Real-Time Path Planning for Time-Optimal Exploration

Motivated by cooperative exploration missions, this paper considers constant velocity, level flight path planning for Unmanned Air Vehicles (UAVs) equipped with range limited, omni-directional sensors. These active energy-based sensors collect information about objects of interest at rates that depend on the range to the objects according to Shannon’s channel capacity equation, where the signal to noise ratio is governed by the radar equation. The mission of the UAVs is to travel through a given area and collect a specified amount of information about each object of interest while minimizing the total flight time. This information can then be used to classify the objects of interest. An optimal path planning problem is examined where the states are the coordinates of the UAVs and the amounts of information collected about each object of interest, the control inputs are the UAV heading angles, the objective function is the elapsed time, and the boundary conditions are subject to inequality constraints that reflect the requirements of information collection. Based on this problem, several technical approaches are suggested for the implementation of a real-time path planner. The computational speed of the path planner is dependent upon onboard processing capability. As an optimal solution may not be feasible during an allowed planning interval, the problem becomes one of bounded rationality, where the optimality of the solution is directly dependent upon the length of computational time available. A parametric approximation and table lookup strategy are discussed as two possible methods of approaching bounded rationality. These strategies are implemented in a receding horizon controller suitable for a time-varying environment. The methods are compared by their various virtues and the results are illustrated on several time-optimal exploration scenarios.