The speed graph method: pseudo time optimal navigation among obstacles subject to uniform braking safety constraints

• Published in: Autonomous robots Vol. 41; no. 2; pp. 385 - 400
• Main Authors: Manor, Gil, Rimon, Elon
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2017; Springer Nature B.V
• Subjects: Artificial Intelligence; Barriers; Braking; Computational geometry; Computer Imaging; Control; Convexity; Engineering; Mechatronics; Navigation; Obstacle avoidance; Optimization; Pattern Recognition and Graphics; Robotics; Robotics and Automation; Robots; Safety; Time dependence; Travel time; Vision; High speed navigation; Mobile robot safety; Mobile robot time optimal navigation
• ISSN: 0929-5593; 1573-7527
• DOI: 10.1007/s10514-015-9538-9

This paper considers the synthesis of pseudo time optimal paths for a mobile robot navigating among obstacles subject to uniform braking safety constraints. The classical Brachistochrone problem studies the time optimal path of a particle moving in an obstacle free environment subject to a constant force field. By encoding the mobile robot’s braking safety constraint as a force field surrounding each obstacle, the paper generalizes the Brachistochrone problem into safe time optimal navigation of a mobile robot in environments populated by polygonal obstacles. Convexity of the safe travel time functional, a path dependent function, allows efficient construction of a  speed graph for the environment. The speed graph consists of safe time optimal arcs computed as convex optimization problems in O ( n 3 log ( 1 / ϵ ) ) total time, where n is the number of obstacle features in the environment and ϵ is the desired solution accuracy. Once the speed graph is constructed for a given environment, pseudo time optimal paths between any start and target robot positions can be computed along the speed graph in O ( n 2 log n ) time. The results are illustrated with examples and described as a readily implementable procedure.