Low-level Controllers

This article details the low-level controllers that run on the Chronos RC car.

Documentation index — full table of contents.

Steer Controller

The cars run a low-level controller to track the reference steer angle \(\delta_r\), which is received from CRS.

The car uses a steer map to convert the feedback voltage from a potentiometer to an estimate of the current steer angle \(\delta\). A PID controller then tries to drive the error \(e = \delta_r - \delta\) to zero.

The low-level controller runs with \(T_s = 4\,\mathrm{ms}\). Let \(k_p, k_i, k_d\) be the PID gains and \(T_f\) be the filter time for the derivative term. The PID controller is given by (where \(\alpha = \exp(-T_s/T_f)\))

\[ \begin{aligned} d_e[k] &= \alpha d_e[k-1] + (1-\alpha) \frac{e[k] - e[k-1]}{T_s},\\ i_e[k] &= i_e[k-1] + e[k] T_s,\\ u[k] &= k_p e[k] + k_i i_e[k] + k_d d_e[k]. \end{aligned} \]

Tuning: The gains \(k_p, k_i, k_d\) can be adjusted in the configuration interface.
Note: Since the sample time is small, the derivative gain can be quite sensitive to noise. Keep the gain "small".

Throttle Controller

The reference throttle does not require a controller, as it is applied directly to the motor. An input in the range \([0, 1]\) is mapped to a PWM duty cycle in the range \([0\%, 100\%]\), which corresponds to a steady-state voltage of \([0\,\mathrm{V}, 5\,\mathrm{V}]\) on the throttle actuator.

Auto-coasting

Two motor driver chips manage the current on the actuators. They offer two different styles of PWM actuation: fast and slow decay. For a more linear response, slow decay is beneficial---during the off time of the PWM signal, the current decays more slowly. Fast decay has a less linear response but will improve coasting behavior of the motor.

The auto-coasting function of the car will automatically switch from the default (slow) decay to fast decay when the input is falling fast enough. In particular, it will coast whenever

\[ \vert \Delta u \vert = \vert u - u_\text{prev} \vert \geq \Delta_\text{thresh} \land u\cdot(u - u_\text{prev}) < 0. \]

The threshold \(\Delta_\text{thresh}\) is in units of [1] and adjustable in the configuration interface

Speed Controller

If the car is equipped with wheel encoders, another low-level controller can be used to track a reference longitudinal velocity \(v_{x,r}\). Here, the feedback is the measured longitudinal velocity from the rear wheel encoders, \(v_x = (\Omega_{rl} + \Omega_{rr}) / 2 \cdot r_w\). The controller is a simple PID, analogous to the steer controller.

Tuning: The gains \(k_p, k_i, k_d\) can be adjusted in the configuration interface.

When is the Speed Controller used?

The speed controller is used when CRS sends a reference velocity instead of a throttle value. This is controlled by setting either the throttle or velocity field in the /control_input message. The car will then use the throttle controller if throttle is set, and the speed controller if velocity is set.