Nonholonomic systems are a classification of systems that essentially denote constraints in motion in a given space. There are a multitude of nonholonomic systems that permeate everyday life, the most classic example is the car. With systems like these being so common it is crucial to develop tools to better utilize these systems. One such utilization especially for the car system is path planning and obstacle avoidance.
The goal of this project is to tackle obstacle avoidance with a nonholonomic motion planner in a novel way. After being exposed to the paper Nonholonomic motion planning: Steering with Sinusoids by R. Murray and S. Sastry we discovered a very interesting approach to this problem. Essentially this method of inputting sinusoids to a nonholnomic system as a way to generate paths can extend to increasingly more or less complex nonholonomic systems relatively easily. Therefore, any additional work done with this method such as obstacle avoidance has the potential to be applied to numerous nonholonomic systems. The goal then of this project was to implement an optimized motion path for obstacle avoidance using sinusoidal inputs.