Vision-based path planning with obstacle avoidance for mobile robots using linear matrix inequalities

In this paper, a vision-based obstacle avoiding path generation problem is considered for autonomous mobile robots under a top-view workspace. The collision-free path planning problem is converted to a convex optimization problem that can be solved numerically using linear matrix inequalities (LMI). A new optimal (shortest) path cost formulation is given for LMI optimization using a novel Line of Sight Meshing (LSM) method. As compared to the traditional meshing algorithms such as Voronoi and Delaunay, the LSM generates fewer mesh cells which results in reduced computation time. A virtual path diagram (VPD), consisting of all collision-free piecewise straight-line paths, is then found for robot navigation. The LMI optimization method is then used to find the optimal (shortest) collision-free path from the VPD set. In addition to distance, other constraints, such as terrain condition and curvature of the path can be incorporated in the cost function for constrained optimal solution. Finally, a rapid prototyping (RP) environment has been developed, which is used for hardware implementation of the algorithm. The generated paths are then converted to motion commands, which are sent wirelessly from a base-station to mobile robots for motion control.