Roll Angle Estimation of a Motorcycle through Inertial Measurements

Abstract

Currently, the interest in creating autonomous driving vehicles and progressively more sophisticated active safety systems is growing enormously, being a prevailing importance factor for the end user when choosing between either one or another commercial vehicle model. While four-wheelers are ahead in the adoption of these systems, the development for two-wheelers is beginning to gain importance within the sector. This makes sense, since the vulnerability for the driver is much higher in these vehicles compared to traditional four-wheelers. The particular dynamics and stability that govern the behavior of single-track vehicles (STVs) make the task of designing active control systems, such as Anti-lock Braking System (ABS) systems or active or semi-active suspension systems, particularly challenging. The roll angle can achieve high values, which greatly affects the general behavior of the vehicle. Therefore, it is a magnitude of the utmost importance; however, its accurate measurement or estimation is far from trivial. This work is based on a previous paper, in which a roll angle estimator based on the Kalman filter was presented and tested on an instrumented bicycle. In this work, a further refinement of the method is proposed, and it is tested in more challenging situations using the multibody model of a motorcycle. Moreover, an extension of the method is also presented to improve the way noise is modeled within this Kalman filter.

Keywords: Kalman filter; LQR controller; inertial sensors; motorcycle lean angle; roll angle estimator.

Figure 1

Multibody model elements and DOFs.

Figure 2

Longitudinal an lateral deflections in a toroidal tire due to tangential forces.

Figure 3

Multibody model transform to Whipple’s model.

Figure 4

Inside, neutral, and outside configurations in a torso controller.

Figure 5

IMU position adjust.

Figure 6

Scenarios created to test the estimator behavior.

Figure 7

Shape of the weight function used to combine the two estimated measurements of the roll angle.

Figure 8

Estimated roll angle and roll angle error for the six different scenarios. All of these tests were performed with the rider in a neutral position. The reference is the black solid line, the red dash dotted line is the Kalman filter as presented in [11], the green dotted line is the variation of that Kalman filter presented here, and the blue dashed line represents the Kalman filter adapted for colored noise.

Figure 9

Estimated roll angle and roll angle error for the Circular test track. The left plot represents the maneuver with the rider in a neutral position, the central plot represents the rider tilting inwards during the turn, and the right plot represents the rider tilting outwards during the turn.