Self-Balancing Mini Segway (MinSeg) Robot
Project Overview
Created a self-balancing robot, with the use of MinSeg, by deriving appropriate electromechanical equations and modeling them within MATLAB and Simulink. Successfully tuned control system parameters to develop balancing abilities and minimize drift.
What?
Created a self-balancing robot capable of compensating for external forces.
Utilizes a pre-made Arduino-based mini Segway robot with MPU-6050 gyroscope/accelerometer and 2 DC motors with encoders.
How?
Derived electromechanical equations - modeled within MATLAB and Simulink.
Designed and tested feedback controllers through Ackerman's Method and a Linear Quadratic Regulator (LQR).
Results
Successfully found LQR control gain to develop a steady system of at least 20 seconds.
Reduced drift by under than ~0.75cm/sec and minimized sensor noise by implementing a complementary filter.
Utilized MATLAB and Simulink to simulate open-loop system and closed-loop systems through Ackerman's and LQR methods - plotted these simulations to observe and test various control gains.
Arduino Compatible Mega 2560
x2 DC Motors
MPU6050 Gyroscope + Accelerometer
MATLAB
Simulink
SJSU: ME 190 (Mechatronics System Design) - Term Project
This Self-Balancing Mini Segway Robot was the term project for my ME 190 course at SJSU. Although the hardware was made readily available, the MATLAB code, Simulink modeling, and equation calculations were all done individually.
Derivation of Electromechanical MinSeg Equations (Snippets)
Modeling started by finding the equations of motion for the robot wheel and robot body (as a pendulum).
Free body diagrams, Newton's second law, Kirchhoff's current law, and Kirchhoff's voltage law were fundamental in this derivation.
A combination of the mechanical and electrical equations ultimately create electromechanical equations in the matrix form - this was then converted into state space to model within MATLAB and Simulink.
State Space Model Development
MATLAB Code
Open-Loop System Simulation
The simulated open-loop system of the MinSeg robot illustrates the following:
The open-loop system is not stable
As shown by the "Angle vs Time" graph, the robot will eventually tip over completely
Relation of x and theta (in terms of direction)
Assuming angle (theta) is positive counterclockwise, the position (x) will move towards the right - meaning right is positive for position
As system is not stable, a closed-loop system must be incorporated
Closed-Loop System: Ackerman's Method
In order to successfully create a feedback controller, the feedback gain vector is a key variable within a feedback loop to correctly monitor the voltage output of the system then ultimately self-balance the robot.
For the first closed-loop system, the Ackerman's Method for control was explored - this finds desirable eigenvalues that result in a stable closed-loop system (desirable being negative and real). This eigenvalue was found through trial and error.
The resulting desirable eigenvalue was one that resulted in a steady-state system relatively quickly while remaining under 5 volts (the maximum GPIO voltage output of the microcontroller).
Linear Quadratic Regulator (LQR)
An alternative method other than Ackerman's Method is the use of a Linear Quadratic Regulator (LQR). The goal within this method is to minimize a cost function, as followed:
After utilizing MATLAB's LQR function to get the feedback gain vector, the closed-loop system was then modeled for varying initial angles.
Implementation of Feedback Controller
After exploring Ackerman's and LQR methods, obtaining the control gain for the MinSeg robot's actual feedback controller can be done - this was primarily made through Simulink.
MinSeg Response Results
The MinSeg was capable of self-balancing - the angular position successfully remains steady. One room for improvement is indicated in its position - it’s clear some drift can be observed within this system.
Input voltage response of the MinSeg robot. The input voltage is capped at -5 and 5 V to avoid overloading the microcontroller and DC motors. As expected, voltage peaks at moments where the angle is greatly unbalanced.