Time Traces — Simulation Results
The following time traces show simulation results of the global chassis control for the ISO 7975 maneuver — braking in a curve — with the ROboMObil in closed-loop operation. The vehicle first drives straight ahead, steers into a circular path, and is then braked while cornering. The simulation uses a detailed multi-body model of the ROMO as the controlled plant, which differs structurally and parametrically from the GCC's design model.
Longitudinal and Lateral Acceleration
Setpoint and actual lateral and longitudinal acceleration for the driven variant of the ISO 7975 maneuver. The maneuver is performed in closed-loop operation with the acceleration profile shown here as the setpoint. The GCC follows the setpoint precisely — the actual traces (red dashed) nearly perfectly match the setpoint traces (black).
Jerk Demand
Jerk demand presented to the inverse model over the driving maneuver. The traces are not smooth because the outer control loop compensates inversion errors through an additionally commanded jerk. The translational jerk demand shows the longitudinal and lateral components, the rotational one shows the yaw jerk.
Yaw Rate and Sideslip Angle
Yaw rate and sideslip angle over the ISO 7975 maneuver. By commanding a suitable yaw rate, a sideslip angle trajectory is achieved that stays close to the reference β_ref = 0. The brief sideslip angle peak during turn-in decays rapidly.
Tire Forces
The eight planar tire forces, represented in the respective tire coordinate system. The tire longitudinal forces build up according to the commanded torques. The tire lateral forces differ between axles despite nearly identical angles, because the wheel loads differ between axles. While the vehicle drives straight, axle-wise opposing tire lateral forces exist — this is due to the set toe angle.
Tire Force Utilization
Tire force utilization ratios, comparison with the theoretical optimum, and the four wheel loads for the ISO 7975 maneuver with the ROboMObil in closed-loop operation. The four tire force utilization ratios are approximately equal. Since the tire force time traces show that tire forces during cornering do not cancel each other's effect on vehicle acceleration, this means: the total tire force potential is utilized close to the theoretical optimum.
Actuator Variables
Drive and braking torques, steering angles, and wheel angular velocities for the ISO 7975 maneuver with the ROboMObil. The actuator variables û = (τ^T, δ̇^T) are commanded by the controller. They act directly on the state variables of wheel angular velocities ω and steering angles δ.
Road Torques and Estimation Error
Torques supported on the road surface τ_road and the absolute error between these actual and the corresponding estimated torques. The torques τ_road qualitatively correspond to the commanded torques with negative sign. However, they are smaller because part of the torques accelerates the wheels in their rotation. Thus, this portion is not supported on the road surface.