Generation of dynamic motion for anthropomorphic systems under prioritized equality and inequality constraints

In this paper, we propose a solution to compute full-dynamic motions for a humanoid robot, accounting for various kinds of constraints such as dynamic balance or joint limits. As a first step, we propose a unification of task-based control schemes, in inverse kinematics or inverse dynamics. Based on this unification, we generalize the cascade of quadratic programs that were developed for inverse kinematics only. Then, we apply the solution to generate, in simulation, wholebody motions for a humanoid robot in unilateral contact with the ground, while ensuring the dynamic balance on a non horizontal surface

Self-motion control of kinematically redundant robot manipulators

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2012Includes bibliographical references (leaves: 88-92)Text in English; Abstract: Turkish and Englishxvi,92 leavesRedundancy in general provides space for optimization in robotics. Redundancy can be defined as sensor/actuator redundancy or kinematic redundancy. The redundancy considered in this thesis is the kinematic redundancy where the total degrees-of-freedom of the robot is more than the total degrees-of-freedom required for the task to be executed. This provides infinite number of solutions to perform the same task, thus, various subtasks can be carried out during the main-task execution. This work utilizes the property of self-motion for kinematically redundant robot manipulators by designing the general subtask controller that controls the joint motion in the null-space of the Jacobian matrix. The general subtask controller is implemented for various subtasks in this thesis. Minimizing the total joint motion, singularity avoidance, posture optimization for static impact force objectives, which include maximizing/minimizing the static impact force magnitude, and static and moving obstacle (point to point) collision avoidance are the subtasks considered in this thesis. New control architecture is developed to accomplish both the main-task and the previously mentioned subtasks. In this architecture, objective function for each subtask is formed. Then, the gradient of the objective function is used in the subtask controller to execute subtask objective while tracking a given end-effector trajectory. The tracking of the end-effector is called main-task. The SCHUNK LWA4-Arm robot arm with seven degrees-of-freedom is developed first in SolidWorks® as a computer-aided-design (CAD) model. Then, the CAD model is converted to MATLAB® Simulink model using SimMechanics CAD translator to be used in the simulation tests of the controller. Kinematics and dynamics equations of the robot are derived to be used in the controllers. Simulation test results are presented for the kinematically redundant robot manipulator operating in 3D space carrying out the main-task and the selected subtasks for this study. The simulation test results indicate that the developed controller’s performance is successful for all the main-task and subtask objectives

Modeling, Control and Estimation of Reconfigurable Cable Driven Parallel Robots

The motivation for this thesis was to develop a cable-driven parallel robot (CDPR) as part of a two-part robotic device for concrete 3D printing. This research addresses specific research questions in this domain, chiefly, to present advantages offered by the addition of kinematic redundancies to CDPRs. Due to the natural actuation redundancy present in a fully constrained CDPR, the addition of internal mobility offers complex challenges in modeling and control that are not often encountered in literature. This work presents a systematic analysis of modeling such kinematic redundancies through the application of reciprocal screw theory (RST) and Lie algebra while further introducing specific challenges and drawbacks presented by cable driven actuators. It further re-contextualizes well-known performance indices such as manipulability, wrench closure quality, and the available wrench set for application with reconfigurable CDPRs. The existence of both internal redundancy and static redundancy in the joint space offers a large subspace of valid solutions that can be condensed through the selection of appropriate objective priorities, constraints or cost functions. Traditional approaches to such redundancy resolution necessitate computationally expensive numerical optimization. The control of both kinematic and actuation redundancies requires cascaded control frameworks that cannot easily be applied towards real-time control. The selected cost functions for numerical optimization of rCDPRs can be globally (and sometimes locally) non-convex. In this work we present two applied examples of redundancy resolution control that are unique to rCDPRs. In the first example, we maximize the directional wrench ability at the end-effector while minimizing the joint torque requirement by utilizing the fitness of the available wrench set as a constraint over wrench feasibility. The second example focuses on directional stiffness maximization at the end-effector through a variable stiffness module (VSM) that partially decouples the tension and stiffness. The VSM introduces an additional degrees of freedom to the system in order to manipulate both reconfigurability and cable stiffness independently. The controllers in the above examples were designed with kinematic models, but most CDPRs are highly dynamic systems which can require challenging feedback control frameworks. An approach to real-time dynamic control was implemented in this thesis by incorporating a learning-based frameworks through deep reinforcement learning. Three approaches to rCDPR training were attempted utilizing model-free TD3 networks. Robustness and safety are critical features for robot development. One of the main causes of robot failure in CDPRs is due to cable breakage. This not only causes dangerous dynamic oscillations in the workspace, but also leads to total robot failure if the controllability (due to lack of cables) is lost. Fortunately, rCDPRs can be utilized towards failure tolerant control for task recovery. The kinematically redundant joints can be utilized to help recover the lost degrees of freedom due to cable failure. This work applies a Multi-Model Adaptive Estimation (MMAE) framework to enable online and automatic objective reprioritization and actuator retasking. The likelihood of cable failure(s) from the estimator informs the mixing of the control inputs from a bank of feedforward controllers. In traditional rigid body robots, safety procedures generally involve a standard emergency stop procedure such as actuator locking. Due to the flexibility of cable links, the dynamic oscillations of the end-effector due to cable failure must be actively dampened. This work incorporates a Linear Quadratic Regulator (LQR) based feedback stabilizer into the failure tolerant control framework that works to stabilize the non-linear system and dampen out these oscillations. This research contributes to a growing, but hitherto niche body of work in reconfigurable cable driven parallel manipulators. Some outcomes of the multiple engineering design, control and estimation challenges addressed in this research warrant further exploration and study that are beyond the scope of this thesis. This thesis concludes with a thorough discussion of the advantages and limitations of the presented work and avenues for further research that may be of interest to continuing scholars in the community

