Lately I've been discussing the topic of coding a good "turn" algorithm for FLL. In other words, how can you make the robot turn toward a desired heading in an accurate and efficient manner. I decided to pose the problem to ChatGPT to see what it comes up with.

Prompt 1:

Given a robotic vehicle with two wheels, I need equations that can be used to accomplish turning the robot a certain number of degrees by rotating the wheels different amounts. I have a gyro sensor to measure the robot heading.

Reddit doesn't handle the equations well, so I'm editing the response from ChatGPT just a bit, but here's what it came up with:

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Using a gyro sensor simplifies turning the robot to a specific angle because you can continuously monitor the robot's actual orientation during the turn and adjust the wheel speeds accordingly. Here's how you can do it:

1. Setup

• Gyro sensor: The sensor provides angular velocity (ω\omega) in degrees per second (or radians per second), which can be integrated over time to estimate the robot's heading (θ\theta).
• Desired Turn Angle (θ desired): The target angle you want the robot to turn.
• Control Strategy: Use feedback control to adjust the wheel speeds until the gyro reports the robot has reached θ desired.

2. Steps to Execute the Turn

a. Initial Setup

• Reset the gyro sensor to 0
• Determine the direction of the turn (clockwise or counterclockwise).

b. Feedback Loop

• Use the gyro's current heading to adjust the wheel speeds dynamically during the turn.
• Controller Logic:
  1. Compute the error: Error = θ desired − θ current
  2. Apply proportional control (or PID if necessary): Speed Difference = Kp⋅Error (Where Kp is the proportional gain. Larger errors lead to faster turns; smaller errors slow down the wheels to stop precisely.)

c. Wheel Speed Commands

• For a spin turn:
  • Left wheel: +S
  • Right wheel: -S, where S is the speed adjusted based on the feedback.
• For a pivot turn:
  • One wheel stops, and the other moves forward or backward at speed S.

3. Stopping Condition

• Continuously monitor the gyro's heading. When θ current ≈ θ desired (within a small tolerance), stop the wheels.

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Alright, that looks pretty good, but there are several problems which I then explained to ChatGPT.

Prompt 2:

There are several problems with that proposal.

1. Attempting to stop the turn when the robot's heading is within a desired tolerance of the target could easily cause the robot to dither back and forth around the target, constantly overshooting the desired tolerance in both directions. Modify the algorithm to stop as soon as the robot has surpassed the target heading rather than trying to correct for overshoot.

2. Using a proportional controller is a good idea to more accurately hit the target heading, but the initial error will be very large which will cause a large jerk as the robot starts turning. Modify the algorithm to ramp up the speed gradually to avoid commanding too much speed too quickly.

3. Using proportional control will cause the robot to slow to zero speed as the robot approaches the target heading and the error approaches zero. However, due to real-world limitations, a robot will not actually move at very low commanded speeds. There is a minimum commanded speed that is required to induce any robot motion at all. Modify the algorithm to include a minimum speed to ensure the robot keeps moving, even when the proportional control equation produces an unrealistically low, commanded speed.

Write out the entire algorithm in pseudo code for turning a robot using proportional control and a gyro sensor. Parameters will include, minimum speed, maximum speed, desired heading, and turning radius.

And wouldn't you know it, ChatGPT came up with a damn fine algorithm that would probably work quite well for FLL. Translating this to SPIKE Scratch might be challenging, but it's doable.

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Here’s a robust pseudo-code algorithm incorporating your suggestions to handle the issues of overshooting, jerky starts, and realistic speed thresholds:

Pseudo-Code for Robot Turn Using Gyro Sensor

FUNCTION TurnRobot(desired_heading, min_speed, max_speed, turning_radius):
    # Initialization
    current_heading ← GyroSensor.get_heading()     # Initialize current heading from gyro
    heading_error ← desired_heading - current_heading
    direction ← SIGN(heading_error)                # Determine turn direction (+1 for clockwise, -1 for counterclockwise)
    proportional_gain ← 0.1                        # Tune this value to scale the response

    # Speed Ramp-Up Initialization
    ramp_up_rate ← 0.05                            # Speed increment per iteration
    current_speed ← min_speed                      # Start at minimum speed

    # Start Turn
    WHILE ABS(current_heading - desired_heading) > 0:  # Loop until surpassing the target heading
        # Update Current Heading
        current_heading ← GyroSensor.get_heading()
        heading_error ← ABS(desired_heading - current_heading)

        # Check if Target Heading Surpassed
        IF (direction > 0 AND current_heading >= desired_heading) OR
           (direction < 0 AND current_heading <= desired_heading):
            BREAK                                   # Exit loop as heading is surpassed

        # Compute Proportional Speed (Capped at Max Speed)
        proportional_speed ← proportional_gain * heading_error
        proportional_speed ← CLAMP(proportional_speed, min_speed, max_speed)

        # Gradually Ramp Up Speed
        current_speed ← MIN(current_speed + ramp_up_rate, proportional_speed)

        # Set Wheel Speeds for Turning
        inner_wheel_speed ← direction * current_speed * (1 - turning_radius / (turning_radius + wheel_base / 2))
        outer_wheel_speed ← direction * current_speed * (1 + turning_radius / (turning_radius + wheel_base / 2))

        MotorController.set_wheel_speeds(inner_wheel_speed, outer_wheel_speed)

    # Stop the Robot After Surpassing the Target Heading
    MotorController.stop()

END FUNCTION

Key Features of the Algorithm

1. Stopping After Surpassing Target Heading:
   • The loop exits as soon as the robot's heading surpasses the target heading, preventing dithering or oscillation around the target.
2. Proportional Control with Speed Limits:
   • The proportional speed is calculated based on the heading error and is clamped between the min_speed and max_speed to avoid excessive speed or robot immobility.
3. Ramp-Up for Smooth Acceleration:
   • The ramp_up_rate ensures that the robot gradually accelerates from the min_speed to the computed proportional speed, avoiding sudden jerks.
4. Minimum Speed Constraint:
   • A floor on the speed (min_speed) ensures the robot moves reliably even when the proportional control produces very small speed values.
5. Differential Wheel Speeds for Turning Radius:
   • The inner and outer wheel speeds are adjusted based on the specified turning_radius and wheel_base to achieve the desired turn geometry.

Parameter Descriptions

• desired_heading: Target orientation in degrees.
• min_speed: Minimum speed to ensure motion occurs (e.g., determined experimentally).
• max_speed: Maximum speed to limit rapid turns.
• turning_radius: Radius of the turning arc (use 0 for spin turns).
• ramp_up_rate: Incremental speed increase per iteration for smooth acceleration.
• proportional_gain: Tuning parameter to control responsiveness of the turn.

Example Use

TurnRobot(desired_heading=90, min_speed=0.1, max_speed=1.0, turning_radius=0)

This call would execute a smooth, spin turn to 90 degrees with controlled acceleration and deceleration, ensuring no dithering or unnecessary corrections.

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AndyMark, Inc

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Our team qualified for the regionals. We are based in SE Michigan.

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Thanks.

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Hello everyone!

Please consider taking this survey created by our FLL Challenge team Beta Artists to provide feedback on their innovation project idea:

https://forms.gle/ZCmL6t5127jwHTqEA

There is a presentation and prototype link in the first section with some explanation of their idea.

Thanks and all the best!

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