An algorithm is presented for wheeled mobile robot trajectory generation that achieves a high degree of generality and efficiency. The generality derives from numerical linearization and inversion of forward models of propulsion, suspension, and motion for any type of vehicle. Efficiency is achieved by using fast numerical optimization techniques and effective initial guesses for the vehicle controls parameters. This approach can accommodate such effects as rough terrain, vehicle dynamics, models of wheel-terrain interaction, and other effects of interest. It can accommodate boundary and internal constraints while optimizing an objective function that might, for example, involve such criteria as obstacle avoidance, cost, risk, time, or energy consumption in any combination. The algorithm is efficient enough to use in real time due to its use of nonlinear programming techniques that involve searching the space of parameterized vehicle controls. Applications of the presented methods are demonstrated for planetary rovers.

Optimal Rough Terrain Trajectory Generation for Wheeled Mobile Robots

This paper focuses on the collision-free coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical programming, consists of identifying collision segments along each robot's path, and then optimizing the robots' velocities along the collision and collision-free segments. First, for each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding two-point boundary value problems. The collision avoidance constraints for pairs of robots can then be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations, which provide schedules that give lower and upper bounds on the optimum; the upper bound schedule is designed to provide continuous velocity trajectories that are feasible. The approach is illustrated with coordination of multiple robots, modeled as double integrators subject to velocity and acceleration constraints. An application to coordination of nonholonomic car-like robots is described, along with implementation results for 12 robots.

https://link.springer.com/content/pdf/10.1007%2F978-3-540-45058-0_14.pdf

Coordinating Multiple Robots with Kinodynamic Constraints Along Specified Paths

This paper addresses trajectory planning in a dynamic workspace, i.e. motion planning for a robot subject to dynamic constraints and moving in a workspace with moving obstacles. First the novel con...

https://hal.inria.fr/inria-00259321/document

Trajectory planning in a dynamic workspace: a 'state-time space' approach

Coordinating Multiple Robots with Kinodynamic Constraints along Specified Paths.

We describe a new approach to the problem of motion planning for mobile robots on natural rough terrain. Our approach computes a multiresolution representation of the terrain using wavelets, and hierarchically plans the path through sections which are well approximated on coarser levels and relatively smooth. Unlike most methods, the hierarchical approximation errors are used explicitly in a cost function to distinguish preferred terrain sections. The error is computed using the corresponding wavelet coefficients. We also propose a new nonscalar path cost measure based on the sorted terrain costs along the path. This measure can be incorporated into standard global path search algorithms and yields paths which avoid high cost terrain areas when possible. Additional constraints for specific robots can be integrated into this approach for efficient hierarchical motion planning on rough terrain. We present the algorithms and experimental results for real terrain data.

Multiresolution rough terrain motion planning

A method is presented for optimally planning the motions of autonomous vehicles, considering vehicle dynamics, terrain topography, obstacles, and surface mobility. The terrain is represented by a smooth cubic B patch, and the geometric path consists of a two dimensional B spline curve mapped to the three-dimensional surface. The path is optimized with a parameter optimization procedure, using motion time as the cost function. The optimal motion time along the path is computed by transforming the constraints between the vehicle and ground to limits on vehicle speeds. The optimal speeds which minimize motion time are then obtained below the velocity limits, using the maximum acceleration of deceleration at all times. Examples are presented which demonstrate the method for a simple dynamic model of a vehicle moving on mountainous terrain. >

J.C. Chen

Papers

Optimal motion planning of autonomous vehicles in three dimensional terrains