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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.