CSCE 452/752 Robotics and Spatial Intelligence, Fall 2025

Homework 4 Solutions

A certain robot that moves on three wheels. The figure below shows two of the wheels, along with the ICC of the robot's motion.
diagram of two wheels
1. The third wheel (not shown) is attached to the robot so that its rolling direction is perpendicular to the rolling direction of the two wheels shown. Is this information sufficient to completely determine the position of the third wheel?
YES    NO
If you answered YES, mark the exact position and rolling direction of the third wheel on the diagram above.
If you answered NO, clearly mark all possible positions of the third wheel on the diagram above.
In either case, explain your answer.
No. A line drawn perpendicular to the third wheel's rolling direction must pass through the ICC. The set of points from which this is possible with the given rolling direction is a line.
2. From this position, the robot drives all three wheels so that it rolls without slipping or sliding, according to the given ICC. Draw the path followed by each of the two wheels shown. Do not draw a path for the third wheel.
The wheels move along circular arcs centered at the ICC.