Single wheel robot: gyroscopical stabilization on ground and on incline.

by Loi-Wah Sun.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 77-81).Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiContents --- p.vList of Figures --- p.viiList of Tables --- p.viiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.1.1 --- Literature review --- p.2Chapter 1.1.2 --- Gyroscopic precession --- p.5Chapter 1.2 --- Thesis overview --- p.7Chapter 2 --- Dynamics of the robot on ground --- p.9Chapter 2.1 --- System model re-derivation --- p.10Chapter 2.1.1 --- Linearized model --- p.15Chapter 2.2 --- A state feedback control --- p.16Chapter 2.3 --- Dynamic characteristics of the system --- p.18Chapter 2.4 --- Simulation study --- p.19Chapter 2.4.1 --- The self-stabilizing dynamics effect of the single wheel robot --- p.21Chapter 2.4.2 --- The Tilting effect of flywheel on the robot --- p.23Chapter 2.5 --- Dynamic parameters analysis --- p.25Chapter 2.5.1 --- Swinging pendulum --- p.25Chapter 2.5.2 --- Analysis of radius ratios --- p.27Chapter 2.5.3 --- Analysis of mass ratios --- p.30Chapter 3 --- Dynamics of the robot on incline --- p.33Chapter 3.1 --- Modeling of rolling disk on incline --- p.33Chapter 3.1.1 --- Disk rolls up on an inclined plane --- p.37Chapter 3.2 --- Modeling of single wheel robot on incline --- p.39Chapter 3.2.1 --- Kinematic constraints --- p.40Chapter 3.2.2 --- Equations of motion --- p.41Chapter 3.2.3 --- Model simplification --- p.43Chapter 3.2.4 --- Linearized model --- p.46Chapter 4 --- Control of the robot on incline --- p.47Chapter 4.1 --- A state feedback control --- p.47Chapter 4.1.1 --- Simulation study --- p.49Chapter 4.2 --- Backstepping-based control --- p.51Chapter 4.2.1 --- Simulation study --- p.53Chapter 4.2.2 --- The effect of the spinning rate of flywheel --- p.56Chapter 4.2.3 --- Simulation study --- p.58Chapter 4.2.4 --- Roll up case --- p.58Chapter 4.2.5 --- Roll down case --- p.58Chapter 5 --- Motion planning --- p.61Chapter 5.1 --- Performance index --- p.61Chapter 5.2 --- Condition of rolling up --- p.62Chapter 5.3 --- Motion planning of rolling Up --- p.65Chapter 5.3.1 --- Method I : Orientation change --- p.65Chapter 5.3.2 --- Method II : Change the initial velocities --- p.69Chapter 5.4 --- Wheel rolls Down --- p.70Chapter 5.4.1 --- Terminal velocity of rolling body down --- p.73Chapter 6 --- Summary --- p.75Chapter 6.1 --- Contributions --- p.75Chapter 6.2 --- Future Works --- p.76Bibliography --- p.7

Master of Science

thesisThis thesis focuses on the design, modeling, fabrication, and testing of a ?ying and walking robot, called the Dynamic Underactuated Flying-Walking (DUCK) robot. The DUCK robot combines a high-mobility ?ying platform, such as a quadcopter (quadrotor helicopter), with passive-dynamic legs to create a versatile system that can ?y and walk. One of the advantages of using passive-dynamic legs for walking is that additional actuators are not needed for terrestrial locomotion, therefore simplifying the design, reducing overall weight, and decreasing power consumption. First, a mathematical model is developed for the DUCK robot, where the modeling combines the passive-dynamic walking mechanism with the swinging mass of the aerial platform. Second, simulations based on the model are used to help guide the design of two prototype robots, speci?cally to tailor the shape of the feet and the dimensions of the passive-dynamic walking mechanism. Third, an energy analysis is performed to compare the performances between ?ying and walking. More specifically, simulation results show that continuous active walking has a comparable energy efficiency to that of flying for the two prototype designs. For design Version 1, it is estimated that the robot is able to walk up to 1600 meters on a 30kJ battery (standard Li-Po battery) with a cost of transport of 1.0, while the robot can potentially fly up to 1800 meters horizontally with the weight of its legs and up to 2300 meters without the weight of its legs. Design Version 2 is estimated to be able to walk up to 4600 meters on a 30kJ battery with a cost of transport of .50, while it could fly up to 2600 meters with the weight of its legs or 4300 meters without its legs. The cost of transport of flying is estimated to be .89 in all scenarios. Finally, experimental results demonstrate the feasibility of combining an aerial platform with passive-dynamic legs to create an effective flying and walking robot. Two modes of walking are experimentally demonstrated: (1) passive walking down inclined surfaces for low-energy terrestrial locomotion and (2) active (powered) walking leveraging the capabilities of the flying platform, where thrust from the quadcopter's rotors enables the DUCK robot to walk on flat surfaces or up inclined surfaces

