What trajectory does the bicycle follow if we provide the following control inputs: 𝑣=1.5v=1.5, 𝛿=0.2δ=0.2?

The trajectory of the bicycle can be determined by the speed (v) and the steering angle (δ). In this case, the speed is 1.5 m/s and the steering angle is 0.2 rad.

1. First, we need to understand that the bicycle model is a simplified version of the dynamics of a car. It assumes that the bicycle moves in a plane and that the front and rear wheels are aligned.

2. The speed (v) determines how fast the bicycle is moving. In this case, the bicycle is moving at a speed of 1.5 m/s.

3. The steering angle (δ) determines the direction of the bicycle. A positive steering angle means the bicycle is turning to the left, while a negative steering angle means the bicycle is turning to the right. In this case, the bicycle is turning to the left with a steering angle of 0.2 rad.

4. The trajectory of the bicycle can be calculated by integrating the speed and steering angle over time. This will give us the path of the bicycle in the plane.

5. Given the constant speed and steering angle, the bicycle will follow a circular path with a radius determined by the ratio of the speed to the steering angle.

6. Therefore, with a speed of 1.5 m/s and a steering angle of 0.2 rad, the bicycle will follow a circular path to the left with a radius of 1.5/0.2 = 7.5 m.