Gyroscopic Precession In Motion Modelling Of Ball-Shaped Robots

This study discusses kinematic and dynamic precession models for a rolling ball with a finite contact area and a point contact respectively. In literature, both conventions have been applied. In this paper, we discuss in detail the kinematic and dynamic models to describe the ball precession and the radius of a circular rolling path. The kinematic model can be used if the contact area and friction coefficient are sufficient to prevent slippage. The dynamic precession model has significance in multi-body simulation environments handling rolling balls with ideal point contacts. We have applied both the kinematic and dynamic precession model to evaluate the no-slip condition of the existing GimBall-robot. According to the result, the necessity of an external precession torque may cause slipping at lower velocities than expected if ignoring this torque.Peer reviewe

가변 토폴로지 트러스 로봇의 안정적인 주행 알고리즘 개발

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 기계공학과, 2020. 8. 김종원.Variable Topology Truss (VTT) is truss structured modular robot that can self-reconfigure its topology and geometric configuration, which can be usefully applied to rescuing work in disaster site. In this thesis, design of VTT is introduced and stable rolling locomotion algorithm for VTT is proposed. To achieve self-reconfiguration feature, VTT are composed specially designed members and nodes. VTTs members consist of Spiral Zippers which are novel linear actuators that has high extension ratio, light weight and high strength. VTTs nodes consist of Passive Member-Ends and Master Member-Ends. Passive Member-Ends are linkage type spherical joint with large angle range that can accommodate many members. Master Member-Ends are spherical manipulators that built in Sphere and it move member to change topology of VTT. Rolling locomotion of VTT is achieved by controlling the center of mass by geometric reconfiguration. However, the locomotion planning is complex problem, because VTT is parallel mechanism with high degree of freedom and many constraints, which makes it difficult to predict and avoid constraints for feasible planning. Thus, it needs stable algorithm that can find locomotion trajectory even in complicated and large environment. In addition, since VTT has many sophisticated components, the algorithm must prevent VTT being damaged from ground by tumbling. To meet the requirements, proposed locomotion algorithm is composed of 3 steps; support polygon planning, center of mass planning and node position planning. In support polygon planning, support polygon path is planned by newly proposed random search algorithm, Polygon-Based Random Tree (PRT). In center of mass planning, trajectory of desired projected center of mass is planned by maximizing stability feature. Planned support polygon path and center of mass trajectory guide VTT to have good-conditioned shape which configuration is far from constraints and makes locomotion planning success even in complex and large environment. In node position planning, Non-Impact Rolling locomotion algorithm was developed to plan position of VTTs nodes that prevent damage from the ground while following planned support polygon path and center of mass trajectory. The algorithm was verified by two case study. In case study 1, locomotion planning and simulation was performed considering actual constraints of VTT. To avoid collision between VTT and obstacle, safety space was defined and considered in support polygon planning. The result shows that VTT successfully reaches the goal while avoiding obstacles and satisfying constraints. In case study 2, locomotion planning and simulation was performed in the environment having wide space and narrow passage. Nominal length of VTT was set to be large in wide space to move efficiently, and set to be small in narrow passage to pass through it. The result shows that VTT successfully reaches the goal while changing its nominal length in different terrain.