Closed-loop form quantization algorithm with bounded accumulative error

Abstract

This paper proposes a closed-loop form quantization algorithm that guarantees the boundness of accumulative error. The algorithm is particularly useful for mobile robot navigation that is usually implemented on embedded systems. If the wheel command of the mobile robot is given by velocity or positional increments at every control instant that are quantized due to the finite word length of the controller's CPU, the quantization error accumulates to produce large position error. Such an error is critical for wheeled mobile robots or autonomous vehicles with non-holonomic constraints. To solve this problem, a non-error accumulative quantization algorithm with a closedloop form is presented. We can extend it to a generalized form corresponding to the nth-order accumulation. The boundness of the accumulative quantization error is proven via mathematic processes and verified by a series of computer simulations. The proposed method is effective to accurately control the autonomous mobile robot, particularly with embedded systems.