Virtual Sphere Algorithms for orthodrome-based collision-free & smooth robot motion

A novel geometric algorithm is proposed that assures a smooth path around the obstacle by generating a virtual sphere around it. The spherical virtual sphere algorithm (SVSA) makes the end-effector (the outermost tip of a closed gripper and hence, considered a point object) of the robot manipulator navigate along the orthodrome, the shortest path connecting the end-points of the obstacle avoidance path on the virtual sphere. The exponential virtual sphere algorithm (EVSA), although uses a virtual sphere to determine the end-points of the obstacle avoidance path, makes the end-effector navigate along an exponential curve around the obstacle. A performance comparison of both these algorithms is presented, followed by achievements over the past algorithms. Unlike some of the existing algorithms that focus on recovering from local minima, virtual sphere algorithms (VSAs) avoid entering a concave obstacle due to the spherical encapsulation. Simplicity due to the geometric nature and guarantee of shortest path are major achievements of VSAs.