Trajectory Optimization and Finite-Time Control for Unmanned Helicopters Formation

Dynamic soaring is an effective method to improve the endurance time and flight distance of small unmanned air vehicles. However, effective use the gradient change of the wind field to plan and track UAV trajectory has always been the focus and difficulty of current research. To solve this problem, trajectory optimization and tracking control for dynamic soaring of small unmanned air vehicles are presented in this paper. Firstly, the six degrees of freedom dynamics model with a consideration of the wind information is established. Secondly, soaring trajectory planning is formulated as an optimization problem and solved by using the Gaussian Pseudospectral method. Thirdly, a cascade dual loop scheme is used to design a tracking controller, where the outer loop employs a PID controller with virtual control signals for position control. A sliding mode control with adaptive non-singular fast terminal sliding mode control is proposed for inner loop attitude control. This method is robust to system parameter perturbation and uncertainties. Simulation shows that the proposed method can generate the trajectory in the gradient wind for dynamic soaring and ensure the aircraft tracks this trajectory even if in the presence of disturbance.

PurposeThe purpose of this paper is to present a new nested rapidly‐exploring random tree (RRT) algorithm for fault tolerant motion planning of robotic manipulators.Design/methodology/approachAnother RRT algorithm is nested within the general RRT algorithm. This second nested level is used to check whether the new sampled node in the first nested level is fault tolerant. If a solution can be found in the second nested RRT, the reduced manipulator after failures at the new sampled node can still fulfill the remaining task and this new sampled node is added into the nodes of RRT in the first level. Thus, the nodes in the first level RRT algorithm are all fault tolerant postures. The final trajectory joined by these nodes is also obviously fault tolerant. Besides fault tolerance, this new nested RRT algorithm also can fulfill some secondary tasks such as improvement of dexterity and obstacle avoidance. Sufficient simulations and experiments of this new algorithm on fault tolerant motion planning of robotic manipulators are implemented.FindingsIt is found that the new nested RRT algorithm can fulfill fault tolerance and some other secondary tasks at the same time. Compared to other existing fault tolerant algorithms, this new algorithm is more efficient.Originality/valueThe paper presents a new nested RRT algorithm for fault tolerant motion planning.

In this paper a novel combination of data structures and algorithms is presented as a fast and efcient practical approach to path planning for unmanned vehicles. This approach utilizes an architecture that integrates effective obstacle representation using an efcient Quadtree data structure, with path planning based on a modied Rapidly-exploring Random Tree (RRT) algorithm, and a path pruning technique based on Dijkstra’s algorithm, resulting in rapid discovery of sub-optimal feasible paths. One of the computationally expensive steps of the RRT algorithm is checking RRT segments for collision with obstacles. To address this problem, an efcient obstacle representation using Quadtrees is implemented enabling fast segment checks. While the RRT approach is guaranteed to nd a feasible path through complex obstacle elds with the probability of discovery approaching one as the number of iterations increases, the resulting paths may be far from optimal as the only criterion embedded in the RRT search is feasibility. For this reason, the paths generated by the RRT algorithm are passed through Dijkstra algorithm that nds a shortest obstacle-free path among the points on the path. Dijkstra algorithm that re-samples the segments of the path and nds the shortest path among the new points is implemented resulting in paths that are very close to the optimal ones. To speed up the computation, the basic search algorithm is implemented as a dual RRT from the initial and nal points. To account for motion transients along the path, a suitable size corridor is introduced, assuring that the vehicle has enough room for maneuvering among the obstacles. This computationally efcient architecture lends itself to real-time implementation for both pre-planning with known obstacles as well as rapid reactive re-planning in the presence of new pop-up obstacles. The proposed technique is evaluated using several challenging path-planning examples characterized by a large number of non-convex constraints arising in cluttered obstacle elds with known and unknown obstacles. A modication that allows an easy way to introduce vehicle dynamics constraints or actuation failures is also implemented. Algorithms have been implemented for two as well as three dimensional path planning applications.

The online cooperative path planning problem is discussed for multi-quadrotor maneuvering in an unknown dynamic environment. Based on the related basic concepts, typical three-dimensional obstacle models, such as spherical and cubic, and their collision checking criteria are presented in this article. An improved rapidly exploring random tree (RRT) algorithm with goal bias and greed property is proposed based on the heuristic search strategy to overcome the shortcomings of the classical RRT algorithm. Not only are the kinematic constraints of the quadrotor established but the time and space coordination strategy matching with the improved RRT algorithm is also presented in this article. Furthermore, a novel online collision avoidance strategy according to the partial information of the surrounding environment is proposed. On the basis of the above work, a distributed online path planning strategy is proposed to obtain the feasible path for each quadrotor. Numerical simulation results show that the improved RRT algorithm has better search efficiency than the classical RRT algorithm. And the satisfactory path planning and path tracking results prove that the above model and related planning strategies are reasonable and effective.