가변 토폴로지 트러스 (Variable Topology Truss, VTT)는 토폴로지와 기하학적 형상의 재구성이 가능한 트러스 구조의 모듈 로봇이다. 본 논문에서는 VTT의 설계 구조를 소개하고 VTT의 안정적인 주행을 알고리즘을 제안한다. VTT는 토폴로지와 기하학적 형상의 재구성을 위해 특수한 구조의 멤버와 노드를 가진다. VTT의 멤버는 높은 압축비, 가벼운 중량, 높은 강도를 가진 신개념 선형 구동기인 스파이럴 지퍼로 구성되어 있다. VTT의 노드는 패시브 멤버 엔드와 마스터 엔드로 구성되어 있다. 패시브 멤버는 링키지 구조의 3 자유도 관절로, 넓은 각도 구동 범위를 가지고 있고 많은 수의 멤버를 연결할 수 있다. 마스터 멤버 엔드는 노드 부의 내장된 구형 매니퓰레이터로, 토폴로지 재구성 시 멤버를 이동시키는데 사용된다. VTT는 기하학적 형상을 변화하여 구르는 움직임을 통해 주행한다. VTT의 주행 알고리즘은 서포트 폴리곤 계획 단계, 무게 중심 계획 단계, 노드 위치 계획 단계로 이루어진다. 서포트 폴리곤 계획 단계에서는 새롭게 제안된 무작위 탐색 (random search) 알고리즘인 Polygon-Based Random Tree (PRT)을 적용해 서포트 폴리곤의 경로를 계획한다. 무게 중심 계획 단계에서는 안정성을 최대화하는 VTT의 무게 중심 궤적을 계획한다. 계획된 서포트 폴리곤 경로와 무게 중심 궤적을 VTT가 제한 조건으로부터 먼 좋은 상태의 형상을 유지하게 하여 복잡한 환경에 대해서도 경로 계획이 실패하지 않고 안정적으로 이루어질 수 있도록 한다. 노드 위치 계획 단계에서는 서포트 폴리곤 경로와 노드 위치의 궤적을 추종하는 노드 위치 궤적을 계획한다. 이 과정에서 비충격 롤링 이동 알고리즘 (Non-Impact Rolling locomotion algorithm)을 적용하여 지면과의 충돌로 인한 충격이 일어나지 않는 궤적을 계획한다. 실제 VTT의 제한 조건을 반영한 모델에 본 알고리즘을 적용하여 시뮬레이션을 수행한 결과, VTT가 모든 제한 조건을 만족하고 장애물을 회피하면서 목표 지점에 도달할 수 있음을 확인하였다.Chapter 1. Introduction 1 1.1 Motivation 1 1.2 Previous Truss Type Modular Robot 4 1.3 Previous Research on VTTs Locomotion 8 1.3.1 Heuristic Based Methods 9 1.3.2 Optimization Based Method 10 1.4 Objectives of Locomotion Algorithm 12 1.5 Contribution of Thesis 13 1.5.1 Introduction to Hardware Design of VTT 13 1.5.2 Stable Rolling Locomotion of VTT 15 Chapter 2. Design of Variable Topology Truss 17 2.1 Member Design 18 2.1.1 Spiral Zipper 20 2.1.2 Tensioner 26 2.2 Node Design 28 2.2.1 Passive Member-End and Sphere 29 2.2.2 Master Member-End 36 2.3 Control System 40 2.4 Node Position Control Experiment 44 Chapter 3. Mathematical Model of Variable Topology Truss 47 3.1 Configuration and Terminology 47 3.2 Inverse Kinematics 50 3.3 Constraints 51 3.4 Stability Criteria 64 Chapter 4. Locomotion Algorithm 66 4.1 Concept of Locomotion Algorithm 67 4.1.1 Method for Successful Planning and Obstacle Avoidance 67 4.1.2 Method to Prevent Damage from the Ground 71 4.1.3 Step of Locomotion Algorithm 72 4.2 Support Polygon Planning 73 4.2.1 Polygon-Based Random Tree (PRT) Algorithm 73 4.2.2 Probabilistic Completeness of PRT Algorithm 79 4.3 Center of Mass Planning 85 4.4 Node Position Planning 86 4.4.1 Concept of Non-Impact Rolling Locomotion 86 4.4.2 Planning Algorithm for Non-Impact Rolling Locomotion 89 4.4.3 Optimization Problem of Moving Phase 94 4.4.4 Optimization Problem of Landing Phase 98 4.4.5 Optimization Problem of Transient Phase 99 Chapter 5. Experimental Verification 100 5.1 Case Study 1: Actual VTT Prototype 101 5.1.1 Simulation Condition 101 5.1.2 Obstacle Avoidance Method 103 5.1.3 Simulation Result 104 5.2 Case Study 2: Environment with Narrow Passage 111 5.2.1 Simulation Condition 111 5.2.2 Support Polygon Planning with Varying Nominal Length 114 5.2.3 Simulation Result 117 Chapter 6. Conclusion 126 Bibliography 129 Abstract in Korean 134Docto

Unified Representation Of Decoupled Dynamic Models For Pendulum-Driven Ball-Shaped Robots

