Based on the control theoryof feedback linearization, the zero dynamics equation for a planar3R
rigid redundant robotwas derived. Using Poincare maps and Lyapunov exponents, the motion state(regular
or chaotic motion) of the redundant robotwas numerically simulated, and the relationship between its self-
motion state and its vectors in the null space was obtained. The research result shows that the chaotic self-
motion of a redundant robot is influenced by the initial conditions and has a direct relationwith its victors in
the null space.