An object pick-and-place system with a camera, a six-degree-of-freedom (DOF) robot manipulator, and a two-finger gripper is implemented based on the robot operating system (ROS) in this paper. A collision-free path planning method is one of the most fundamental problems that has to be solved before the robot manipulator can autonomously pick-and-place objects in complex environments. In the implementation of the real-time pick-and-place system, the success rate and computing time of path planning by a six-DOF robot manipulator are two essential key factors. Therefore, an improved rapidly-exploring random tree (RRT) algorithm, named changing strategy RRT (CS-RRT), is proposed. Based on the method of gradually changing the sampling area based on RRT (CSA-RRT), two mechanisms are used in the proposed CS-RRT to improve the success rate and computing time. The proposed CS-RRT algorithm adopts a sampling-radius limitation mechanism, which enables the random tree to approach the goal area more efficiently each time the environment is explored. It can avoid spending a lot of time looking for valid points when it is close to the goal point, thus reducing the computing time of the improved RRT algorithm. In addition, the CS-RRT algorithm adopts a node counting mechanism, which enables the algorithm to switch to an appropriate sampling method in complex environments. It can avoid the search path being trapped in some constrained areas due to excessive exploration in the direction of the goal point, thus improving the adaptability of the proposed algorithm to various environments and increasing the success rate. Finally, an environment with four object pick-and-place tasks is established, and four simulation results are given to illustrate that the proposed CS-RRT-based collision-free path planning method has the best performance compared with the other two RRT algorithms. A practical experiment is also provided to verify that the robot manipulator can indeed complete the specified four object pick-and-place tasks successfully and effectively.

In this paper, an improved APF-GFARRT* (artificial potential field-guided fuzzy adaptive rapidly exploring random trees) algorithm based on APF (artificial potential field) guided sampling and fuzzy adaptive expansion is proposed to solve the problems of weak orientation and low search success rate when randomly expanding nodes using the RRT (rapidly exploring random trees) algorithm for disinfecting robots in the dense environment of disinfection operation. Considering the inherent randomness of tree growth in the RRT* algorithm, a combination of APF with RRT* is introduced to enhance the purposefulness of the sampling process. In addition, in the context of RRT* facing dense and restricted environments such as narrow passages, adaptive step-size adjustment is implemented using fuzzy control. It accelerates the algorithm’s convergence and improves search efficiency in a specific area. The proposed algorithm is validated and analyzed in a specialized environment designed in MATLAB, and comparisons are made with existing path planning algorithms, including RRT, RRT*, and APF-RRT*. Experimental results show the excellent exploration speed of the improved algorithm, reducing the average initial path search time by about 46.52% compared to the other three algorithms. In addition, the improved algorithm exhibits faster convergence, significantly reducing the average iteration count and the average final path cost by about 10.01%. The algorithm’s enhanced adaptability in unique environments is particularly noteworthy, increasing the chances of successfully finding paths and generating more rational and smoother paths than other algorithms. Experimental results validate the proposed algorithm as a practical and feasible solution for similar problems.

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.

Recent advances in path-planning algorithms have transformed robotics. The Rapidly exploring Random Tree (RRT) algorithm underpins autonomous robot navigation. This paper systematically examines the uses and development of RRT algorithms in single and multiple robots to demonstrate their importance in modern robotics studies. To do this, we have reviewed 70 works on RRT algorithms in single and multiple robot path planning from 2015 to 2023. RRT algorithm evolution, including crucial turning points and innovative techniques, have been examined. A detailed comparison of the RRT Algorithm versions reveals their merits, limitations, and development potential. The review’s identification of developing regions and future research initiatives will enable roboticists to use RRT algorithms. This thorough review is essential to the robotics community, inspiring new ideas, helping problem-solving, and expediting single- and multi-robot system development. This highlights the necessity of RRT algorithms for autonomous and collaborative robotics advancement.

In the present paper, a composite formation strategy for multiple missiles is proposed, which is composed of the optimal formation configuration trajectory and a robust controller for trajectory tracking and formation keeping. Motion models describing multiple missiles formation configuration and keeping are established. Many constraints such as initial position, terminal position and collision avoidance are taken into account. Based on the Gauss Pseudospectral method, an optimal trajectory is designed which makes multiple missiles configurate the designated shape in the shortest time with less control energy. With the consideration of practical situations such as missiles' position error, measurement error of information between missiles and their limited control input, a robust controller is designed to track the optimal formation configuration trajectory and then keep the designated formation shape by adopting dynamic surface control. Simulation results demonstrate that by adopting the composite formation strategy, multiple missiles can configurate the designated shape in the shortest time with less control energy and then keep the formation shape in spite of much disturbance.

