The purpose of this project was to construct a 2-axis stabilized model platform, as a proof of concept, intended to use for a cockpit base of a terrain vehicle or a combat boat. The stabilization of the platform in the roll and pitch axes is realized using a feedback control system that contains a proportional-integral-derivative (PID) controller, two DC motors driving the roll and pitch movements, and a 6-axis inertial measurement unit (IMU) measuring the roll and pitch angles. The project started with a study of various stabilized platforms and the theories behind them and a model of the system was created in SimuLink to simulate the system and design the controller. After the simulations where satisfactory a model platform of a scaled-down actual size was constructed. The platform’s frame was printed in a 3D printer. The control system for the platform has been implemented. The PID controller was implemented on the Arduino Mega 2560 development board, and it regulates the pitch and roll movements through two DC motors. The platform’s pitch and roll angles are measured by a 3-axis gyroscope in an IMU sensor (MPU-6050). The measurements are processed by a Kalman filter implemented on the Arduino board to reduce the noise. The Simulink simulation provided a functioning control system. However, the prototype of the implemented model platform does not work with god stability as expected. The reason for this result is mostly due to the unsuccessful construction of the platform frame and the bad choice of motors.

For their inherent stability and simple dynamics of motion, wheeled robots are very common in robotics applications. Many highly complex robots are being developed in research laboratories, but wheeled robots remain the most used robot in real-world situations. One of the most significant downfalls of wheeled robots is their inability to navigate over large obstacles or steps without assistance. A wheeled robot is capable of climbing steps that are no larger than the radius of the robot's tires, but steps larger than this are impassable by simply rolling over the object. Active systems that have been designed for use on wheeled robots to lift the robot over a step are effective, but are generally not easily implemented on a range of robotic platforms. Also, the additional size, cost, and power required for the additional actuators is a major drawback to these options. A solution to these problems is a novel, passive dynamic system that is inertially excited by the motion of the robot to allow the robot to rotate on each axle and "hop" over the step. The system that was investigated for this project is a sliding mass-spring that shifts forward and backward based on the acceleration of the base robot. With high acceleration, the mass is pushed towards the rear wheel from an inertial force and compresses a spring that creates a moment on the body to induce rotation. This torque can cause the robot to "pop a wheelie", lifting its front wheels off the ground. To pull the rear wheels up, the inertial force from a large deceleration of the robot shifts the mass forward and extends a spring. These effects result in a moment acting in the opposite direction that can rotate the robot on its front axle and pull the rear wheels up. By coordinating the acceleration and deceleration of the robot, the front wheels can lift over a step and the rear wheels can be pulled up afterward — both actions being a product of inertial actuation. This passive system does not need additional actuators or direct control of the sliding mass, so it can be more durable over a robot's lifetime. Other advantages of this system are that the design is simple, cost-effective, and can be adjusted and retrofit to a different wheeled robot in the future with little effort. By deriving the equations of motion of this inertially actuated sliding mass, the dynamics show how design parameters of the system can be tuned to better optimize the overall step-climbing process. A computer simulation was created to visualize the robotic step-climbing process and demonstrate the effects of changing design parameters. An implementation of this sliding mass system was added to a wheeled robot, and the results from experiments were compared to simulated trials. This research has shown that an inertially actuated sliding mass can effectively enable a wheeled robot to climb a step that was previously impassable and that the system can be tuned for other wheeled robots using an understanding of the system dynamics. / Master of Science

A sign pattern(matrix) is a matrix whose entries are from the set {+,-,0}. An n x n sign pattern matrix is a spectrally arbitrary pattern(SAP) if for every monic real polynomial p(x) of degree n, there exists a real matrix B whose entries agree in sign with A such that the characteristic polynomial of B is p(x). An n x n pattern A is an inertialy arbitrary pattern(IAP) if (r,s,t) belongs to the inertia set of A for every nonnegative triple (r,s,t) with r+s+t=n. Some elementary results on these two classes of patterns are first exhibited. Tree sign patterns are then investigated, with a special emphasis on 4 x 4 tridiagonal sign patterns. Connections between the SAP(IAP) classes and the classes of potentially nilpotent and potentially stable patterns are explored. Some interesting open questions are also provided.