This paper introduces a channel algorithm of transversal passing through singularities for non-redundant manipulators. An approach to a singular configuration is monitored by examining singular values of the Jacobian matrix of the manipulator which attain their zero values at singularities. The algorithm forces to smoothly change singular values of the Jacobian matrix. It results in continuous joint coordinates without jerks and extensive errors in tracking a desired path in a task space. An apparent advantage of the channel algorithm is its simplicity and utilization of a basic Newton algorithm only. The algorithm introduced is illustrated with examples including macro motions of the PUMA manipulator.

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.

A computationally effective method is presented able to generate controls steering a driftless nonholonomic system in a desired direction. By using the Campbell-Baker-Hausdorff-Dynkin formula piecewise constant controls are obtained that realize the desired motion. Then, the controls are expanded into the Fourier series with filtered out higher frequencies. Resulting continuous controls are applied to a driftless nonholonomic system in order to identify a linear combination of Ph. Hall basis elements corresponding to the controls. This approach allows us to generate a desired vector field of the lowest degree keeping at the same time under control the influence of higher degree vector fields.