Numerical computation and avoidance of manipulator singularities

This thesis develops general solutions to two open problems of robot kinematics: the exhaustive computation of the singularity set of a manipulator, and the synthesis of singularity-free paths between given configurations. Obtaining proper solutions to these problems is crucial, because singularities generally pose problems to the normal operation of a robot and, thus, they should be taken into account before the actual construction of a prototype. The ability to compute the whole singularity set also provides rich information on the global motion capabilities of a manipulator. The projections onto the task and joint spaces delimit the working regions in such spaces, may inform on the various assembly modes of the manipulator, and highlight areas where control or dexterity losses can arise, among other anomalous behaviour. These projections also supply a fair view of the feasible movements of the system, but do not reveal all possible singularity-free motions. Automatic motion planners allowing to circumvent problematic singularities should thus be devised to assist the design and programming stages of a manipulator. The key role played by singular configurations has been thoroughly known for several years, but existing methods for singularity computation or avoidance still concentrate on specific classes of manipulators. The absence of methods able to tackle these problems on a sufficiently large class of manipulators is problematic because it hinders the analysis of more complex manipulators or the development of new robot topologies. A main reason for this absence has been the lack of computational tools suitable to the underlying mathematics that such problems conceal. However, recent advances in the field of numerical methods for polynomial system solving now permit to confront these issues with a very general intention in mind. The purpose of this thesis is to take advantage of this progress and to propose general robust methods for the computation and avoidance of singularities on non-redundant manipulators of arbitrary architecture. Overall, the work seeks to contribute to the general understanding on how the motions of complex multibody systems can be predicted, planned, or controlled in an efficient and reliable way.Aquesta tesi desenvolupa solucions generals per dos problemes oberts de la cinemàtica de robots: el càlcul exhaustiu del conjunt singular d'un manipulador, i la síntesi de camins lliures de singularitats entre configuracions donades. Obtenir solucions adequades per aquests problemes és crucial, ja que les singularitats plantegen problemes al funcionament normal del robot i, per tant, haurien de ser completament identificades abans de la construcció d'un prototipus. La habilitat de computar tot el conjunt singular també proporciona informació rica sobre les capacitats globals de moviment d'un manipulador. Les projeccions cap a l'espai de tasques o d'articulacions delimiten les regions de treball en aquests espais, poden informar sobre les diferents maneres de muntar el manipulador, i remarquen les àrees on poden sorgir pèrdues de control o destresa, entre d'altres comportaments anòmals. Aquestes projeccions també proporcionen una imatge fidel dels moviments factibles del sistema, però no revelen tots els possibles moviments lliures de singularitats. Planificadors de moviment automàtics que permetin evitar les singularitats problemàtiques haurien de ser ideats per tal d'assistir les etapes de disseny i programació d'un manipulador. El paper clau que juguen les configuracions singulars ha estat àmpliament conegut durant anys, però els mètodes existents pel càlcul o evitació de singularitats encara es concentren en classes específiques de manipuladors. L'absència de mètodes capaços de tractar aquests problemes en una classe suficientment gran de manipuladors és problemàtica, ja que dificulta l'anàlisi de manipuladors més complexes o el desenvolupament de noves topologies de robots. Una raó principal d'aquesta absència ha estat la manca d'eines computacionals adequades a les matemàtiques subjacents que aquests problemes amaguen. No obstant, avenços recents en el camp de mètodes numèrics per la solució de sistemes polinòmics permeten ara enfrontar-se a aquests temes amb una intenció molt general en ment. El propòsit d'aquesta tesi és aprofitar aquest progrés i proposar mètodes robustos i generals pel càlcul i evitació de singularitats per manipuladors no redundants d'arquitectura arbitrària. En global, el treball busca contribuir a la comprensió general sobre com els moviments de sistemes multicos complexos es poden predir, planificar o controlar d'una manera eficient i segur

