer performance, direct methods such as pseudospectral method show promising potential for real-time optimal guidance. It removes the need for computing analytical gradients of aerodynamic coefficients, and remains high accurate solution similar to indirect methods. In this work, optimal ascent trajectory generation problem was formulated as a fuel-optimal control problem. Gauss pseudospectral method (GPM) was presented to generate the optimal ascent trajectories. Optimal solutions from GPM were compared with an indirect method based on finite difference method (FDM). Numerical simulations were studied with various initial conditions to investigate the optimal trajectory characteristics for hypersonic air-breathing vehicles. The results verified the validity and accuracy of GPM for ascent trajectory optimization.

Multimode electric propulsion system is widely used in deep space exploration. Its thrust is output in stages with the change of input power, which also means that continuous power changes lead to discontinuous thrust changes. In the design and optimization of low-thrust trajectory, the discontinuity of thrust is often neglected and regarded as a continuous parameter. The optimal design of low-thrust transfer trajectory constrained by multimode electric propulsion is studied, and the influence of thrust grading characteristics on the trajectory is analyzed in this paper. A specific optimization strategy is proposed, including three main steps: model discretization based on direct method, fast generation of initial value based on particle swarm optimization (PSO), and optimization based on sequential quadratic programming (SQP). The dynamic model and optimization model of low-thrust transfer trajectory is established. Then, the optimization model is discretized based on the direct method and the original optimal control problem is transformed into a parameter optimization problem in the form of nonlinear programming (NLP). A hybrid optimization algorithm based on PSO and SQP is proposed to solve the new NLP problem. PSO is used to search the initial value efficiently and guarantee the global performance of the initial value and SQP is used for local optimization based on initial value, which can give full play to the excellent global optimization performance of PSO and the outstanding local optimization performance of SQP. The effectiveness of the proposed optimization strategy is verified by a simulation example of the main belt asteroid Metis (1974 QU2) rendezvous mission with once Mars gravity assist. The results show that the optimal control curve obtained is in accordance with the optimal control form of bang-bang control derived from the theory, and the thruster has just two situations at any time: shutdown or startup with maximum thrust. In the working power range, increasing the number of thrust stages can improve the rate of energy utilization, thereby improving the efficiency of thruster, shortening the startup time and reducing fuel consumption. Meanwhile, ineffective grading should be avoided in the non-working power range.

An improved hp adaptive pseudo-spectral method ia scaling parameters designed for the hypersonic vehicle trajectory optimization problem. In this paper, we take hypersonic vehicle as the research object, consider its ascent phase with various constraints, and establish a multi-constrained climbing segment trajectory optimization model with the shortest ascent time as the objective function. Because the nonlinear programming problem (NLP) obtained by applying the hp adaptive pseudo-spectral method to discretize the trajectory optimization model has high dimensionality, which makes the trajectory optimization problem difficult to solve, we propose an improved hp adaptive pseudo-spectral method. The algorithm uses the improved wild horse optimizer (IWHO) algorithm to adjust the distribution of interpolation nodes and the order of interpolation polynomials in the trajectory optimization subinterval, which avoids unnecessary mesh refinement and reduces the dimensionality of the discretized obtained NLP with a given precision, and improves the efficiency of the trajectory optimization solution. Simulation results show that the trajectories solved by the designed hybrid optimization algorithm satisfy all process constraints and terminal constraints.

Boost-skipping trajectory optimization for air-breathing hypersonic missile

Aiming at the problem of multiple constraints and low solving efficiency in the process of vehicle path tracking, an improved hp-adaptive Radau pseudospectral method (I-hp-ARPM) which uses a double-layer optimization iteration strategy and the residual of differential algebraic constraints at sampling points with a Gaussian distribution as the error evaluation criterion is proposed. Firstly, a four-DOF vehicle motion model is established. Secondly, on the basis of establishing algebraic differential constraints and path constraints and satisfying the optimization objective function, the I-hp-ARPM is used to transform the optimal control problem (OCP) into a general nonlinear programming problem for solution. Finally, the effectiveness of the proposed method is verified compared with the traditional hp-adaptive pseudospectral method. The simulation results and the virtual test show that there are peak values at 3.5 s and 4.8 s, as well as 6 s, for both the steering wheel angle and the sideslip angle with the condition of μ = 0.8. And also, there are peak values at the times of 3.5 s and 5.5 s, as well as 7.5 s, with the condition of μ = 0.4. This indicates the vehicle can track the reference path well with the control of the proposed algorithm. Both the initial and final constraints, as well as the path constraint, meet the requirements. The proposed method can generate the optimal trajectory that meets various constraint requirements. This method provides a design basis for path tracking of autonomous vehicles and has significance in engineering.

A Gauss pseudospectral method is proposed in this study to solve the optimal trajectory-planning problem for satellite rapid large-angle maneuvers. In order to meet the requirement of rapid maneuver capability of agile small satellites, Single Gimbal Control Moment Gyros (SGCMGs) are adopted as the actuators for the attitude control systems (ACS). Because the singularity problem always exists for SGCMGs during the large-angle maneuvering of the satellites, a trajectory optimization method for the gimbal rates is developed based on the Gauss pseudospectral method. This method satisfies the control requirement of satellite rapid maneuvers and evades the singularity problem of SGCMGs. The method treats the large-angle maneuver problem as an optimization problem, which meets the boundary condition and a series of the physical constraints including the gimbal angle constraint, the gimbal rates constraint, the singularity index constraint, and some other performance criteria. This optimization problem is discretized as a nonlinear programming problem by the Gauss pseudospectral method. The optimal nonsingularity gimbal angle trajectory is obtained by the sequence of quadratic programming (SQP). This approach avoids the difficulties in solving the boundary value problem. The simulations reveal that the Gauss pseudospectral method effectively plans an optimal trajectory and satisfies all the constraints within a short time.

Real-time trajectory optimization for collision-free asteroid landing based on deep neural networks

Fuel-optimal powered descent guidance with free final-time and path constraints