Path Planning Based on Parametric Curves

Parametric curves are extensively used in engineering. The most commonly used parametric curves are, Bézier, B-splines, (NURBSs), and rational Bézier. Each and every one of them has special features, being the main difference between them the complexity of their mathematical definition. While Bézier curves are the simplest ones, B-splines or NURBSs are more complex. In mobile robotics, two main problems have been addressed with parametric curves. The first one is the definition of an initial trajectory for a mobile robot from a start location to a goal. The path has to be a continuous curve, smooth and easy to manipulate, and the properties of the parametric curves meet these requirements. The second one is the modification of the initial trajectory in real time attending to the dynamic properties of the environment. Parametric curves are capable of enhancing the trajectories produced by path planning algorithms adapting them to the kinematic properties of the robot. In order to avoid obstacles, the shape modification of parametric curves is required. In this chapter, an algorithm is proposed for computing an initial Bézier trajectory of a mobile robot and subsequently modifies it in real time in order to avoid obstacles in a dynamic environment

Smooth 3D Path Planning by Means of Multiobjective Optimization for Fixed-Wing UAVs

[EN] Demand for 3D planning and guidance algorithms is increasing due, in part, to the increase in unmanned vehicle-based applications. Traditionally, two-dimensional (2D) trajectory planning algorithms address the problem by using the approach of maintaining a constant altitude. Addressing the problem of path planning in a three-dimensional (3D) space implies more complex scenarios where maintaining altitude is not a valid approach. The work presented here implements an architecture for the generation of 3D flight paths for fixed-wing unmanned aerial vehicles (UAVs). The aim is to determine the feasible flight path by minimizing the turning effort, starting from a set of control points in 3D space, including the initial and final point. The trajectory generated takes into account the rotation and elevation constraints of the UAV. From the defined control points and the movement constraints of the UAV, a path is generated that combines the union of the control points by means of a set of rectilinear segments and spherical curves. However, this design methodology means that the problem does not have a single solution; in other words, there are infinite solutions for the generation of the final path. For this reason, a multiobjective optimization problem (MOP) is proposed with the aim of independently maximizing each of the turning radii of the path. Finally, to produce a complete results visualization of the MOP and the final 3D trajectory, the architecture was implemented in a simulation with Matlab/Simulink/flightGear.The authors would like to acknowledge the Spanish Ministerio de Ciencia, Innovacion y Universidades for providing funding through the project RTI2018-096904-B-I00 and the local administration Generalitat Valenciana through projects GV/2017/029 and AICO/2019/055. 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A Two-Stage Real-Time Path Planning: Application to the Overtaking Manuever

This paper proposes a two-stage local path planning approach to deal with all kinds of scenarios (i.e. intersections, turns, roundabouts). The first stage carries out an off-line optimization, considering vehicle kinematics and road constraints. The second stage includes all dynamic obstacles in the scene, generating a continuous path in real-time. Human-like driving style is provided by evaluating the sharpness of the road bends and the available space among them, optimizing the drivable area. The proposed approach is validated on overtaking scenarios where real-time path planning generation plays a key role. Simulation and real results on an experimental automated platform provide encouraging results, generating real-time collision-free paths while maintaining the defined smoothness criteria.INRIA and VEDECOM Institutes under the Ph.D. Grant; 10.13039/501100011688-Electronic Components and Systems for European Leadership (ECSEL) Project AutoDriv

Control of free-ranging automated guided vehicles in container terminals

Container terminal automation has come to the fore during the last 20 years to improve their efficiency. Whereas a high level of automation has already been achieved in vertical handling operations (stacking cranes), horizontal container transport still has disincentives to the adoption of automated guided vehicles (AGVs) due to a high degree of operational complexity of vehicles. This feature has led to the employment of simple AGV control techniques while hindering the vehicles to utilise their maximum operational capability. In AGV dispatching, vehicles cannot amend ongoing delivery assignments although they have yet to receive the corresponding containers. Therefore, better AGV allocation plans would be discarded that can only be achieved by task reassignment. Also, because of the adoption of predetermined guide paths, AGVs are forced to deploy a highly limited range of their movement abilities while increasing required travel distances for handling container delivery jobs. To handle the two main issues, an AGV dispatching model and a fleet trajectory planning algorithm are proposed. The dispatcher achieves job assignment flexibility by allowing AGVs towards to container origins to abandon their current duty and receive new tasks. The trajectory planner advances Dubins curves to suggest diverse optional paths per origin-destination pair. It also amends vehicular acceleration rates for resolving conflicts between AGVs. In both of the models, the framework of simulated annealing was applied to resolve inherent time complexity. To test and evaluate the sophisticated AGV control models for vehicle dispatching and fleet trajectory planning, a bespoke simulation model is also proposed. A series of simulation tests were performed based on a real container terminal with several performance indicators, and it is identified that the presented dispatcher outperforms conventional vehicle dispatching heuristics in AGV arrival delay time and setup travel time, and the fleet trajectory planner can suggest shorter paths than the corresponding Manhattan distances, especially with fewer AGVs.Open Acces

Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems

The article of record as published may be found at http://dx.doi.org/10.3390/s22051869This paper presents a method for the generation of trajectories for autonomous system operations. The proposed method is based on the use of Bernstein polynomial approximations to transcribe infinite dimensional optimization problems into nonlinear programming problems. These, in turn, can be solved using off-the-shelf optimization solvers. The main motivation for this approach is that Bernstein polynomials possess favorable geometric properties and yield computationally efficient algorithms that enable a trajectory planner to efficiently evaluate and enforce constraints along the vehicles� trajectories, including maximum speed and angular rates as well as minimum distance between trajectories and between the vehicles and obstacles. By virtue of these properties and algorithms, feasibility and safety constraints typically imposed on autonomous vehicle operations can be enforced and guaranteed independently of the order of the polynomials. To support the use of the proposed method we introduce BeBOT (Bernstein/B�zier Optimal Trajectories), an open-source toolbox that implements the operations and algorithms for Bernstein polynomials. We show that BeBOT can be used to efficiently generate feasible and collision-free trajectories for single and multiple vehicles, and can be deployed for real-time safety critical applications in complex environments.This research was supported by the Office of Naval Research, grants N000141912106, N000142112091 and N0001419WX00155. Antonio Pascoal was supported by H2020-EU.1.2.2-FET Proactive RAMONES, under Grant GA 101017808 and LARSyS-FCT under Grant UIDB/50009/2020. Isaac Kaminer was supported by the Office of Naval Research grant N0001421WX01974.This research was supported by the Office of Naval Research, grants N000141912106, N000142112091 and N0001419WX00155. Antonio Pascoal was supported by H2020-EU.1.2.2-FET Proactive RAMONES, under Grant GA 101017808 and LARSyS-FCT under Grant UIDB/50009/2020. Isaac Kaminer was supported by the Office of Naval Research grant N0001421WX01974

Silhouette-Informed Trajectory Generation Through a Wire Maze for Small UAS

Current rapidly-exploring random tree (RRT) algorithms rely on proximity query packages that often include collision checkers, tolerance verification, and distance computation algorithms for the generation of safe paths. In this paper, we broaden the information available to the path-planning algorithm by incorporating silhouette information of nearby obstacles in conflict. A silhouette-informed tree (SIT) is generated through the flight-safe region of a wire maze for a single unmanned aerial system (UAS). The silhouette is used to extract local geometric information of nearby obstacles and provide path alternatives around these obstacles. Thus, focusing the search for the generation of new tree branches near these obstacles, and decreasing the number of samples required to explore the narrow corridors within the wire maze. The SIT is then processed to extract a path that connects the initial location of the UAS with the goal, reduce the number of line segments in this path if possible, and smooth the resulting path using Pythagorean Hodograph Bezier curves. To ensure that the smoothed path remains in the flight-safe region of the configuration space, a tolerance verification algorithm for Bezier curves and convex polytopes in three dimensions is proposed. Lastly, temporal specifications are imposed on the smoothed path in the shape of an arbitrary speed profile

Automatic Lane-Changing Decision Based on Single-Step Dynamic Game with Incomplete Information and Collision-Free Path Planning

Traffic accidents are often caused by improper lane changes. Although the safety of lane-changing has attracted extensive attention in the vehicle and traffic fields, there are few studies considering the lateral comfort of vehicle users in lane-changing decision-making. Lane-changing decision-making by single-step dynamic game with incomplete information and path planning based on Bézier curve are proposed in this paper to coordinate vehicle lane-changing performance from safety payoff, velocity payoff, and comfort payoff. First, the lane-changing safety distance which is improved by collecting lane-changing data through simulated driving, and lane-changing time obtained by Bézier curve path planning are introduced into the game payoff, so that the selection of the lane-changing start time considers the vehicle safety, power performance and passenger comfort of the lane-changing process. Second, the lane-changing path without collision to the forward vehicle is obtained through the constrained Bézier curve, and the Bézier curve is further constrained to obtain a smoother lane-changing path. The path tracking sliding mode controller of front wheel angle compensation by radical basis function neural network is designed. Finally, the model in the loop simulation and the hardware in the loop experiment are carried out to verify the advantages of the proposed method. The results of three lane-changing conditions designed in the hardware in the loop experiment show that the vehicle safety, power performance, and passenger comfort of the vehicle controlled by the proposed method are better than that of human drivers in discretionary lane change and mandatory lane change scenarios.</jats:p