SRC2 - Explicit Steering - Wheel Speed

SRC2 Rover

This fourth post about the qualifying round of the NASA Space Robotics Challenge - Phase 2 (SRC2) addresses the speed of the wheels of the rover, shown to the right, under the various possible motions. The rover uses Explicit Four Wheel Steering which allows the orientation of the wheels to be independently changed. The second and third posts explored the geometry to determine the position of the wheels for a turn, pivoting in place, and crab / straight movement. See the first post for the basics of the competition. 

Wheel Orientation

The orientation of the wheels on the rover determines the speed for the wheels. In straight or crab movement the speed is the same for all wheels. When turning, shown in the diagram below, the speeds are different for the inner and outer wheels. The requested overall speed of the rover, determined at the center of the rover, is used to calculate the inner and outer speeds. 

Term	Description
ICR	Instantaneous Center of Rotation
Rr	Radius from ICR to center of rover
Ri, Ro	Radius of  rover's inner (i) and outer (o) sides through ICR
Wb, Wt	Wheel base and wheel track of rover. Lengths are representative of actual size.
WRi, WRo	Radius of inner(i) and outer (o) wheels
δi, δo	Steering angle for inner (i) and outer (o) wheels

Visualize on the diagram three concentric circles drawn from the ICR. One circle passes through the center of the rover while the others pass through the inner and outer corners, or wheels, of the rover. The second post calculated the wheel's turning radius as:

The rover radius is Rr, the distance from the ICR to the center of the rover. 

The speed (Sr)  and turn radius of the rover determine the time (Tr) to complete a full circle, as shown in the first equation below. The next equation calculates the speed of either set of wheels (WR) using the circumference of the respective circles. Subsequently, that equation can be simplified as shown in the formulations that follow. 

Twist Calculation

The standard ROS movement command is the twist message. It contains two 3 dimensional vectors. One specifies the linear movement for the x, y, and z dimensions. The other specifies the orientation, also as x, y, and z, but meaning roll, pitch, and yaw respectively. 

The calculations for steering orientation and speed are all based on the radius of the turn. That turn radius needs to be calculated using the X velocity and the Yaw from the message. Recall from post three that turning during a crab movement is not under consideration so the linear Y value is ignored. 

Getting to how to do the calculation requires some interesting analysis but the final, actual calculation is extremely simple. The starting point is the Yaw in radians / second. The first equation determines the time it would take to turn a full 2𝜋 radians at the Yaw rate. Or, how long to traverse a full circle. 

Next, that time is used to determine the circumference of the circle using the X speed. Knowing the circumference the radius is determined. The equations show the individual steps but then combine them to reduce them to a simple calculation. Everything should reduce to such simplicity. Note that dimensional units are included to assure the final units are valid.

SRC2 - Explicit Steering - Crab, Straight, and Pivot Movements

SRC2 Rover

This is the third in a series of post about my involvement with the qualifying round of the NASA Space Robotics Challenge - Phase 2 (SRC2). The first post introduced the basics of the competition. One aspect of the challenge is there is no controller for the rover depicted to the right. It uses Explicit Four Wheel Steering which allows the orientation of the wheels to be independently changed. This provides multiple ways for the rover to move, e.g. straight, crab, turn, pivot.

The second post explored the geometry on positioning the wheels for a turn. This post will address pivoting in place and crab movement, i.e. moving sideways. It also addresses the trivial crab case of moving straight forward or back. 

SRC2 - Explicit Steering - Wheel Orientation for Turning

SRC2 Rover

The first post in this series explained I'm currently involved with the qualifying round of the NASA Space Robotics Challenge - Phase 2 (SRC2). The competition requires controlling the rover to the right. It uses Explicit Four Wheel Steering which allows the orientation of the wheels to be independently changed, This provides multiple ways for the rover to move, e.g. straight, crab, turn, pivot.

The challenge is there is no controller for the rover in the Robot Operating System (ROS) because the rover wheels are controlled by effort, not the typical speed control.

This article address the geometry of controlling the rover when it is turning. The diagram below illustrates the rover making a counter-clockwise turn around the Instantaneous Center of Rotation (ICR). The arrows represent the wheel orientation. The dotted box is drawn proportional to the wheel base and track of the rover. Note the orientation of the X/Y axis which is ROS standard for robots.

Explicit Steering - Rover Turning

Term	Description
ICR	Instantaneous Center of Rotation
Rr	Radius from ICR to center of rover
Ri, Ro	Radius of  rover's inner (i) and outer (o) sides through ICR
Wb, Wt	Wheel base and wheel track of rover. Lengths are representative of actual size.
WRi, WRo	Radius of inner(i) and outer (o) wheels
δi, δo	Steering angle for inner (i) and outer (o) wheels

NASA Space Robotics Challenge - Phase 2

Another NASA Centennial Challenge began earlier this year. It will be the 3rd I've entered. I also entered the 2019 ARIAC competition which makes 4 competitions. The current competition is the Space Robotics Challenge - Phase 2 (SRC2). In this competition robotic mining rovers explore the Moon to detect volatiles and collect them, detect a low orbiting cube sat, and position one rover aligned with a fiducial on a processing station.

Links to Follow-on Posts

• SRC2 - Explicit Steering - Wheel Orientation for Turning
• SRC2 - Explicit Steering - Crab, Straight, and Pivot Movements
• SRC2 - Explicit Steering - Wheel Speed

In the following posts I'll explain what I can about this topic. There are a number of research papers available however my posts will provide a simplified explanation. 

Explicit Steering

The biggest challenge in this competition is controlling the rover. It is the size of a small SUV with Explicit Four Wheel Steering, i.e. each of the four wheels is steered separately. If you've seen the Mars rover it is a similar design. That's the base rover, above.

Explicit steering allows flexibility in movement of the rover. It can turn all four wheels to the same angle to move sideways in a crab movement. This also provides straight forward movement. By orienting the wheels at different angles the rover can turn. An extreme example of this is pivoting in place.

Robot Operating System

The base software for the competition is the Robot Operating System (ROS) which consists of the fundamentals for communicating amongst software nodes and a large number of packages that provide useful capabilities. Unfortunately there isn't one for controlling the SRC2 rover.

There are two ways of controlling the wheels for locomotion. The predominant one is issuing a speed command. A number of ROS controller packages provide this capability. Another specified the effort or torque. There are effort controllers but none directly apply to the SRC2 rover.

The location of the rover on the surface is required for reporting the position of volatiles, moving to them, and generally controlling the rover's movement. This requires deriving odometry from wheel movement, vision processing via stereo cameras and an inertial measurement unit (IMU). Again, this is not provided. It is especially challenging due to the low friction between the wheels and simulated Moon surface which allows slippage of the wheels.