Control of nonholonomic systems via direct gradient descent control -variable constraint control based approach

This work is concerned with control of nonholonomic systems. As is well known, symmetric affine system is uncontrollable with continuously differentiable state feedback control. But variable constraint control was proposed for the symmetric affine system as a two-stage control method that makes use of an invariant manifold. In this paper we apply the direct gradient descent control (DGDC) of two-stage type for the symmetric affine system, based on the variable constraint control approach, where the control law is switched from the first stage to the second one. DGDC is such a method that manipulates control inputs directly so as to decrease a performance function by the steepest descent method. Applying the DGDC, we can control the symmetric affine system without transforming into the "chained form". Simulation results for a two-wheeled vehicle and a flying robot demonstrate the effectiveness of the proposed method.