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2017 | OriginalPaper | Chapter

2. Robust Shared-Control for Rear-Wheel Drive Cars

Authors : Jingjing Jiang, Alessandro Astolfi

Published in: Trends in Control and Decision-Making for Human–Robot Collaboration Systems

Publisher: Springer International Publishing

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Abstract

The chapter studies the shared-control problem for the kinematic model of a group of rear-wheel drive cars in a static (i.e., time-invariant) and in a dynamic (i.e., time-varying) environment. The design of the shared controller is based on either absolute positions or “correlated positions”, such as distances to the obstacles and angle differences. The shared control is used to guarantee the safety of the car when the driver behaves dangerously. Formal properties of the closed-loop-system with shared control are established by a Lyapunov-like analysis. We also consider uncertainties in the dynamics and prove that the shared controller is able to help the driver drive the car safely in the presence of bounded disturbances. Finally, the effectiveness of the controller is verified by typical case studies, such as turning, overtaking, and emergency braking, through MATLAB simulations.

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Footnotes
1
We use (x(t), y(t)) to denote the Cartesian coordinates of the center of the rear-axle at the time instant t. The admissible Cartesian configuration set \(\mathcal{P}_a(t)\) is such that
$$ (x(t),y(t))\in \mathcal{P}_a(t), \text { for all } t\ge 0. $$
.
 
2
For each human input \(v_h\) and heading angle \(\theta \), the \(i^\mathrm{th}\) constraint is active at position p if there exists a positive \(\eta \) such that \(s_i\left( p+\eta \left[ \begin{array}{c}v_h\cos \theta \\ v_h\sin \theta \end{array}\right] \right) +t_i=0\). As a results, the constraint is said to be “active” if the car is moving towards the constraint.
 
3
The definition of the function \(\mathrm{atg}(\cdot )\), given in [8], is close to that of the standard four quadrant arctan function except that its range equals to \((-\infty ,+\infty )\) rather than \([-\pi , \pi )\). In addition, it is a smooth function with values in the range \((-\infty ,+\infty )\). Therefore \(\dot{\theta }_r^i\) always exist, which is a necessary condition for calculating \(\dot{L}^i\), where \(L^i\) is given by (2.9).
 
4
The notation \(S^i\mathcal{P}_a+T^i\) with \(S^i\in \mathbb {R}^{2\times 2}, \mathcal{P}_a\in \mathbb {R}^2\) and \(T^i\in \mathbb {R}^2\), denotes the set defined by
$$ \{x\in \mathbb {R}^2|x=S^iy+T^i, y\in \mathcal{P}_a\}. $$
.
 
5
Recall that the definition of the function atg(\(\cdot \)) is given in [8].
 
6
Note that this is a Lyapunov function only for the \(\phi \) system.
 
7
Recall that the definition of the function atg(\(\cdot \)) is given in [8].
 
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Metadata
Title
Robust Shared-Control for Rear-Wheel Drive Cars
Authors
Jingjing Jiang
Alessandro Astolfi
Copyright Year
2017
Book
Trends in Control and Decision-Making for Human–Robot Collaboration Systems

Print ISBN: 978-3-319-40532-2

Electronic ISBN: 978-3-319-40533-9

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-40533-9_2