Controllers

Intro

• The control algorithms on our bicycle are separated into three cascaded controllers. The output of one controller is input to another controller.
• In order from high level to low level:

1. Navigation controller, which tries to follow a desired path
2. Balance controller, which tries to achieve a desired lean angle (φ_d) and desired steer angle (δ_d). For straight line balance (no navigation), this controller attempts to achieve φ_d = 0 and δd = 0. In this position, the bicycle is balanced (upright and steered straight ahead).
3. Front motor controller, which controls front wheel angle (δ).

• Using cascaded controllers allows us to develop each controller semi-independently.

Front Motor Controller

• The front motor controller works to minimize the angle between the current steer angle (δ) and the commanded steer angle (δ_c).
• Currently (Spring 2018), the front motor controller is PD (Proportional-Derivative) controller. Specifically,

total_error = k_p(δ_c − δ) + k_d d/dt(δ_c − δ).

• total_error is converted into a direction (DIR) and a magnitude (motor_output).

Balance Controller

• The balance controller attempts to achieve a desired lean angle (φ_d) and steer angle (δ_d). In navigation mode, the navigation algorithm sets φ_d and δ_d. Without navigation (in balance only mode), φ_d = 0 and δ_d = 0.
• In addition to the desired state (φ_d, δ_d), the balance controller takes as input current lean angle (φ), lean angle rate (φ), and steer angle (δ). The balance controller outputs a steer angle rate (δ).
• Currently (Spring 2018), the balance controller is the linear controller:

̇δd' = kd(φ − φd) + k2φ'+ k3(δ − δd)

• For balance only, φ_d=0, δ_d=0. The balance controller reduces to:

̇ δ_d' = k₁φ + k₂φ' + k₃δ