Constrained Trajectory Optimization Problems Research Articles

Vector Trajectory Method for Obstacle Avoidance Constrained Planetary Landing Trajectory Optimization

Considering the requirement of avoiding obstacles in different planetary landing missions, this article presents a generalized method dealing with the obstacle avoidance constrained landing trajectory optimization problem with vectorized strategy, i.e., vector trajectory method (VTM). By introducing a trajectory direction constraint with vectorized description, the character of the obstacle avoidance trajectory can be more specifically depicted. Moreover, by satisfying proper trajectory direction constraint, the lander’s particular performances, such as the observation to the target or probability of a safe flight, can be improved. To this end, the VTM and relevant theorem are first developed, revealing the relationship between the two aspects of obstacle avoidance constraint (i.e., distance constraint and trajectory direction constraint). Then, both aspects of constraints are uniformly transformed as the auxiliary angle magnitude constraint with the vectorized strategy, which significantly simplifies the solving procedure of obstacle avoidance constrained trajectory optimization problem. Finally, the proposed VTM is illustrated in detail through the examples with the planetary landing background of atmospheric entry and powered descent landing.

Robust Multi-Robot Trajectory Optimization Using Alternating Direction Method of Multiplier

Wepropose a variant of alternating direction method of multiplier (ADMM) to solve constrained trajectory optimization problems. Our ADMM framework breaks a joint optimization into small sub-problems, leading to a low iteration cost and decentralized parameter updates. Starting from a collision-free initial trajectory, our method inherits the theoretical properties of primal interior point method (P-IPM), i.e., guaranteed collision avoidance and homotopy preservation throughout optimization, while being orders of magnitude faster. We have analyzed the convergence and evaluated our method for time-optimal multi-UAV trajectory optimizations and simultaneous goal-reaching of multiple robot arms, where we take into consider kinematics-, dynamics-limits, and homotopy-preserving collision constraints. Our method highlights an order of magnitude’s speedup, while generating trajectories of comparable qualities as state-of-the-art P-IPM solver.

Tube Stochastic Optimal Control for Nonlinear Constrained Trajectory Optimization Problems

Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control problem. This problem is among the most complex in control theory, and no practically applicable method to low-thrust trajectory optimization problems has been proposed to date. This paper presents a new algorithm to solve stochastic optimal control problems with nonlinear systems and constraints. The proposed algorithm uses the unscented transform to convert a stochastic optimal control problem into a deterministic problem, which is then solved by trajectory optimization methods such as differential dynamic programming. Two numerical examples, one of which applies the proposed method to low-thrust trajectory design, illustrate that it automatically introduces margins that improve robustness. Finally, Monte Carlo simulations are used to evaluate the robustness and optimality of the solution.

Solving Multiobjective Constrained Trajectory Optimization Problem by an Extended Evolutionary Algorithm.

Highly constrained trajectory optimization problems are usually difficult to solve. Due to some real-world requirements, a typical trajectory optimization model may need to be formulated containing several objectives. Because of the discontinuity or nonlinearity in the vehicle dynamics and mission objectives, it is challenging to generate a compromised trajectory that can satisfy constraints and optimize objectives. To address the multiobjective trajectory planning problem, this paper applies a specific multiple-shooting discretization technique with the newest NSGA-III optimization algorithm and constructs a new evolutionary optimal control solver. In addition, three constraint handling algorithms are incorporated in this evolutionary optimal control framework. The performance of using different constraint handling strategies is detailed and analyzed. The proposed approach is compared with other well-developed multiobjective techniques. Experimental studies demonstrate that the present method can outperform other evolutionary-based solvers investigated in this paper with respect to convergence ability and distribution of the Pareto-optimal solutions. Therefore, the present evolutionary optimal control solver is more attractive and can offer an alternative for optimizing multiobjective continuous-time trajectory optimization problems.

Reentry Trajectory Optimization using Gradient Free Algorithms

In this work, a study on atmospheric reentry trajectory optimization using gradient free optimization techniques is presented. Genetic Algorithm (GA), Pattern Search (PS) and Simulated Annealing (SA) approaches are explored for the considered nonlinear constrained trajectory optimization problem. Aerodynamic performance indicator, (L/D), is used as a control variable to minimize the objective function subject to various terminal and in-flight path constraints. Results and findings on the performance comparison of the considered methods are discussed.

Decentralized trajectory optimization using virtual motion camouflage and particle swarm optimization

This paper investigates a decentralized trajectory optimization method to solve a nonlinear constrained trajectory optimization problem. Especially, we consider a problem constrained on the terminal time and angle in a multi-robot application. The proposed algorithm is based on virtual motion camouflage (VMC) and particle swarm optimization (PSO). VMC changes a typical full space optimal problem to a subspace optimal problem, so it can reduce the dimension of the original problem by using path control parameters (PCPs). If PCPs are optimized, then the optimal path can be obtained. In this work, PSO is used to optimize these PCPs. In multi-robot path planning, each robot generates its own optimal path by using VMC and PSO, and sends its path information to the other robots. Then, the other robots use this path information when planning their own paths. Simulation and experimental results show that the optimal paths considering the terminal time and angle constraints are effectively generated by decentralized VMC and PSO.

Trajectory optimization of industrial robots with application to computer-aided robotics and robot controllers

The workcycle time in automated car manufacturing lines CSLYI be reduced by optinizing the robot trajectories for off-line programming. Thus, improved set points for the on-line robot controller are obtained. In this paper, direct transcription methods are described for solving the constrained trajectory optimization problems by using full dynamic robot models. The optimization methods can be used conveniently in combination with computer-aided robotics (CAR) tools and current robot controllers. This is demonstrated by simulation and experimental results for an ABB IRB 6400 industrial robot