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Thread: How to find kinematics of a system with 2 differential drives attached together?

  1. How to find kinematics of a system with 2 differential drives attached together?

    I have a system like shown in the [diagram](https://imgur.com/a/lcc6GMP~~~~) where 2 robots having differential drive are physically constrained together. [Traditionally for a single robot, we find the Instantaneous center of curvature \(ICC\)](http://www.cs.columbia.edu/~allen/F1...kinematics.pdf) by equating the "omega" for both wheels. That would work since there are 2 equations (the relationship between the wheel velocities and angular velocity) and 2 unknowns (the distance of ICC from the center of the wheels and the angular velocity). However, in my system, there will be 4 equations and 2 unknowns. So should I solve it as an over-determined system? Or should I only consider the extreme cases ie. left most wheel speed for the left robot and rightmost wheel speed for the right robot?

  2. #2

    Re: How to find kinematics of a system with 2 differential drives attached together?

    Why do you think you only have two unknowns? Two drive wheels per robot, times two robots, equals four unknowns.

    This is assuming the robots are attached with an articulating joint. If the joint is rigid, then your problem is instead that two of the four wheels will likely slip if you drive them incorrectly. Knowing which wheels slip, and which have traction, is pretty hard without a camera or other form of global localization support.

    Without knowing which wheels slip, you will not know how the robot is actually behaving. OR you can make your control such that the wheels won't slip -- know exactly the diameter of the wheels, and drive the controllers such that they match perfectly the motion of the overall robot. In that case, control the outer two wheels, and derive the inner two wheels through simple interpolation based on distance to center compared to the outer wheels.

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