Trajectory optimization with obstacles avoidance via strong duality equivalent and hp‐pseudospectral sequential convex programming

Abstract

A trajectory optimization algorithm is developed in this article to compute a trajectory that avoids obstacles for an unmanned aerial vehicle and minimize the load factor. Quadratic and polyhedron obstacles are both considered in this article. To satisfy the safety distance requirements in engineering practice, a distance‐based obstacle avoidance constraint is formulated, which restricts the minimum distance that a vehicle can approach the obstacle. Strong duality equivalent converts the constraints into equivalent forms without introducing binary variables. Subsequently, the trajectory optimization problem is numerically solved via a hp‐pseudospectral sequential convex programming method, which iteratively solves a sequence of second‐order cone programming subproblems until convergence is attained. Furthermore, a modified trust‐region constraint and a customized nominal trajectory update rule are proposed to accelerate the convergence of the algorithm. A group of simulations are performed to demonstrate that the algorithm is computationally efficient and capable of generating a trajectory that satisfies safety distance requirements, preventing conservativeness in the trajectory, reducing the incidence of intersample constraints violation.

Trajectory Planning of Autonomous Underwater Vehicles Based on Gauss Pseudospectral Method

“…In [ 14 ], a multi-objective excavation trajectory optimization framework based on the RPM is proposed for the trajectory planning of the unmanned electric shovel in autonomous mining scenarios. In [ 15 ], the trajectory optimization problem is numerically solved via a hp-pseudospectral sequential convex programming method, which iteratively solves a sequence of second-order cone programming subproblems until convergence is attained. The hp-adaptive pseudospectral method combines the finite element method with the traditional pseudospectral method.…”

Innovative Optimal Control Path Planning for PMCU in Cruise Ship Construction: A Kinematic and Obstacle Avoidance Model

“…In contrast, the direct method has stronger applicability by discretizing the time variables of the continuous optimal control problem and then transforming the NLP problem for solving. Among many methods, the pseudospectral method has been widely used in the field of path planning and trajectory optimization [38][39][40]. The method uses a global polynomial function as the basis function to interpolate the control and state over a series of discrete configuration points to approximate them, and then satisfies the path constraints and boundary conditions at each collocation point and solves for the cost function.…”

An improved adaptive hp mesh refinement method in solving optimal control problems

“…[24][25][26][27][28] Li et al 29,30 apply the adaptive hp method to solve trajectory optimization problem of missile, which obtain satisfactory solving precision. Considering obstacles avoidance and overload minimization, Xia et al 31 propose an hp-pseudospectral sequential convex programming method to achieve trajectory optimization of unmanned aerial vehicle. Based on adaptive hp method, Xu et al 32 complete the optimal motion planning of the space manipulator.…”

“…Although the aforementioned works [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] on the adaptive hp method has made great progress, there still are several issues that need further consideration.…”

“…Although the aforementioned works 21–39 on the adaptive hp method has made great progress, there still are several issues that need further consideration. When there are sudden change points in the optimal control curve (such as bang‐bang control, 44,45 switch control 46 ), in order to obtain a satisfactory solution, some existing adaptive hp methods often configure a large number of collocation points near the sudden change point, or segments the mesh frequently, which largely increases the dimensions of the NLP, therefore, affects the computational efficiency. Most of the existing hp methods divide the mesh evenly according to the criterion, which is inefficient and may lead to frequent segmentation in the process of mesh refinement.…”