Dynamic models describing the ball-robot motion form the basis for developments in ball-robot mechanics and motion control systems. For this paper, we have conducted a literature review of decoupled forward-motion models for pendulum-driven ball-shaped robots. The existing models in the literature apply several different conventions in system definition and parameter notation. Even if describing the same mechanical system, the diversity in conventions leads into dynamic models with different forms. As a result, it is difficult to compare, reproduce and apply the models available in the literature. Based on the literature review, we reformulate all common variations of decoupled dynamic forward-motion models using a unified notation and formulation. We have verified all reformulated models through simulations, and present the simulation results for a selected model. In addition, we demonstrate the different system behavior resulting from different ways to apply the pendulum reaction torque, a variation that can be found in the literature. For anyone working with the ball-robots, the unified compilation of the reformulated dynamic models provides an easy access to the models, as well as to the related work.Peer reviewe

Parallel robots with unconventional joints to achieve under-actuation and reconfigurability

The aim of the thesis is to define, analyze, and verify through simulations and practical implementations, parallel robots with unconventional joints that allow them to be under-actuated and/or reconfigurable. The new designs will be derived from the: * 6SPS robot (alternatively 6UPS or 6SPU, depending on the implementation) when considering the spatial case (i.e., robots with 3 degrees of freedom of rotation and 3 degrees of freedom of translation). * S-3SPS robot (alternatively S-3UPS or S-3SPU, depending on the implementation) when considering spherical robots (i.e., robots with 3 degrees of freedom of rotation). In both cases, we will see how, through certain geometric transformations, some of the standard joints can be replaced by lockable or non-holonomic joints. These substitutions permit reducing the number of legs (and hence the number of actuators needed to control the robot), without losing the robot's ability to bring its mobile platform to any position and orientation (in case of a spatial robot), or to any orientation (in case of a spherical robot), within its workspace. The expected benefit of these new designs is to obtain parallel robots with: * larger working spaces because the possibility of collisions between legs is reduced, and the number of joints (with their intrinsic range limitations) is also reduced; * lower weight because the number of actuators and joints is reduced; and * lower cost because the number of actuators and controllers is also reduced. The elimination of an actuator and the introduction of a motion constraint reduces in one the dimension of the space of allowed velocities attainable from a given configuration. As a result, it will be necessary, in general, to plan maneuvers to reach the desired configuration for the moving platform. Therefore, the obtained robots will only be suitable for applications where accuracy is required in the final position and a certain margin of error is acceptable in the generated trajectories.El objetivo de esta tesis es definir, analizar y verificar, mediante simulaciones e implementaciones prácticas, robots paralelos con articulaciones no-convencionales con el fin de incorporarles propiedades de sub-actuación y reconfigurabilidad. Los nuevos diseños se basaran en robots paralelos tipo: * 6SPS (alternativamente 6UPS o 6SPU, dependiendo de la implementación) para el caso de robot espacial (es decir, robots con 3 grados de libertad de rotación y de 3 grados de libertad de la traducción). * S-3SPS (alternativamente S-3UPS o S-3SPU, dependiendo de la implementación) para el caso de robot esférico (es decir, robots con 3 grados de libertad de rotación). En ambos casos, veremos cómo, a través de ciertas transformaciones geométricas, algunas de la articulaciones convencionales pueden ser sustituidas por articulaciones bloqueables o no holonómicos. Estas sustituciones permiten la reducción de la número de patas (y por tanto el número de actuadores necesarios para controlar el robot), sin perder la capacidad del robot para llevar su plataforma móvil a cualquier posición y orientación (en el caso de un robot espacial), o para cualquier orientación (en el caso de un robot esférico), dentro de su espacio de trabajo. El beneficio esperado de estos nuevos diseños es la obtención de robots paralelos con: * Espacios de trabajo mayores debido a que la posibilidad de colisiones entre las patas se reduce, y el número de articulaciones (con sus limitaciones intrínsecas de rango) también se reduce; * Menor peso debido a que el número de actuadores y de articulaciones se reduce; y * Un menor coste debido a que el número de actuadores y controladores también se reduce. La eliminación de un actuador y la introducción de una restricción de movimiento reduce, en uno, la dimensión del espacio de velocidades alcanzables para una configuración dada. Como resultado, será necesario, en general, planificar maniobras para llegar a la configuración deseada de la plataforma móvil. Por lo tanto, los robots obtenidos sólo serán adecuados para aplicaciones donde la precisión se requiera en la posición final y exista un cierto margen de error aceptable en las trayectorias generadasPostprint (published version

Parallel robots with unconventional joints to achieve under-actuation and reconfigurability

