Generating Patterns With a Unicycle

The objective of the technical note is to make a unicycle trace hypotrochoid like patterns using a simple range based control scheme. These patterns have applications in surveillance, exploration, coverage, etc. In this technical note, the patterns have been characterized in terms of the minimum and maximum radial distance from the center of the pattern. We have shown that under the control scheme and given any controller gain, the agent always achieves a hypotrochoidal pattern. Further, we have shown the existence of controller gains necessary to achieve any desired hypotrochoidal pattern starting from any initial position. We have also analyzed the conditions necessary for the generating patterns in presence of turn rate constraints of the unicycle. The simulations have been performed for the proposed scheme and the mathematical results have been validated.