Steering control of nonholonomic control systems using model decomposition: A fire truck example

This paper presents a simple feedback control strategy for steering the nonholonomic control systems based on the construction of a cost function V which is the sum of two semi-positive definite functions V₁ and V₂. These semi-positive definite functions are obtained by decomposing the system into two subsystems. The task of the control strategy is to decay the non-differentiable cost function V along the controlled system trajectories in an average sense by first decaying the function V₁ using the trajectory interception approach and then decaying the function V₂ by using sinusoidal inputs. The individual functions are hence not restricted to decrease monotonically but their oscillations are limited and coordinated in a way to guarantee convergence. The effectiveness of the strategy is tested on a fire truck model which is a typical example of nonholonomic control systems. This approach does not necessitate the conversion of the system model into a ldquochained formrdquo, and thus does not rely on any special transformation techniques. The approach presented is general and can be employed to control a variety of mechanical systems with velocity constraints.