The aim of the thesis is to define, analyze, and verify through simulations and practical implementations, parallel robots with unconventional joints that allow them to be under-actuated and/or reconfigurable. The new designs will be derived from the: * 6SPS robot (alternatively 6UPS or 6SPU, depending on the implementation) when considering the spatial case (i.e., robots with 3 degrees of freedom of rotation and 3 degrees of freedom of translation). * S-3SPS robot (alternatively S-3UPS or S-3SPU, depending on the implementation) when considering spherical robots (i.e., robots with 3 degrees of freedom of rotation). In both cases, we will see how, through certain geometric transformations, some of the standard joints can be replaced by lockable or non-holonomic joints. These substitutions permit reducing the number of legs (and hence the number of actuators needed to control the robot), without losing the robot's ability to bring its mobile platform to any position and orientation (in case of a spatial robot), or to any orientation (in case of a spherical robot), within its workspace. The expected benefit of these new designs is to obtain parallel robots with: * larger working spaces because the possibility of collisions between legs is reduced, and the number of joints (with their intrinsic range limitations) is also reduced; * lower weight because the number of actuators and joints is reduced; and * lower cost because the number of actuators and controllers is also reduced. The elimination of an actuator and the introduction of a motion constraint reduces in one the dimension of the space of allowed velocities attainable from a given configuration. As a result, it will be necessary, in general, to plan maneuvers to reach the desired configuration for the moving platform. Therefore, the obtained robots will only be suitable for applications where accuracy is required in the final position and a certain margin of error is acceptable in the generated trajectories.El objetivo de esta tesis es definir, analizar y verificar, mediante simulaciones e implementaciones prácticas, robots paralelos con articulaciones no-convencionales con el fin de incorporarles propiedades de sub-actuación y reconfigurabilidad. Los nuevos diseños se basaran en robots paralelos tipo: * 6SPS (alternativamente 6UPS o 6SPU, dependiendo de la implementación) para el caso de robot espacial (es decir, robots con 3 grados de libertad de rotación y de 3 grados de libertad de la traducción). * S-3SPS (alternativamente S-3UPS o S-3SPU, dependiendo de la implementación) para el caso de robot esférico (es decir, robots con 3 grados de libertad de rotación). En ambos casos, veremos cómo, a través de ciertas transformaciones geométricas, algunas de la articulaciones convencionales pueden ser sustituidas por articulaciones bloqueables o no holonómicos. Estas sustituciones permiten la reducción de la número de patas (y por tanto el número de actuadores necesarios para controlar el robot), sin perder la capacidad del robot para llevar su plataforma móvil a cualquier posición y orientación (en el caso de un robot espacial), o para cualquier orientación (en el caso de un robot esférico), dentro de su espacio de trabajo. El beneficio esperado de estos nuevos diseños es la obtención de robots paralelos con: * Espacios de trabajo mayores debido a que la posibilidad de colisiones entre las patas se reduce, y el número de articulaciones (con sus limitaciones intrínsecas de rango) también se reduce; * Menor peso debido a que el número de actuadores y de articulaciones se reduce; y * Un menor coste debido a que el número de actuadores y controladores también se reduce. La eliminación de un actuador y la introducción de una restricción de movimiento reduce, en uno, la dimensión del espacio de velocidades alcanzables para una configuración dada. Como resultado, será necesario, en general, planificar maniobras para llegar a la configuración deseada de la plataforma móvil. Por lo tanto, los robots obtenidos sólo serán adecuados para aplicaciones donde la precisión se requiera en la posición final y exista un cierto margen de error aceptable en las trayectorias generada

Darboux-Frame-Based Parametrization for a Spin-Rolling Sphere on a Plane: A Nonlinear Transformation of Underactuated System to Fully-Actuated Model

This paper presents a new kinematic model based on the Darboux frame for motion control and planning. In this work, we show that an underactuated model of a spin-rolling sphere on a plane with five states and three inputs can be transformed into a fully-actuated one by a given Darboux frame transformation. This nonlinear state transformation establishes a geometric model that is different from conventional state-space ones. First, a kinematic model of the Darboux frame at the contact point of the rolling sphere is established. Next, we propose a virtual surface that is trapped between the sphere and the contact plane. This virtual surface is used for generating arc-length-based inputs for controlling the contact trajectories on the sphere and the plane. Finally, we discuss the controllability of this new model. In the future, we will design a geometric path planning method for the proposed kinematic model.Comment: 17 pages, 7 figures, Accepted at Mechanism and Machine Theory Elsevie