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Chen et al. Complex Eng Syst 2023;3:8 I http://dx.doi.org/10.20517/ces.2022.50 Page 11 of 15

Table 2. Parameters of vehicle and in-wheel motors
Parameter Description Value/Unit Parameter Description Value/Unit
Vehicle mass 812 kg Wheelbase 1.65 m
Vehicle mass 20 kg Rated power 7.5 KW

Distance from mass center to front axle 1.1 m Peak power 12 KW

Distance from mass center to rear axle 1.25 m Rated speed 750 rpm

Moment of vehicle inertia around Z axis 808 kg ·m 2 Peak speed 1,000 rpm

Moment of tire inertia around rotation axis 0.5 kg ·m 2 Rated torque 150 Nm

ℎ Distance between roll center and center of sprung mass 0.27 m Peak torque 250 Nm
Distance between roll center and center of sprung mass 0.29 m

4. TORQUE ALLOCATION ALGORITHM
The proposed torque allocation algorithm based on the equal adhesion rate rule is described in this section.
We adopt the equal adhesion rate rule by considering only the adhesion rate of longitudinal force because the
deviations due to the lateral and longitudinal forces are excessive, meaning that no solution can be obtained.
Therefore, the longitudinal forces on the left and right sides of the vehicle are expressed as follows.

/ = | | /
(30)

/ = | | /
The total longitudinal forces on the left and right sides of the vehicle can be calculated as follows:

+ = /2 + Δ /
(31)
+ = /2 − Δ /

Therefore, each longitudinal tire force can be solved quickly by using Eqs. (30) and (31). By using the solved
longitudinal tire force and algorithm of equal-adhesion-rate-rule, the torque acting on each wheel can be
determined as follows.

 = / + + +



 
= / + + +
(32)
 = ( ) / + + +



 = ( ) / + + +
5. CO-SIMULATION AND RESULTS
To verify the proposed control algorithm, we compared it to the proportional-integral-derivative (PID) control
strategy. The co-simulation method was used for this purpose. Two main typical driving conditions, namely
1 ⃝ double lane change (DLC) maneuver under high-adhesion-coefficient condition ( = 0.9) and 2 ⃝ DLC
maneuver under low-adhesion-coefficient condition ( = 0.3), were considered. The parameters of the vehicle
and in-wheel motors are summarized in Table 2.

The consistency of human driving cannot be guaranteed, and it would be unsuitable for real drivers to drive a
vehicle at dangerously high speeds or on low-adhesion roads. For this reason, we conducted a simulation to
validate the effectiveness of the proposed control scheme.