Lowest-order rate control of mechanisms near singularities

Resolved motion rate control, which uses a linear approximation to the kinematic function to find joint velocities, can fail at kinematic singularities. Pohl and Lipkin (1991) proposed rate control using a quadratic approximation to the full kinematic function, but this algorithm has disadvantages. Here we propose a hybrid algorithm that works at singularities, is computationally efficient, and finds all physically meaningful solution trajectories. Furthermore, it is shown that this algorithm finds smoother solutions than, the damped least squares algorithm for paths passing through singular points.