Small radius attainability spheres for driftless nonholonomic systems

In this paper a constructive and analytic method is presented to obtain small radius attainability spheres for driftless nonholonomic systems. Sinusoidal controls generating points on spheres are derived from the generalized Campbell-Baker-Hausdorff-Dynkin formula. Nonholonomic spheres are constructed in Hall coordinate frame, thus they are independent of a particular nonholonomic system. Attainability spheres for two-input driftless systems with a three dimensional state space as well as geodesic curves are provided. The usefulness of construction of nonholonomic spheres in nonholonomic motion planning is highlighted.