Chassis System Evaluation Using Force and Moment Allocation

Active Chassis Systems

In a conventional vehicle, the driver controls the trajectory of the vehicle by performing functions like steering, acceleration and braking. These actions generate necessary tire traction forces and moments at the tire road interaction to modify the path of the vehicle.

However what if there is a system where these tire traction forces/moments can be controlled independently. Active Chassis Systems use actuators to modify individual tire traction forces which can bring a lot of opportunities as well as challenges.It increases the degree of mobility. If the rear wheels were allowed to steer, parking maneuvers would be enhanced at low speeds. It also helps in better disturbance handling like crash avoidance and post impact when the driver’s control ability is affected. However, there are only 4 tyres in a car and therefore, eventually, extra actuation or control systems will overlap with each other.

A certain Active Chassis System is described here which can distribute the tire forces optimally using active torque vectoring (traction or braking at each wheel)as well as independent four-wheel-steering to make the best use of available friction. It is an ideal chassis which is then used as an evaluation tool for comparing passive chassis systems. For this study, I used Carsim ( ) for Vehicle Dynamics Simulation and Matlab for optimization.

Control Scheme

Tire Force Redistribution

I used a low Center of Gravity vehicle model to maintain the 3DOF assumption . A standard double-lane-change maneuver is taken to perform the run and conduct performance analysis. Global vehicle forces and moments, as well as vertical tire forces, are determined from the baseline run (assuming a passive chassis system). These global forces are then used as input to an optimal force allocation algorithm; this makes use of the vehicle geometry and fixed vertical loads, but redistributes the in-plane forces base on a cost function with friction constraints. The aim was to equalize tire forces across the chassis, reducing demands on any single tire. Once the individual required individual tire forces are known, an inverse tire model is used to evaluate the required actuator inputs: steering angle and braking/driving torques.


Vehicle Forces

Two cost functions were used: one with position control and one without. The position control only cost function was not giving good results in cases where the vehicle somehow ends up away from the desired path.

Design Variables: Individual 2D tire forces. Here fx, fy and fz refers to the tire forces

Cost Function 1: without position control

Cost Function 2: with position control

The constraints used in the optimization problem were the tire friction circle constraints.

Inverse Tire Modeling

Generally a tire model gives the tire lateral and longitudinal forces based on the given values of tire slip ratio and slip angle. In the inverse tire model these slip values are estimated with the help of known tire forces. A lookup table approach is used :

–For a number of vertical loads, a full 2D sweep of slip ratio and slip angle is performed

–Interpolation is applied to these data to determine an inversion map with a uniform grid in the 2D space of forces

Tire inversion is complex because of the nature of the inversion (i.e. more than one set of slip values can generate the same force vector). To address indeterminacy, the smallest longitudinal slip vector is used.

Now that we have tire slips, steering angles are calculated using change of frame from tire to local vehicle and an advanced sweep algorithm. The steer angle increment in the algorithm is chosen to be small enough to minimize chatter in the force outputs while maintaining small errors in slip angle. Similarly in the case of torque actuators, longitudinal slip is converted into torque while taking into account the limitations of actuators. Rolling resistance is neglected.

Performance Evaluation

A standard double lane change maneuver is first completed with passive chassis model and then repeated with optimal allocation of forces. The vehicle was able to replicate the desired path which validates the algorithm.

Vehicle trajectory

A tighter double lane change is then taken for limit handling evaluation. The optimized mu shows how the vehicle was able to complete the desired path with lower tire friction utilization.

four tires friction force utilization during limit handling

Having validated the overall procedure, a measure of passive chassis performance is formulated, based on its ability to cope with reductions in surface friction.The same maneuver is attempted as surface friction is varied, and the mean squared error of the displacement from the original path is calculated. The passive chassis configuration used a driver model. The “active chassis” uses the algorithm described

Comparison of Active and Passive Chassis

The comparison shows that this active chassis can be used as a general metric for the performance of the passive chassis. There is little difference until a certain value of friction. This can be used as a measure of objective performance of a passive chassis system.

This work was done at University of Michigan as part of my thesis in 2013

Written while listening to Seedhe Maut

Vehicle Dynamics | Self Driving Cars | Comedy

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