A robot made to balance a ball on a platform. The platform is controlled by two servo motors, and the ball's position is detected using a camera. A Raspberry Pi is the brain of the project, and calculates the incline of the plane needed to get the ball to the desired position.
This is the exact dimensions of the robot:
To calculate the forward kinematics, I simplified it to the following:
C is the center of the disk, and J1 is the center of rotation of the servo. J2 is where the servo-arm (L1) connects to the arm with ball-joints (L2). J3 is the location where the ball joint attaches to the disk. There are mainly two simplifications made in the model: in reality the disk pivots around a point that is offset from the disk and J3 is connected to the disk at an offset.
Given a fixed position of J2, we want to find the angle of the plane (v). We know that J3 must be a fixed distance from C (lie on the circle perimeter in blue). We also know that J2 and J3 are at a fixed distance from each other (L2).
Where J2 is given by
where u is the angle of the servo located at J1, and x(J1) and y(J1) are the x- and y-position of J1 relative to C.
As the function used to calculate the forward kinematics is monotonic (at least with the dimensions of my robot), I did not bother calculating the inverse kinematics. Instead, I perform a binary search on the forward kinematics function (shown below, where the inputs will range from -1.05 to 0.82)
Martin Ansteensen 2022