Validating observer based on-line slip estimation for improved navigation by a mobile robot

Abstract

Wheel-slippage is a crucial but one of the marginally attended subjects regarding indoor navigation. Uncompensated slippage has the potential to introduce serious consequences in the form of safety-violation while manipulating obstacles and degraded performance when the vehicle is subjected to tracking and interception. This paper aims at establishing an alternative approach to dynamic modeling and robust control by proposing online estimation of slip parameters and modifying the kinematic model such that it is capable to accommodate slip-disturbance inputs. This approach works in a minimally invasive way, without interfering with or replacing the existing controller. The proposed approach has a low computational requirement and can be easily implemented without any major changes in the control architecture.

Appendix

1.1 Derivation of slip-ratio propagation model

Representing observed velocity by estimated velocity of the vehicle, ${\hat{v}}$, we can write:

$$\begin{aligned}&\sigma =\frac{|v_{encoder}(t)-{\hat{v}}(t)|}{\max \{v_{encoder}(t),{\hat{v}}(t)\}} \\&\left. \begin{aligned} {\dot{\sigma }}(t)= \frac{d}{dt}\Bigg (\frac{|v_{encoder}(t)-{\hat{v}}(t)|}{v_{encoder}(t)}\Bigg ) ~\text {if} (a)\\ =\frac{d}{dt}\Bigg (\frac{|v_{encoder}(t)-{\hat{v}}(t)|}{{\hat{v}}(t)}\Bigg ) ~\text {if} (b) \end{aligned}\right\} \\&\left. \begin{aligned} {\dot{\sigma }}(t)= \frac{-{\hat{v}}(t)}{v_{encoder}(t)}\frac{{\dot{v}}_{encoder}(t)}{v_{encoder}(t)}+ \frac{\dot{{\hat{v}}}(t)}{v_{encoder}(t)} ~\text {if} (a) \\ = \frac{v_{encoder}(t)}{{\hat{v}}(t)}\frac{\dot{{\hat{v}}}(t)}{{\hat{v}}(t)}- \frac{{\dot{v}}_{encoder}(t)}{{\hat{v}}(t)} ~\text {if} (b) \end{aligned}\right\} \\&\left. \begin{aligned} {\dot{\sigma }}(t)= (\sigma (t)-1)\Bigg ( \frac{{\dot{v}}_{encoder}(t)}{v_{encoder}(t)}-\frac{\dot{{\hat{v}}}(t)}{{\hat{v}}(t)}\Bigg ) ~\text {if} (a)\\ = (\sigma (t)+1)\Bigg (\frac{\dot{{\hat{v}}}(t)}{{\hat{v}}(t)} - \frac{{\dot{v}}_{encoder}(t)}{v_{encoder}(t)}\Bigg ) ~\text {if} (b) \end{aligned}\right\} \end{aligned}$$

where, $(a) : v_{encoder}(t)>{\hat{v}}(t)$ and $(b) : v_{encoder}(t)<{\hat{v}}(t)$.