Invariant feedback control for the kinematic car on the sphere

The design of an invariant tracking control law for the kinematic car driving on a sphere is discussed. Using a Lie group framework a left-invariant description on SO ( 3 ) is derived. Basic geometric considerations allow a direct comparison of the model with the planar case. Using a geometrically motivated invariant tracking error on S 2 an invariant feedback design is proposed. Finally, one possible design of an invariant asymptotic observer is sketched.