Optimal Control for Constrained Coverage Path Planning

The problem of constrained coverage path planning involves a robot trying to cover maximum area of an environment under some constraints that appear as obstacles in the map. Out of the several coverage path planning methods, we consider augmenting the linear sweep-based coverage method to achieve minimum energy/ time optimality along with maximum area coverage. In addition, we also study the effects of variation of different parameters on the performance of the modified method. INTRODUCTION Most Coverage Path Planning algorithms rely on breaking down the free space(i.e the obstacle-free space) into simple, non-overlapping sub-regions called cells. A survey of the coverage path planning problem is given in [3]. Two of the most popular offline (environment assumed to be known a priori) cellular decomposition approaches are the trapezoidal decomposition and the boustrophedon decomposition. The trapezoidal decomposition technique [1] divides the free space into trapezoidal cells, and each cell, having two parallel sides, can be covered by simple back and forth motions parallel to either side called slices with the sweep direction being between the non-parallel sides. Therefore, coverage is ensured by visiting each cell in the adjacency graph. The shortcoming of this method is that it requires far too much redundant back and forth motions to guarantee complete coverage. The boustrophedon decomposition [2] compensates for the redundant movements by merging the cells that do not contribute to change in connectivity of the nodes in the adjacency graph. This merging technique reduces the number of cells in the decomposition, thereby, reducing the overall number of back and forth motions. However, all these methods rely on maximizing the area covered without considering the time and energy spent. We introduce these additional requirements in our project. In our project, we have modeled the mobile robot as a point that can move on a 2D plane. The robot has a coverage represented as a circle centered at the location of the robot and a radius that represents the extent of coverage. The goal is to cover the entire area in minimum time and by expending minimum energy. We can make the problem more challenging by including obstacles. We will primarily keep the shape of obstacles as circular. We will introduce various constraints other than that of the system dynamics. Firstly, the point robot should not move beyond the area constraints. Secondly, the point robot should not move into the obstacle region. We allow the mobile robot to move on the boundary of the area or the boundary of the obstacle. We will represent the performance criterion, the system dynamics and the constraints mathematically in the subsequent sections.