Research on Torque Optimization Allocation Strategy About Multi-wheel Vehicles

Abstract

Multi-wheel vehicles are extensively used in military, agricultural machinery, and construction machinery. Since multi-wheel vehicle is one type of over-actuated systems, it is required that the kinematics and dynamics of all wheels have to be coordinately controlled. Therefore, the coordinated wheel torque control is the key factor. In this paper, the torque optimization allocation strategy of multi-wheel skid steering vehicle with independent in-wheel motors has been studied based on its dynamic model. The dynamic rule based on wheel torque distribution method has been studied in this paper, as well as optimal torque allocation method based on control allocation. Weighting control allocation error and control energy as the optimization target, wheel torque control allocation problem can be solved mathematically using quadratic programming method. Integrating with wheel slip control and actuator fault redundancy control schemes, the optimization algorithm is correspondingly designed, which improved the dynamic performance and safety of steering vehicle. The effectiveness of wheel torque distribution strategy was validated using Matlab/Simulink software and the simulation platform of the multi-wheel vehicle, and the simulation results show that the wheel torque, when a wheel motor fails, can be redistributed among the effective motors.

Symbol Table

Symbol	Unit	Meaning
B		Control efficiency matrix, $B \in R^{m \times p}$
c		Linear parts of the cost function
$c_{s}$		Damping coefficient of the absorber
$F_{si}$	N	Force of the damper
$F_{txi}$	N	Driving force of the wheel
$F_{fi}$	N	Rolling resistance
$F_{zi}$	N	Vertical force of the wheel
$fault_{i}$		Actuator fault status indicator, 0 stands for “no fault”, 1 stands for “faulty”
$I_{z}$	kg m2	Moment of inertia of the trailing arm
$i_{w}$		Transmission ratio from motor to the wheel
$J(u)$		Cost function
$k_{s}$		Stiffness coefficient of the absorber
$\Delta l_{s}$	m	Moving stroke of the absorber
$l_{s0}$	m	Free installation length of the absorber
$l_{si1}$	m	Length of the absorber under static condition of the vehicle
$l_{rf} ,l_{rm} ,l_{rr}$	m	Distance from the center of gravity of the vehicle body to the front axle, middle axle, and rear axle of the vehicle in the x-y plane
$l_{sf} ,l_{sm} ,l_{sr}$	m	Distance from the center of gravity to the front axle, the countershaft and the rear axle damper to the hinge of the vehicle body along the x axis direction in the x-y plane
$M_{ti}$	Nm	Self-aligning torque of the tire
$P_{e\hbox{max} }$	kW	Motor maximum output power
Q		Weight coefficients of the quadratic
R	m	Radius of curvature of the steering path
$\ddot{r}_{i}$		Linear acceleration vector of the rotation center of the trailing arm
$\ddot{r}_{ri}$		Linear acceleration vectors of the trailing arm
$\ddot{r}_{ti}$		Linear acceleration vectors of the wheel
$T_{i\hbox{max} }$	N/m	Motor maximum output torque
$u$		Actuator output vector
$u_{i}$		Control output
$u_{0}$		Ideal actuator input
$\Delta u$		Actual control input increment, $\Delta u = u - u_{0}$
$u_{des}$		Ideal control input vector
$u_{\phi }$		Adhesion coefficient between the tire and the ground
$u_{\hbox{min} } ,u_{\hbox{max} }$		Lower bounds and upper bounds of actuator vector constraints
$\dot{u}_{\hbox{min} } ,\dot{u}_{\hbox{max} }$		Lower bounds and upper bounds of actuator vector change rate constraints
$v$	m/s	Relative speed of the piston rod and cylinder body of the absorber
$V_{d}$		Ideal control input vector
$W_{u}$		Weight values of the priority of the actuator
$W_{v}$		Weight values of the control input diagonal matrix
$W_{d}$		Weight diagonal matrix that characterizes the utilization of the actuator
$\dot{\omega }_{rxi} ,\dot{\omega }_{ryi} ,\dot{\omega }_{rzi}$	rad/s	Angular velocity vector of ith trailing arm relative to the body hinge
$\ddot{\omega }_{rxi} ,\ddot{\omega }_{ryi} ,\ddot{\omega }_{rzi}$	rad/s2	Angular acceleration vector of ith trailing arm relative to the body hinge
$\ddot{\omega }_{cg}$	rad/s2	Angular acceleration vector at the center of mass of the vehicle
$\varphi ,\theta ,\omega$	rad	Vehicle’s roll angle, pitch angle, and yaw angle
$\theta_{ri0}$	rad	Vertical arm swing angle under static load
$\gamma$		Weighting factor for balancing the different optimization targets
$\gamma_{i}$		Weight factor of the optimization target, $0 < \gamma_{i} < 1$
$\mu_{\phi }$		Adhesion coefficient of the tire and the ground