Time Distance: A Novel Collision Prediction and Path Planning Method

Motion planning is an active field of research in robot navigation and autonomous driving. There are plenty of classical and heuristic motion planning methods applicable to mobile robots and ground vehicles. This paper is dedicated to introducing a novel method for collision prediction and path planning. The method is called Time Distance (TD), and its basis returns to the swept volume idea. However, there are considerable differences between the TD method and existing methods associated with the swept volume concept. In this method, time is obtained as a dependent variable in TD functions. TD functions are functions of location, velocity, and geometry of objects, determining the TD of objects with respect to any location. Known as a relative concept, TD is defined as the time interval that must be spent in order for an object to reach a certain location. It is firstly defined for the one-dimensional case and then generalized to 2D space. The collision prediction algorithm consists of obtaining the TD of different points of an object (the vehicle) with respect to all objects of the environment using an explicit function which is a function of TD functions. The path planning algorithm uses TD functions and two other functions called Z-Infinity and Route Function to create the collision-free path in a dynamic environment. Both the collision prediction and the path planning algorithms are evaluated in simulations. Comparisons indicate the capability of the method to generate length optimal paths as the most effective methods do.