Steering Adjustment Using PID

Overview

In autonomous wall following, maintaining a consistent distance from the wall requires smooth and responsive steering control. Instead of using simple proportional control that can cause oscillations, a Proportional-Integral-Derivative (PID) controller provides precise steering adjustments based on distance error and its rate of change.

This approach ensures stable wall tracking with minimal oscillations, improving both navigation accuracy and vehicle stability.

1️⃣ Why Use PID Control for Steering?

Simple proportional control (steering angle = K × error) may cause:

  • Oscillations, where the car weaves back and forth along the wall.

  • Overshooting, where corrections are too aggressive.

  • Steady-state error, where the car never quite reaches the desired distance.

  • Poor response to curves, causing the car to hit walls on turns.

A PID controller provides:

✅ Smooth steering adjustments based on distance error.

✅ Predictive control, adjusting before the car drifts too far.

✅ Elimination of steady-state error through integral action.

✅ Stable tracking, minimizing oscillations and overshooting.

2️⃣ PID Control Formula for Steering Adjustment

The error is defined as the difference between desired and actual distance to the wall:

\[e(t) = D_{\text{desired}} - D_{\text{actual}}\]

The steering angle output is calculated using:

\[\theta = K_p e(t) + K_i \int e(t) dt + K_d \frac{de(t)}{dt}\]

Where:

  • \(\theta\) = Steering angle (positive = turn away from wall, negative = turn toward wall).

  • \(K_p\) = Proportional gain (reacts to the distance error).

  • \(K_i\) = Integral gain (corrects accumulated distance errors).

  • \(K_d\) = Derivative gain (predicts future distance changes).

  • \(e(t)\) = Distance error.

3️⃣ How Each Term Contributes

Proportional Term (P)

The proportional term provides immediate response to distance error:

If car is too close to wall → Steer away from wall proportionally.

If car is too far from wall → Steer toward wall proportionally.

If car is at desired distance → No steering correction needed.

Integral Term (I)

The integral term eliminates steady-state error by accumulating past errors:

Persistent error on one side → Gradually increase steering to correct.

Helps maintain exact desired distance over long periods.

Prevents drift on straight walls.

Derivative Term (D)

The derivative term predicts future errors by monitoring rate of change:

If drifting away from wall rapidly → Steer aggressively toward wall.

If approaching wall rapidly → Steer aggressively away from wall.

If distance is stable → Minimal derivative correction (avoid jittery steering).

Reduces overshoot and dampens oscillations.

4️⃣ Example: PID-Based Steering Control

Scenario: Maintaining Distance While Wall Following

  • Desired Distance = 0.5 meters

  • Actual Distance = 0.7 meters (too far from wall)

  • Proportional Gain = \(K_p\) = 1.5

  • Integral Gain = \(K_i\) = 0.05

  • Derivative Gain = \(K_d\) = 0.8

  • Distance is increasing at 0.1 m/s (drifting away)

Step 1: Compute the Error

\[e(t) = 0.5 - 0.7 = -0.2 \text{ meters}\]

(Negative error means too far from wall)

Step 2: Compute Steering Angle

\[\theta = (1.5 \times -0.2) + (0.05 \times \int -0.2 dt) + (0.8 \times -0.1)\]

If the accumulated integral error over time is -1.0, then:

\[\theta = (1.5 \times -0.2) + (0.05 \times -1.0) + (0.8 \times -0.1)\]
\[\theta = -0.3 + (-0.05) + (-0.08) = -0.43 \text{ radians}\]

Thus, the vehicle will steer toward the wall by 0.43 radians (≈ 24.6°), bringing it back to the desired distance.

5️⃣ Handling Curves and Corners

Wall following becomes challenging in curves. The lookahead distance \(D_{t+1}\) helps predict future distance:

\[D_{t+1} = D_t + L\sin(\alpha)\]

Where:

  • \(D_t\) = Current distance to wall

  • \(L\) = Lookahead distance (typically 1-2 meters)

  • \(\alpha\) = Angle between car’s heading and wall

Using \(D_{t+1}\) instead of \(D_t\) in the PID error calculation allows:

✅ Early correction before entering a curve.

✅ Smoother navigation through corners.

✅ Prevention of wall collisions on tight turns.

6️⃣ Considerations & Tuning

🛠 Tuning Kp (Proportional Gain)

  • Kp too high → Aggressive steering, oscillations, instability.

  • Kp too low → Slow response, poor tracking, drifts off course.

  • Start with: \(K_p\) = 1.0 to 2.0

🛠 Tuning Ki (Integral Gain)

  • Ki too high → Overshoot, slow settling time.

  • Ki too low → Steady-state error remains.

  • Start with: \(K_i\) = 0.01 to 0.1

🛠 Tuning Kd (Derivative Gain)

  • Kd too high → Sensitive to noise, jittery steering.

  • Kd too low → Overshooting, slow damping.

  • Start with: \(K_d\) = 0.5 to 1.0

🚗 Tuning Strategy

  1. Set \(K_i = 0\) and \(K_d = 0\), tune \(K_p\) until response is reasonable but oscillatory.

  2. Add \(K_d\) to dampen oscillations and improve stability.

  3. Add \(K_i\) to eliminate steady-state error if car consistently stays too close or too far.

  4. Test on curves and adjust gains for smooth corner navigation.

7️⃣ Integrating Speed Control

For optimal performance, adjust speed based on steering angle:

if abs(steering_angle) < 0.174:  # < 10 degrees
    speed = 1.5  # m/s (straight sections)
elif abs(steering_angle) < 0.349:  # < 20 degrees
    speed = 1.0  # m/s (gentle curves)
else:
    speed = 0.5  # m/s (sharp turns)

This prevents:

  • Loss of control in sharp turns at high speed.

  • Wall collisions when steering aggressively.

  • Inefficient slow driving on straight sections.

8️⃣ Summary

✅ PID steering control provides smooth and stable wall following.

✅ The derivative term predicts and prevents oscillations.

✅ The integral term eliminates steady-state distance errors.

✅ Lookahead distance helps navigate curves safely.

✅ Speed adjustment based on steering angle improves safety.