Feasibility and performance analyses for an active geometry control suspension system for over-actuated vehicles

Abstract

To build an over-actuated vehicle, the chosen equipment is composed of an active four-wheel drive and steering systems, a torque vectoring system, and an active braking system. In general, the goal of the over-actuated vehicle is to improve stability and handling performance for both conventional and autonomous vehicles. This paper presents an active geometry control suspension system (AGVS), based on a 3-DOF parallel mechanism, which is capable of acting simultaneously on the camber, the rear-wheel steering and the body roll angles. The aim of this study is to analyse the performance and feasibility of this active suspension mechanism when assembled in a C-class vehicle. These analyses were developed through a co-simulation scheme implemented in CarSim and Simulink software for three different manoeuvres: steady-state cornering, fishhook and double lane change. The performance analysis provides a comparison of the same C-class vehicle equipped with different systems, from the original to the fully actuated one. The conducted simulations reveal how superior a multi-purpose control system is when compared to the other single-actuated systems, and how it can manage the necessary trade-off among the selected metrics, namely, the roll gradient, the understeer gradient, the yaw rate, the body roll angle, and the lateral acceleration. In the feasibility analysis of AVGS the demanded actuator power and force in typical manoeuvres was assessed. In addition, the required ranges for the camber and rear-wheel steering actuations, as well as for the mechanism joints, were determined. The vehicle equipped with AGVS demonstrates improvements of dynamic behaviour in both steady-state and transient manoeuvres.

Appendix

• Mechanism parameters

The mechanism parameters employed in the simulations are listed in Table 9, which are shown in Fig. 4.

Table 9 Mechanism parameters (i = 1,2,3)

• Inverse kinematic model

Three reference systems were applied to develop the kinematic model for the suspension mechanism: the fixed frame ${\text{Ox}}_{0}{{\text{y}}}_{0}{{\text{z}}}_{0}$ (Fig. 14a, b), the first moving frame ${\text{Ox}}_{1}{{\text{y}}}_{1}{{\text{z}}}_{1}$ (Figs. 14a–c and 15a, b), which is attached to the car body, and the second moving frame ${{\text{A}}_{1}{\text{x}}}_{2}{{\text{y}}}_{2}{{\text{z}}}_{2}$ (Fig. 15a, b), which is attached to the end-effector. The actuators 1 and 2, and the bars 1 and 2 are in the Oy₀z₀ plane.

The goal of the inverse kinematic model is to obtain a mathematical transformation between the end-effector location, defined by the vector $\chi = [\Theta\ \Gamma\ \Psi ]^{{\text{T}}}$ (Fig. 15a, b), and the displacements provided by the actuators, defined by the vector ${\text{s}} \, \text{=} \, {\text{[}{\text{s}}_{1 }\ {\text{s}}_{2} \ {\text{s}}_{3}\text{]}}^{\text{T}}$ (Fig. 15a, b). Both vectors are defined in the moving frame ${\text{Ox}}_{1}{{\text{y}}}_{1}{{\text{z}}}_{1}$.

The relationship between the reference frames was obtained by applying homogeneous transformation matrix, as detailed in [40].

Fig. 14

Frames employed in the kinematic model: a the fixed frame and body roll angle ϕ; b the fixed frame (${\text{Ox}}_{0}{{\text{y}}}_{0}{{\text{z}}}_{0}$), the moving frames (${\text{Ox}}_{1}{{\text{y}}}_{1}{{\text{z}}}_{1}$ and ${{\text{A}}_{1}{\text{x}}}_{2}{{\text{y}}}_{2}{{\text{z}}}_{2}$) and the body roll angle ϕ; c mechanism parameters nomenclature employed in the kinematic model [40]

Fig. 15

Nomenclature for kinematic model and location of the A_i, B_i, C_i (i = 1, 2, 3) points: a front view; b top view [40]