Contributions to the modelling and control of two-wheeled mobile robots

Wheeled mobile robots moving on uneven terrain are attracting interest at an impressive pace. In the work reported here two distinct architectures of two-wheeled mobile robots are proposed.The first architecture, corresponding to the case where the two wheels linked by a frame lie in a vertical plane, constitutes the material of our earlier research and is laid out in the appendix. The system being unilaterally constrained by the environment, slipping or losing contact with the ground can occasionally occur. Therefore, nine distinct topologies are identified and accounted for in the model describing all the possible motion modes of the system. The mathematical model is formulated using the Natural Orthogonal Complement (NOC) and takes into account the terrain geometry. Additionally, the model includes necessary conditions for the switching between the distinct topologies.The second architecture pertains to an Anti-Tilting Outdoor Mobile robot, ATOM, composed of two spherical wheels and a cylindrical central body. The spherical shape of the wheels allows the robot to restore its posture after flipping over, thus giving it the anti-tilting property. Moreover, this particular shape ensures pure-rolling motion on uneven terrain without resorting to any adaptive structure; i.e., without increasing the complexity of the system. Here, also, the mathematical model is developed using the NOC, while taking into account the terrain geometry. Moreover, constraints on the terrain curvatures are derived in order to ensure pure rolling. Although the design of ATOM is simple, this brings about new challenges in terms of control. According to its structure, ATOM pertains to the class of Mobile Wheeled Pendulums (MWP). A feature common to MWPs, that is not encountered in other wheeled robots, is that their central body, which constitutes the platform of the robot, can rotate about the wheel axis. Therefore, aside the nonholonomy aspects encountered in conventional wheeled robots; the central body stabilization problem is pointed out here and rigorously treated in order to avoid unstable zero-dynamics. For that, an intrinsic dynamcal property, referred to as the natural behaviour of the system, is brought forward and employed to control the heading velocity of the robot using the inclination of the central body. Moreover, a particular selection of the generalized coordinates and the system outputs allows a global stabilization of the system without resorting to any linearization. Furthermore, a posture control (preceded by a velocity and orientation control) is proposed based on sliding mode and Lyapunov function for navigation. Finally, the robust aspect of the controller is underlined by showing the control behaviour versus an over/under estimation of system parameters

Optimisation of bipedal walking motion with unbalanced masses.

Commercial prosthetic feet weigh about 25% of their equivalent physiological counterparts. The human body has a tendency to overcome the walking asymmetry resulting from the mass imbalance by exerting more energy. A two link passive walking kinematic model, with realistic masses for prosthetic, physiological legs and upper body, has been proposed to study the gait pattern with unbalanced leg masses. The 'heel to toe' rolling contact has significant influence on the dynamics of biped models. This contact is modelled using the roll-over shape defined in the local co-ordinate system aligned with the stance leg. The effect of rollover shape curvature and arc length has been studied on various gait descriptors such as average velocity, step period, inter leg angle (and hence step length), mechanical energy. The bifurcation diagrams have been plotted for point feet and different gain values. The insight gained by studying the bifurcation diagrams for different gain and length values is not only useful in understanding the stability of the biped walking process but also in the design of prosthetic feet. It is proposed that the stiffness and energy release mechanisms of prosthetic feet be designed to satisfy amputee's natural gait characteristics that are defined by an effective roll-over shape and corresponding ground reaction force combinations. Each point on the roll-over shape is mapped with a ground reaction force corresponding to its time step. The resulting discrete set of ground reaction force components are applied to the prosthetic foot sole and its stiffness profile is optimised to produce a desired deflection as given by the corresponding point on the roll-over shape. It is shown that the proposed methodology is able to provide valuable insights in the guidelines for selection of materials for a multi-material prosthetic foot

Large scale modeling, model reduction and control design for a real-time mechatronic system

Mechatronics is the synergistic integration of the techniques from mechanical engineering, electrical engineering and information technology, which influences each other mutually. As a multidisciplinary domain, mechatronics is more than mechanical or electronics, and the mechatronic systems are always composed of a number of subsystems with various controllers. From this point of view, a lot of such systems can be defined as large scale system. The key element of such systems is integration. Modeling of mechatronic system is a very important step in developing control design of such products, so as to simulate and analyze their dynamic responses for control design, making sure they would meet the desired requirements. The models of large scale systems are always resulted in complex form and high in dimension, making the computation for modeling, simulation and control design become very complicated, or even beyond the solutions provided by conventional engineering methods. Therefore, a simplified model obtained by using model order reduction technique, which can preserve the dominant physical parameters and reveal the performance limiting factor, is preferred. In this dissertation, the research have chosen the two-wheeled self-balancing scooter as the subject of the study in research on large scale mechatronic system, and efforts have been put on developing a completed mathematical modeling method based on a unified framework from varitional method for both mechanical subsystem and electrical subsystem in the scooter. In order to decrease the computation efforts in simulation and control design, Routh model reduction technique was chosen from various model reduction techniques so as to obtain a low dimensional model. Matlab simulation is used to predict the system response based on the simplified model and related control design. Furthermore, the final design parameters were applied in the physical system of two-wheeled self-balancing scooter to test the real performance so as to finish the design evaluation. Conclusion was made based on these results and further research directions can be predicte

Kinematic and dynamic analysis of mobile robot

Master'sMASTER OF SCIENC

Nonprehensile Manipulation of Deformable Objects: Achievements and Perspectives from the RobDyMan Project

International audienceThe goal of this work is to disseminate the results achieved so far within the RODYMAN project related to planning and control strategies for robotic nonprehensile manipulation. The project aims at advancing the state of the art of nonprehensile dynamic manipulation of rigid and deformable objects to future enhance the possibility of employing robots in anthropic environments. The final demonstrator of the RODYMAN project will be an autonomous pizza maker. This article is a milestone to highlight the lessons learned so far and pave the way towards future research directions and critical discussions

A novel mathematical formulation for predicting symmetric passive bipedal walking motion with unbalanced masses

Commercial prosthetic feet weigh about 25% of their equivalent physiological counterparts. The human body is able to overcome the walking asymmetry resulting from this mass imbalance by exerting more energy. It is hypothesised that the passive walking dynamics coupled with roll-over shapes has potential to suggest energy efficient walking solutions. A two link passive walking kinematic model has been proposed to study the gait pattern with unbalanced leg masses. An optimal roll-over shape for the prosthetic foot that minimises the asymmetry in the inter-leg angle and the step period is determined. The proposed mathematical formulation provides insights into the variation of step length and inter-leg angle with respect to the position and location of the centres for mass of both prosthetic and physiological legs