As discussed in the Chapter 5, the car and uncycle have very close relationship that allows controllability to propagate between the two systems. However, it was shown that the uniycle is not traceable by the car. This means that there exists a unicycle trajectory that does not the
-mapping of any car trajectory. The particular trajectory that causes problems is that of the rotating unicycle and addressing this problem in the open-loop setting is the focus of this chapter.
In this chapter, an open-loop optimal control algorithm is presented that utilizes the
-traceability of the unicycle by the car. The algorithm is developed and simulation results are given for different initial car inputs. Their results are compared.