A Vector Algebra Formulation of Kinematics of Wheeled Mobile Robots

Abstract

This document presents a straightforward yet general approach for solving problems in the kinematics of wheeled mobile robots. There are two problems. Control algorithms must translate the desired linear and angular velocity of the vehicle into the velocities and steer angles of the wheels. Conversely, estimation systems must do the reverse - compute the linear and angular velocity given the steer angles and wheel rotation rates. It turns out that the problem is very elegantly solved in the general case by appealing to the physics of rigid body motion, especially the instantaneous center of rotation, and the mathematics of moving coordinate systems. The presented approach is general enough to handle any number of driven and steered wheels in any configuration, and each wheel may be offset from its steering pivot point. Flat terrain is assumed in the examples but the underlying technique makes no such assumption. The solution also does not assume that all wheels are at the same elevation - they may articulate in arbitrary ways. While the examples assume that the booms connecting wheels to the body are fixed, the general formulation can easily incorporate knowledge of the steering rates. The formulation elegantly avoids the solution of nonlinear simultaneous equations by working, at times, in terms of the velocities of the wheel pivot points. In this way, the wheel steer angles are not expressed in terms of themselves in the actuated inverse solution. The approach is applied to several examples including differential steer, Ackerman steer, a generalized bicycle model, and the difficult case of 4 steered and driven wheels whose steer axes are offset from the wheel contact points.