Project Breakdown:  

The project consists of an electro-mechanical mechanism that is placed on a ball and regulates itself to remain balanced on the top of the ball despite disturbances. This robot resting on the ball consists of three motors positioned in a polyhedron manner in which the actuators control the maneuvering of the robot with respect to the ball. While the ball is in motion, to ensure the mechanism remains balanced on top, the actuators are activated to counteract the ball’s movement. An Arduino Mega is used to calculate the necessary control responses based on the feedback from the main sensor, namely the Inertial Measuring Unit (IMU). The actuators are instructed to move accordingly by the Arduino board. 

The tilt angles of the device in the x and y directions is measured by the gyroscope situated on the breadboard centered at the top of the robot. These angles will serve as the control input to the system. Using the angles of the robot about the x and y axis, velocities for the mechanism in the x and y direction are calculated to regulate the system back to its desired balanced equilibrium position. This x and y velocity in the frame of the robot are then converted into individual wheel speeds using simple geometry. 

Using the x- and y-related angles, a PID controller could be implemented to both these angles to regulate the mechanism to always remain on the top of the ball and thus have both these angles with a desired angle of 0 degrees. The error in this PID control would be the angle by which the mechanism was tilted in the x and y direction. Once applying an appropriate PID control in both directions, three corresponding outputs to balance the mechanism would be sent as a signal to each of the three stepper motors.

Initially, a P control was applied to try to stabilize the system and was found to be the best after testing with PI, PD and PID controllers. As this controller was tested on numerous balls, it became clear that this proportional P constant depended on the weight and size of the ball. With this P control, it was observed that the mechanism had very harsh movements, especially around the equilibrium point. As such, in an attempt to filter out the effect of the small angles, a test was set up such that the proportional control would only be in effect if the displacement angle in either the x or y direction was greater than a particular threshold. Thus if the angle was, for example, less than two degrees with respect to the x or y axis, no control output would be produced. This technique was attempted for numerous thresholds, however, it was found that this was not a very successful idea given typically when the mechanism surpassed roughly eight degrees in the x or y direction, it would fail due to the gravitational force of the structural components of the mechanism which counteracted the stabilizing force of the control of the motor wheels. As such, this dead zone caused the mechanism to react too late. The best Kp value found was of 0.3.

Brief mention on setting the velocity of the motors:

The code structure was split into three parts: Velocity control of the motors, reading IMU data, and a PID control loop 

To precisely control the velocity of the motors all that is needed is to change the time between each step the stepper motor takes. The stepper motor steps on a positive or negative edge of the digital direction pin. Therefore, given a large delay between steps, the motor moves slower, and if there is a small delay between steps, the motor moves faster. Therefore we have the relationship for the stepper motor to be v ∝ 1/delay. Knowing this means for a given velocity, it is possible to calculate what the delay between steps should be. Once the delay is calculated, a hardware timer interrupt running at 10kHz decides when to step. To do this, each time in the ISR a check to see if enough time (the desired delay) has passed since the last step is carried, and, if so, a step and reset on our counter occurs. A library was used to take advantage of the onboard timer interrupts on the Arduino Mega. This library allows for the frequency to be set and then just provide it an ISR.

Brief mention of the IMU used:

The only sensor we needed was an IMU. We do not need encoders on the motors because stepper motors enable precise position (and thus speed) control with no external hardware given we control when it steps and know the size of the steps. When looking for an IMU, we selected the MPU6050 because it is cost effective, and also one of the only IMUs available that has digital motion processing built in. It has 16 bit ADC for both gyro and acceleration data, and can output angle data at a maximum of 200 Hz which is more than required as past attempts at this project used less than 100 Hz for their sensor data. This IMU communicates over I2C and is widely used so it has a lot of support and libraries that are easily accessible. When testing the sensor we observed that it took a 5-10 seconds for the position data to stabilize and then it did not drift at all after 2 minutes of stationary and shaking motions. Furthermore, we observed the precision of the sensor to be less than 0.01 degrees which would not be a significant source of error compared to other factors in our device like surface grip and surface irregularities.