Estimation of the Speed From the Odometer Readings Using Optimized Curve-Fitting Filter

What is it about?

Odometry is one of the most-used techniques used in mobile robotics and autonomous vehicles, especially when indoor navigation is required or when a robot or vehicle moves inside the tunnel. The output of the odometer is usually a count of pulses corresponding to the distance run by the given wheel. Due to the quantization noise, estimation of the velocity (first derivative of the distance) is challenging. This article is focused on the curve-fitting filter used for the speed estimation and optimization of its parameters, considering the physical constraints of the robot, the sampling frequency of the system, and the quantization step. The paper proposes an empirical formula for estimating the optimal parameters of the curve fitting filter. The optimized filter has been evaluated using both simulation and real experiments and compared with several standard differentiation methods.

Featured Image

Photo by Scott Rodgerson on Unsplash

Photo by Scott Rodgerson on Unsplash

Why is it important?

The main contribution of this article is the formula that computes the optimal order of the well-known curve-fitting filter from the sampling frequency, quantization step, and the maximal rate of the acceleration of an odometrical system. The formula is empirical, obtained by multi-parametric simulation. The optimal order of the curve is 2; the fitting curve is quadratic. Experiments with real odometer signal showed, that the curve-fitting filter has similar precision to the extended backward Euler differentiation, but it has a smaller delay. Other types of discrete differentiators are significantly worse because the more the differentiator matches the ideal (continuous) differentiator, the more it amplifies the quantization noise of the odometer.

Perspectives