Path planning for simple wheeled robots : sub-Riemannian and elastic curves on SE(2)

This paper presents a motion planning method for a simple wheeled robot in two cases: (i) where translational and rotational speeds are arbitrary and (ii) where the robot is constrained to move forwards at unit speed. The motions are generated by formulating a constrained optimal control problem on the Special Euclidean group SE(2). An application of Pontryagin’s maximum principle for arbitrary speeds yields an optimal Hamiltonian which is completely integrable in terms of Jacobi elliptic functions. In the unit speed case, the rotational velocity is described in terms of elliptic integrals and the expression for the position reduced to quadratures. Reachable sets are defined in the arbitrary speed case and a numerical plot of the time-limited reachable sets presented for the unit speed case. The resulting analytical functions for the position and orientation of the robot can be parametrically optimised to match prescribed target states within the reachable sets. The method is shown to be easily adapted to obstacle avoidance for static obstacles in a known environment

A path planning and path-following control framework for a general 2-trailer with a car-like tractor

Maneuvering a general 2-trailer with a car-like tractor in backward motion is a task that requires significant skill to master and is unarguably one of the most complicated tasks a truck driver has to perform. This paper presents a path planning and path-following control solution that can be used to automatically plan and execute difficult parking and obstacle avoidance maneuvers by combining backward and forward motion. A lattice-based path planning framework is developed in order to generate kinematically feasible and collision-free paths and a path-following controller is designed to stabilize the lateral and angular path-following error states during path execution. To estimate the vehicle state needed for control, a nonlinear observer is developed which only utilizes information from sensors that are mounted on the car-like tractor, making the system independent of additional trailer sensors. The proposed path planning and path-following control framework is implemented on a full-scale test vehicle and results from simulations and real-world experiments are presented.Comment: Preprin

Continuous-curvature paths for mobile robots

This paper discusses how to plan continuous-curvature paths for car-like wheeled mobile robots. The task is to generate a trajectory with upper-bounded curvature and curvature derivative. To solve this problem we use three path planning primitives, namely straight line segments, circular segments, and continuous-curvature turns (CC turns) in the path planning. We give a classification of the CC turns and we also describe the motion along different kinds of CC turns. We focus on giving computational effective formulae for real-time usage

Learning from Experience for Rapid Generation of Local Car Maneuvers

Being able to rapidly respond to the changing scenes and traffic situations by generating feasible local paths is of pivotal importance for car autonomy. We propose to train a deep neural network (DNN) to plan feasible and nearly-optimal paths for kinematically constrained vehicles in small constant time. Our DNN model is trained using a novel weakly supervised approach and a gradient-based policy search. On real and simulated scenes and a large set of local planning problems, we demonstrate that our approach outperforms the existing planners with respect to the number of successfully completed tasks. While the path generation time is about 40 ms, the generated paths are smooth and comparable to those obtained from conventional path planners

Path following hybrid control for vehicle stability applied to industrial forklifts

The paper focuses on a closed-loop hybrid controller (kinematic and dynamic) for path following approaches with industrial forklifts carrying heavy loads at high speeds, where aspects such as vehicle stability, safety, slippage and comfort are considered. The paper first describes a method for generating Double Continuous Curvature (DCC) paths for non-holonomic wheeled mobile robots, which is the basis of the proposed kinematic controller. The kinematic controller generates a speed profile, based on slow-in and fast-out policy, and a curvature profile recomputing DCC paths in closed-loop. The dynamic controller determines maximum values for decelerations and curvatures, as well as bounded sharpness so that instantaneous vehicle stability conditions can be guaranteed against lateral and frontal tip-overs. One of the advantages of the proposed method, with respect to full dynamic controllers, is that it does not require dynamic parameters to be estimated for modelling, which in general can be a difficult task. The proposed kinematic dynamic controller is afterwards compared with a classic kinematic controller like Pure-Pursuit. For that purpose, in our hybrid control structure we have just replaced the proposed kinematic controller with Pure-Pursuit. Several metrics, such as settling time, overshoot, safety and comfort have been analysed.This work was supported by VALi+d and PROMETEO Programs (Conselleria d'Educacio, Generalitat Valenciana), DIVISAMOS (DPI-2009-14744-C03-01) and SAFEBUS (IPT-2011-1165-370000): Ministry of Economy and Competitivity.Girbés, V.; Armesto Ángel, L.; Tornero Montserrat, J. (2014). Path following hybrid control for vehicle stability applied to industrial forklifts. Robotics and Autonomous Systems. 62(6):910-922. https://doi.org/10.1016/j.robot.2014.01.004S91092262

Real-time motion planning methods for autonomous on-road driving: state-of-the-art and future research directions

Currently autonomous or self-driving vehicles are at the heart of academia and industry research because of its multi-faceted advantages that includes improved safety, reduced congestion, lower emissions and greater mobility. Software is the key driving factor underpinning autonomy within which planning algorithms that are responsible for mission-critical decision making hold a significant position. While transporting passengers or goods from a given origin to a given destination, motion planning methods incorporate searching for a path to follow, avoiding obstacles and generating the best trajectory that ensures safety, comfort and efficiency. A range of different planning approaches have been proposed in the literature. The purpose of this paper is to review existing approaches and then compare and contrast different methods employed for the motion planning of autonomous on-road driving that consists of (1) finding a path, (2) searching for the safest manoeuvre and (3) determining the most feasible trajectory. Methods developed by researchers in each of these three levels exhibit varying levels of complexity and performance accuracy. This paper presents a critical evaluation of each of these methods, in terms of their advantages/disadvantages, inherent limitations, feasibility, optimality, handling of obstacles and testing operational environments. Based on a critical review of existing methods, research challenges to address current limitations are identified and future research directions are suggested so as to enhance the performance of planning algorithms at all three levels. Some promising areas of future focus have been identified as the use of vehicular communications (V2V and V2I) and the incorporation of transport engineering aspects in order to improve the look-ahead horizon of current sensing technologies that are essential for planning with the aim of reducing the total cost of driverless vehicles. This critical review on planning techniques presented in this paper, along with the associated discussions on their constraints and limitations, seek to assist researchers in accelerating development in the emerging field of autonomous vehicle research

Implications of Motion Planning: Optimality and k-survivability

We study motion planning problems, finding trajectories that connect two configurations of a system, from two different perspectives: optimality and survivability. For the problem of finding optimal trajectories, we provide a model in which the existence of optimal trajectories is guaranteed, and design an algorithm to find approximately optimal trajectories for a kinematic planar robot within this model. We also design an algorithm to build data structures to represent the configuration space, supporting optimal trajectory queries for any given pair of configurations in an obstructed environment. We are also interested in planning paths for expendable robots moving in a threat environment. Since robots are expendable, our goal is to ensure a certain number of robots reaching the goal. We consider a new motion planning problem, maximum k-survivability: given two points in a stochastic threat environment, find n paths connecting two given points while maximizing the probability that at least k paths reach the goal. Intuitively, a good solution should be diverse to avoid several paths being blocked simultaneously, and paths should be short so that robots can quickly pass through dangerous areas. Finding sets of paths with maximum k-survivability is NP-hard. We design two algorithms: an algorithm that is guaranteed to find an optimal list of paths, and a set of heuristic methods that finds paths with high k-survivability