On the basis of a unified definition of the dual operation and the (anti )self dual operation, the connections of the su(2,2｜1) main cluster was used as the fundamental field variables to construct the self dual Lagrangian of conformal supergravity. A Yang Mill like Lagrangian is obtained and a new gauge theory of supergravity is put forward. The spatial projects of its spin connection are Ashtekar variables.
To obtain the near optimal path for the mobile robots in the present of the obstacles, where the robots are subject to both the nonholonomic constraints and the bound to the curvature of the path, a simple planning is applied by the heuristic searching method in which Reeds and Shepp’s shortest paths are chosen as heuristic functions. It has performed well in simulation of mobile robots moving in a cluttered environment.
