Lateral acceleration, yaw rate, speed and steer angle which can be acquired by ordinary sensors are used as inputs.
Measurement of angular velocity of the bicycle frame, acceleration of three points fixed to the frame, steer angle, and wheel spin rates is implemented.
The observer design is based on the well-known Immerse and Invariance (I&I) technique to estimate the lateral velocity, roll angle and roll velocity of the vehicle from the measurements of the longitudinal/lateral accelerations, longitudinal velocity, yaw rate and steer angle.
In this idealized and linearized model, there are many geometric parameters (wheelbase, head angle, mass of each body, wheel radius, etc)., but only four significant variables: lean angle, lean rate, steer angle, and steer rate.
It is possible to calculate eigenvalues, one for each of the four state variables (lean angle, lean rate, steer angle, and steer rate), from the linearized equations in order to analyze the normal modes and self-stability of a particular bike design.
The integration of drive wheel speeds and steer angles of non-driven wheels maximises tractive effort and minimises scuffing losses.
On the basis of prior work, a linear controller design is used to control the front steer angle and the resulting steering control loop behaviour is explicitly considered in the prediction model of the outer MPC.
The roll steer is defined as undesirable and uncontrollable changes in the steering angle of the steered wheels during the rolling action of the vehicle body due to cornering maneuver or asymmetric bumps.
The resulting radius can be roughly approximated (within 2% of exact value) by: :r = \frac{w\cos \left (\theta \right )}{\delta \cos \left (\phi \right )} where r is the approximate radius, w is the wheelbase, θ is the lean angle, δ is the steer angle, and φ is the caster angle of the steering axis.
