SUMMARY

The field of robotic path planning is rich and diverse; however, as more complicated systems have become automated, the need for simple methods that can navigate high dimensional spaces has increased. This research will be dedicated to developing a new form of path planning which will be applicable for robotic manipulators, nonholonomic vehicles, and cooperative systems. Generally, robotic path planning occurs within a system's configuration space, which is inherently dependent on the number of degrees-of-freedom within the system. Thus, path planning for complicated robotic systems can quickly become very computationally expensive. An alternative approach would be to operate in the task space, which is typically a fixed dimension, and perform a transformation into a robot's configuration space to control the system. This approach would allow for a path planning routine to operate in a low dimensional space regardless of the robot's complexity.

An established form of path planning: Artificial Potential Fields (APF), allows for path planning within the task space. APF navigates based on a device's system dynamics and a set of fictitious forces, which attract the robot towards a goal while repelling it away from obstacles. In this way, the path planning routine for a system could be found in task space and then transformed into configuration space via the dynamics of the system. Unfortunately, APF methods have well-known convergence and performance issues. However, based on recent work, the concepts behind potential field methods could be modified to create a globally convergent path planning scheme. Initial research shows that by modifying the fictitious force equations to consider the velocity of the robot as well as its position, a dynamic system can be created that is globally asymptotically stable at the target position. Since this adjustment considers the velocity and the position of the system, it has been named the Traveling Artificial Potential Field (TAPF) approach. Furthermore, initial research has demonstrated that TAPF removes the known performance issues from the general APF routine. TAPF was designed to be a path planning scheme that does not rely on a system's configuration space; it navigates the device's task space. With these recent developments, robotic control and path planning could be drastically simplified, even for complex systems.