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.

This paper introduces an efficient motion planning method for on-road driving of the autonomous vehicles, which is based on the rapidly exploring random tree (RRT) algorithm. RRT is an incremental sampling-based algorithm and is widely used to solve the planning problem of mobile robots. However, due to the meandering path, the inaccurate terminal state, and the slow exploration, it is often inefficient in many applications such as autonomous vehicles. To address these issues and considering the realistic context of on-road autonomous driving, we propose a fast RRT algorithm that introduces a rule-template set based on the traffic scenes and an aggressive extension strategy of search tree. Both improvements lead to a faster and more accurate RRT toward the goal state compared with the basic RRT algorithm. Meanwhile, a model-based prediction postprocess approach is adopted, by which the generated trajectory can be further smoothed and a feasible control sequence for the vehicle would be obtained. Furthermore, in the environments with dynamic obstacles, an integrated approach of the fast RRT algorithm and the configuration-time space can be used to improve the quality of the planned trajectory and the replanning. A large number of experimental results illustrate that our method is fast and efficient in solving planning queries of on-road autonomous driving and demonstrate its superior performances over previous approaches.

Aiming at the problems of long planning time and path feasibility existing in genetic algorithm (GA) for path planning, an improved method integrating GA with Rapidly-exploring Random Tree (RRT) algorithm is proposed. By generating initial path populations using the RRT algorithm, eliminating redundant paths with a deletion operator, and introducing an elite selection strategy to optimize the selection operation, the continuity of paths and the convergence speed of the algorithm are effectively improved. Additionally, a path point backtracking method is utilized to further optimize path length and turning points. Experimental results show that the improved algorithm outperforms the traditional <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A^{*}$</tex> algorithm and other improved GA in terms of path length, number of inflection points, and iteration times. The path length is shortened by an average of 8%, and the iteration times are reduced to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$53 \%-85 \%$</tex> of those of the comparative algorithms, verifying its high efficiency and robustness in complex environments.

Rapidly-exploring Random Tree (RRT) algorithm has been used for motion planning in numerous and diverse robotic applications. For applications which demands higher motion resolution, the computational cost increases together with the number of motion primitives used to expand the RRT. In this paper we present a method based on optimization by elimination which is applied to the Rapidly-exploring Random Tree algorithm to reduce its computational cost. This method optimizes the efficiency of motion primitives generation. It identifies tree expansion in promising areas by initially generating and analyzing only few motion primitives. Then it increases the number of primitives for motion resolution enhancement in those promising areas. The results achieved by applying this method evidence a substantial decrease in the computational cost.

Dynamics modeling and motion planning for snakeboard systems were investigated, and a hybrid optimization strategy based on the genetic algorithm (GA) and the Gauss pseudospectral method (GPM) was presented. Firstly, the Euler-Lagrange equations for the snakeboard system were derived based on the Riemannian manifold and the affine connection theory in differential geometry. The configuration space of the snakeboard corresponds to the manifold space, the velocity space corresponds to the tangent space, the torque space corresponds to the cotangent space, and the inertia matrix provides a Riemannian measure on the manifold. The set of admissible velocities were represented by the appropriate bases to simplify the kinematics equations. Then the optimal motion planning problem was transformed into a nonlinear programming problem with the GPM. The optimal trajectory and the optimal control inputs were obtained with the sequential quadratic programming (SQP) algorithm. The GA was applied to generate the initial values of the GPM. Finally, through numerical simulation, the optimal trajectory agrees well with actual conditions, and the control inputs match the various constraints closely. The results demonstrate the effectiveness of the proposed method.

Aiming at the problems of strong randomness, unsmooth path and local optimum in the path planning of the Rapidly-exploring Random Trees (RRT) algorithm. The paper designs an improved RRT algorithm with variable step size and goal orientation (VO-RRT), which introduces variable step size, oriented expansion node, optimized initial path and smoothed path four parts. Through several experiments in 2D and 3D space to prove that the VO-RRT algorithm has enhanced obstacle avoidance ability and improved path smoothness in different obstacle spaces. The path nodes generated by the VO-RRT algorithm in 3D space are tested in URsim simulation software and manipulator body to verify the executability of the optimized path.