Ackermann Steering 'Turning Radius' Confusion

[Doge-God]

Environment

• OS Version: Ubuntu 22.04
• Sourced, gz-sim8, 9e31084

Description

• Expected behavior: <steering_limit> is the maximum ideal-wheel steering angle and we can derive a minimum turning radius from it.
• Actual behavior: <steering_limit> does not have any semantic meaning OR the simulator does not follow the correct minimum turning radius.
  

According to the doc, <steering_limit> should be asin(wheel_base / turning_radius)(https://gazebosim.org/api/sim/8/classgz_1_1sim_1_1systems_1_1AckermannSteering.html), see the graph and formula, that means the turning_radius here should refer to RF.

This turning radius is later extracted to be used in the code:

gz-sim/src/systems/ackermann_steering/AckermannSteering.cc

Line 839 in 9e31084

double minimumTurningRadius = this->wheelBase / sin(this->steeringLimit);

Everywhere else in the following calculation turning_radius is assumed to be RR: notice the usage of tan

gz-sim/src/systems/ackermann_steering/AckermannSteering.cc

Lines 863 to 866 in 9e31084

	double leftSteeringJointAngle =
	atan(this->wheelBase / (turningRadius - (this->kingpinWidth / 2.0)));
	double rightSteeringJointAngle =
	atan(this->wheelBase / (turningRadius + (this->kingpinWidth / 2.0)));

This is especially obvious in the differential simulation calculations:

gz-sim/src/systems/ackermann_steering/AckermannSteering.cc

Line 867 in 9e31084

double phi = atan(this->wheelBase / turningRadius);

The left and right joint speed calculation below can be simplified to (Linear Velocity / Wheel Radius) * (1 +- 0.5KingPinWidth / TurningRadius)

gz-sim/src/systems/ackermann_steering/AckermannSteering.cc

Lines 869 to 875 in 9e31084

	// Partially simulate a simple differential
	this->rightJointSpeed =
	(linVel * (1.0 + (this->wheelSeparation * tan(phi)) /
	(2.0 * this->wheelBase))) / this->wheelRadius;
	this->leftJointSpeed =
	(linVel * (1.0 - (this->wheelSeparation * tan(phi)) /
	(2.0 * this->wheelBase))) / this->wheelRadius;

This checks out if the left and right joint speed refers to angular velocities of the 2 non-steering wheels at the back axel and turning radius being drawn to the center between the back wheels, meaning TurningRadius should be refering to RR and NOT RF.

HOWEVER if we blindly follow the documentation and mistakenly use RR as 'turning_radius' of our physical car and follow <steering_limit> = asin(wheel_base / turning_radius), the behavior of the car in the simulator will actually be correct since

gz-sim/src/systems/ackermann_steering/AckermannSteering.cc

Line 839 in 9e31084

double minimumTurningRadius = this->wheelBase / sin(this->steeringLimit);

will then extract RR and use it as RR correctly in the following calculations, but in this case our steering_limit is no longer SA in the diagram and doesn't have any useful meaning.

We should update line 839 to use tan instead of sin then update and clarify the documentation to avoid any confusion.

[scpeters]

it looks like it would be more consistent to use tan in that line as you propose. would you like to open a pull request for this change?