Minimum distance influence coefficients for obstacle avoidance in manipulator motion planning

One weakness of current robotic technology is motion planning. Current robots especially struggle to effectively operate in cluttered environments. In this report, first and second order influence coefficients for minimum distance magnitudes are developed. These coefficients provide fundamental analytics for rates of change of minimum distance magnitudes and allow for deeper insight into the interaction between a manipulator and its environment. They are also demonstrated as viable tools for use in manipulator obstacle avoidance. Influence coefficients are rigorously developed for three simple manipulator and workspace modeling primitives: a sphere, a cylisphere, and a quadrilateral plane. In addition, a general method to use for similar derivations for new modeling primitives is presented. Also, a comparison of the speed and accuracy of using finite differencing to calculate the second order coefficients instead of calculating them analytically is given. The developed influence coefficients provide extraordinary insight into the interactions between a robot and its environment because they isolate the geometry of the distance functions from system inputs (manipulator joint commands). As a demonstration of potential uses of these coefficients, twelve obstacle avoidance criteria based on minimum distances and artificial forces are developed and demonstrated using criteria-based inverse kinematics on a ten degree of freedom manipulator operating around three obstacles. In the demonstration, the zeroth and first order criteria run at an average rate of 1042 hertz and the second order criteria run at an average rate of 2.045 hertz. Using the developed criteria one at a time, the manipulator successfully completed a demanding end-effector path, 5200 setpoints in length, for many of the criteria. In some cases, using higher-order criteria improved manipulator performance. None of the criteria allowed the manipulator to strike the obstacles. This research successfully demonstrates the usefulness of first and second order influence coefficients for minimum distance magnitudes in solving the obstacle avoidance motion-planning problem. The obstacle avoidance results also point to the feasibility of using the developed coefficients to solve a wide range of additional motion-planning problems that focus on how a system interacts with its environment.