Collision avoidance in a two-point system via Liapunovʹs second method Original Research Article

The geometric problem of finding a path for a moving solid among other solid obstacles is well known in robotics in the area of real-time obstacle avoidance for manipulators and mobile robots. In this paper, a solution to the problem, also known as the findpath problem, is provided via the second or direct method of Liapunov. The method is used to construct control functions for the collision avoidance between two point masses which are required to move to designated areas or targets located in the horizontal plane. Two new results are presented. The first result opens up the possibility of analysing in a more effective manner the dynamics of more than two point masses. The second new result addresses, via generalized control functions, important collision avoidance issues which are (1) improving collision avoidance between objects, (2) obtaining low control inputs for collision avoidance and convergence to targets, and (3) having the best time to reach a target safely.