Designing an actuated metamorphic mechanism based on polyhedral structures

My theses assignment for the inspection group at the University of Twente is to design an actuated metamorphic polyhedral structure. A metamorphic polyhedral structure can be used as a robot that can change it shape and size. A problem with inspection of tunnels/pipes is that the current robots cannot handle obstacles or diameter changes. The aim of this research is to test if a metamorphic polyhedral structure can be used in tunnels/pipes with varying diameters and that it can achieve a controlled expansion. This project was not only intended for tunnel inspection but could also be used in a broader spectrum. When scaled up or down it could be used for stents in blood vessels or in construction. The literature research and design choices for this project are performed for a 3D metamorphic polyhedral structure, however the design and testing phases handles the 2D case. This choice is made to check if the problem in infrastructure can be solved with this research. The first step of the research is to investigate the various metaphoric polyhedral structures. With the analysis of the structures, the Hoberman sphere is chosen to be best suited for the problem description. The Hoberman sphere is chosen because it has the highest expansion ratio and can sustain stress better. However it has less space for sensors than other structures. The Hoberman sphere is build up of 2-3 rings connected onto a tetragon with multiple scissor joints. During this research the expansion ratio is checked with respect to the theory. With the Hoberman sphere chosen, a motor set-up is selected where a slider crank mechanism is used. This set-up is selected because it stays inside the sphere while it is expanding and has the highest range of motion. To control the Hoberman sphere in an enclosed space where it touches the surface of that space, an interaction controller is chosen. This controller can handle forces from the environment, for example an obstacle pushing on the system. To have a stable system with an interaction controller the velocity of the system is necessary. The velocity of a system can be obtained with multiple various methods. One of the methods is using an observer. For an observer to work a model of the system is necessary. A mathematical model of the Hoberman sphere is calculated by using the Lagrangian method. With the Lagrangian method, an equation of motion of the Hoberman sphere was found. From the mathematical model a physical prototype is build using 3D printing and laser cutting. With a prototype made and the model known, various tests are performed to check if the model has the same behaviour as the prototype. The first test is to check the relation between the angle of the Hoberman sphere and the angle of the motor. The second test is an open loop simulation of the model. In this test an impulse response is set onto the plant to get the crossover frequency of the system. The crossover frequency was found to be 82rad/s. To verify the model a new controller is designed using the crossover frequency in the controller design. This controller is a PID controller. When the model is correct and the velocity of the system is correctly estimated, the PID controller can be replaced with an interaction controller. The final test that is performed on the prototype is a response test with a DC-motor. A reference signal is set onto the system and the angle & current are measured during that process. The results of those measurements are then compared to the simulation. The main conclusion of this research project is that the model of the Hoberman sphere needs to be improved to better reflect the practice. If the model is further improved the interaction controller can be implemented. The design and selecting of a metamorphic polyhedral structure part of the research project is done successfully. The expansion ratio of the Hoberman sphere is however different from the theory. The theory described an expansion ratio between 2-3, where in practice the ratio is about 1.23. The difference here is mainly due to the added motor set-up. In the closed loop test the error angle signals of the response are compared and the prototype has a RMS value 3 times higher than the simulation. This value needs to be lower when the model is implemented in the interaction controller.