Kinematics of Wheeled Mobile Robots Pt. 2

I discovered a few minor issues with my previous derivation. I had not converted the unit vectors from one frame to the other correctly, and I left some of the expressions in the unit vectors of an inappropriate frame. MATLAB was used to verify the equations. Simple inputs were sent to the equations and various outputs were plotted for evaluation. The rainbow plots show the physical path of the robot in the XY plane. The color indicates the angle of rotation in degrees. The last graph shows my original eureka moment when I finally realized I fixed the problem. Previously, there was a cusp in the magnitude of velocity when it should have been constant. When I saw the constant red line, I knew I was on the right track. 

Because the control inputs are centered to the robot's frame, if you hold constant translational inputs with a rotation, the robot will end up taking a curved path. However if you hold constant translational inputs with no rotation, the robot will travel straight. This is shown by the graphs with no color change.

Kinematics of Wheeled Mobile Robots

After many discussions, our group has decided that four-wheel drive simply does not permit adequate control of the robot for aligning with the circuit breaker cubicle. So we are reverting to our original drive train choice: swerve drive. Swerve drive is a holonomic locomotion system in which each wheel can pivot about its own vertical axis. Using a swerve drive, the robot will strafe sideways along the face of the circuit breaker cubicle, detecting the edges of the cubicle and using those edges to laterally align the robot. Then, the robot will perform an angular alignment to the face of the cubicle, and advance forward to extract the breaker. The angular alignment and subsequent forward motion would not have been possible with a four-wheel drive system; as the translation and rotation of the robot are coupled.

I derived the inverse kinematics of the robot for our computer engineers to use in their control algorithms. The derivation is quite simple mathematically, but it can easily get confusing to understand from a physical sense. I like to imagine what I would experience if I were sitting on the different points where the wheels are located on the robot. This helps me to see why certain terms are in the resulting equations and verify if the results make sense. 

PDF derivation of the kinematics.

Omniwheel Design

Currently working on a high load capacity omniwheel design for our circuit breaker removal robot (BreakerBot). Off the shelf omniwheels of this load capacity (750lb) are very expensive! This design is an exercise to see if constructing our own wheels is a feasible solution. Our other options are to choose an alternative drive train system that doesn't require these expensive and complex omniwheels. However, those systems are either non-holonomic (ackerman steering) or even more complex (swerve drive). I am hoping that we will be able to use these wheels with sort of H-drive system. We do not need full holonomic control, but the ability to strafe and turn on a point would be very useful for aligning the robot with the breaker's cubicle for extraction.