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

ABSTRACTAn efficient trajectory optimisation approach combining the classical control variable parameterisation (CVP) with a novel smooth technology and two penalty strategies is developed to solve the trajectory optimal control problems. Since it is difficult to deal with path constraints in CVP method, the novel smooth technology is firstly employed to transform the complex constraints into one smooth constraint. Then, two penalty strategies are proposed to tackle the converted path and terminal constraints to decrease the computational complexity and improve the constraints satisfaction. Finally, a nonlinear programming problem, which approximates the original trajectory optimisation problem, is obtained. Error analysis shows that the proposed method has good convergence property. A general hypersonic cruise vehicle trajectory optimisation example is employed to test the performance of the proposed method. Numerical results show that the path and terminal conditions are well satisfied and better trajectory profiles are obtained, showing the effectiveness of the proposed method.

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

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

Trajectory Optimization for Planetary Multi-Point Powered Landing

The best race driver is the one that, with a given vehicle, is able to drive on a given track in the shortest possible time. Thus, the only target is the lap time. A race driver model has to do the same. The first step towards this target is to decide which trajectory to follow. In fact, the optimal trajectory is the best compromise between the shortest track and the track that allows to achieve the highest speeds (least curvature track). Thus, the problem of trajectory planning is a bounded optimisation problem that has to take into account not only the geometry of the circuit but also the dynamics of the vehicle. A simplified vehicle dynamic model is used for this purpose. Due to the fact that the vehicle will be driven at its limit performances, although simplified the model has to correctly reproduce the maximum possible acceleration, a function of the vehicle speed, the maximum possible deceleration, again a function of the vehicle speed, and the maximum lateral acceleration, a function of both the vehicle speed and the steering angle. Knowing the trajectory, the vehicle model allows to determine the lap time. Through an optimisation algorithm it is therefore possible to determine the best compromise between shortest track and track with the minimum curvature, i.e. the trajectory (in terms of track and speed profile) that allows to minimise the time lap.

In this paper, we introduce a new approach to control wheeled acrobots. The proposed method consist of two steps; stabilization and trajectory optimization. Fisrt, we apply hierarchical linearization and bakstepping method to stabilize systems in a neighborhood of an equilibrium point. Next, we solve a trajectory optimization problem of the closed-loop system using a direct collocation method. Using the trajectory optimization, we obtain a trajectory with which path constraints are satisfied. In a numerical simulation, the validity of the controller designed by the proposed method is verified.

A near-optimal multicast scheme for mobile ad hoc networks using a hybrid genetic algorithm

Although the solar radiation pressure decreases with the square of solar distance, solar sails enable missions to the outer solar system and even beyond. For such missions, the solar sail can gain a large amount of energy by first making one or more close approaches to the sun. Within this paper, optimal trajectories for solar-sail missions to the outer planets and into near interstellar space are presented, both for ideal and for nonideal sails. Therefore, also, near-/medium-term solar sails with a relatively moderate performance are considered. The minimum flight time to the outer solar system depends not only on the lightness of the solar sail, but also on the allowed minimum solar distance. The minimum solar distance, however, is constrained by the temperature limit of the sail film. Within this paper, it is demonstrated that faster trajectories can be obtained for a given sail temperature limit, if not, as usual, the allowed minimum solar distance, but the allowed maximum sail temperature is directly used as a path constraint for optimization. Although, especially for moderate-performance solar sails, the geometry of optimal trajectories becomes quite sophisticated, the required flight times and the achieved solar system escape velocities obey very simple laws.

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>

Ascent Trajectory Optimization of Launch Vehicles with Air-Breathing Propulsion

Trajectory optimization of aerial slung load release for piloted helicopters

Rendezvous and docking operations have been an integral component of manned spaceflight from the beginning of the space age. However, there is now a growing interest in close proximity spacecraft operations in the new areas of orbital debris removal, on-orbit assembly, on-orbit refueling, and on-orbit servicing and repair missions. Current trajectory planning methods focus on performing rendezvous and docking to very well-known targets and in very well-known conditions. Inherent to these new mission types, however, is an increasing element of uncertainty to which new trajectory optimization architectures will need to be robust. There is an inherent tradeoff here between safety and performance. This paper attempts to address the uncertainties underlying path constraints while maintaining a probabilistically optimal level of performance. The goal is to find baseline trajectories with the best expected performance over large uncertainties in mission critical parameters, such as knowledge of an obstacle’s position or attitude of a target spacecraft while knowing that the trajectory is able to be replanned on board the spacecraft when higher-precision information is obtained. Results specific to this problem and the associated analysis motivate the use of this probabilistic planning framework in future space missions.

This paper presents an analysis of the precise soft landing problem for lunar missions focusing on the Decent & Landing (DL) trajectory optimization and the guidance scheme. The first step is the design of optimal solutions for different Descent & Landing strategies by evaluating the impact on the cost function (landed mass) of the problem relevant parameters. In addition, different optimal strategies are analyzed considering constraints from the navigation and hazard avoidance systems. The second step is to define an autonomous guidance scheme able to reach the desired landing site. The guidance strategy must cancel the deviations of the nominal trajectory due to the presence of execution errors and also be able to reach a new landing site (retargeting). A hybrid direct/indirect optimization scheme is implemented that can cope with different DL strategies and provides optimal DL trajectories defined by a reduced number of parameters easily flyable. The algorithm includes a continuation method for initial guess computation and is very fast and robust to compute sensitivity and off-nominal analyses. The guidance algorithm is based on an analytical approach for initial guess computation that is also used for analysis and definition of the guidance strategy. In the unconstrained problem, the guidance strategy is such that the guidance algorithm solves a non-linear system of equations. If navigation constraints are included, the guidance algorithm becomes a hybrid direct/indirect optimization algorithm that optimizes the final landed mass fulfilling the boundary conditions and some path constraints.

The forced vibration of a cylindrical shell is controlled using the distributed piezoelectric actuators and hybrid control method. The shell is constructed from a polyester film in the middle surface and two piezoelectric films, one on each side. The electrodes on the surfaces of the piezoelectric films are divided into several parts, and two parts of the films are used as actuators. The shell is vertically mounted on a vibration table and excited by the horizontal motion of the table. The hybrid control method which is a combination of it-synthesis control and disturbance cancellation method is used. Simulation and experiment were carried out and the results show that the hybrid control is more effective than each individual control method.

This paper considers the control synthesis problem and its solution using symbolic regression. Symbolic regression methods, which were previously called genetic programming methods, allow one to use a computer to find not only the parameters of a given regression function but also its structure. Unlike other works on solving the control synthesis problem using symbolic regression, the novelty of this paper is that for the first time this work employs a training dataset to address the problem of general control synthesis. Initially, the optimal control problem is solved from each point in a given set of initial states, resulting in a collection of control functions expressed as functions of time. A reference model is then integrated into the control object model, which generates optimal motion trajectories using the derived optimal control functions. The control synthesis problem is framed as an approximation task for all optimal trajectories, where the control function is sought as a function of the deviation of the object from the specified terminal state. The optimization criterion for solving the synthesis problem is the accuracy of the object’s movement along the optimal trajectory. The paper includes an example of solving the control synthesis problem for a mobile robot using a supervised machine learning method. A relatively new method of symbolic regression, the method of variational complete binary genetic programming, is studied and proposed for the solution of the control synthesis problem.