Contribution à la planification de mouvement pour robots humanoïdes

cette thèse porte sur des algorithmes de contrôle et de planification de mouvements pour les robots humanoïdes. Le grand nombre de paramètres caractérisant ces systèmes a conduit au développement de méthodes numériques, d'abord appliquées aux bras manipulateurs et récemment adaptées pour les structures plus complexes. On relève particulièrement les formalismes de commande cinématique et dynamique par priorité qui permettent de produire un mouvement selon une hiérarchie préétablie des tâches. Au cours de ce travail, nous avons identifié le besoin d'étendre ce formalisme afin de tenir compte de contraintes unilatérales. Nous nous sommes par ailleurs intéressés à la planification de la locomotion en fonction des tâches. Nous proposons une modélisation jointe du robot et de sa trajectoire de marche comme une structure articulée unique saisissant à la fois les degrés de liberté actionnés (articulations motorisées du robot) et non actionnés (positionnement absolu dans l'espace). L'ensemble de ces algorithmes, qui seront longuement illustrés, ont été implémentés au sein du projet HPP (Humanoid Path Planner) et validés sur le robot humanoïde HRP-2.this thesis is related to motion control and planning algorithms for humanoid robots. For such highly-parameterized systems, numerical methods are well adapted and have thus been the enter of increasing attention in the recent years. Among the prominent numerical schemes, we recognized the prioritized inverse kinematics and dynamics frameworks to hold key features to plan motion for humanoid robots, such as the possibility to control the motion while enforcing a strict priority order among tasks. We have, however, identified a lack of support of strict priority enforcement when inequality constraints are to be accounted for in the numerical schemes and we were successful in proposing a solution to this shortcoming. We also considered the problem of planning bipedal locomotion according to any given tasks. We proposed to model this problem as an inverse kinematics problem, by considering the kinematic structure of the robot and its walk path as a single unified structure that captures both the degrees of freedom of the robot which are actuated (motorized joints) and those which are not (position and orientation in space). The presented algorithms, which will be abundantly illustrated, have been implemented within the HPP (Humanoid Path Planner) project and validated on the humanoid robot HRP-2

Workspace and singularity determination of a 7-DoF wrist-partitioned serial manipulator towards graffiti painting

Els robots estan sent utilitzats, cada cop més, en la realització de tasques en la indústria. Molts d'ells també són dissenyats pensats per a realitzar les tasques de la llar. En general, els robots són dissenyats per a facilitar el dia a dia del éssers humans. Però quan es tracta d'obres artístiques, és menys comú trobar-se robots realitzant-les. Nosaltres pretenem sortir de la norma mitjançant l'ús d'un robot per a pintar un grafiti. La motivació per a aconseguir-ho convergeix en la formulació de dues preguntes: "Quin és el volum de treball d'un robot, quan l'orientació del seu efector final està fixada?" i "Donat un pla arbitrari, quina és la major àrea de treball lliure de singularitats en aquest?" Aquesta tesi proposa un mètode per a l'obtenció de les singularitats de posició en un pla qualsevol d'un manipulador serial amb un canell esfèric. El mètode s'ha obtingut mitjançant la combinació d'un mètode de determinació de singularitats de posició, el qual està basat en una tècnica per al decoplat de manipuladors que presenten un canell esfèric, i un algorisme branch-and-prune per a la resolució de sistemes d'equacions. S'ha obtingut el volum de treball d'un manipulador serial de 7 graus de llibertat a través d'un enfocament de cinemàtica directa. Es presenta una metodologia per a obtenir el volum de treball del manipulador serial quan el seu efector final té l'orientació constant i s'aplica per a obtenir aproximacions per al cas de certes orientacions. Es mostra com les singularitats poden ser analitades a través de separar-les en singularitats de posició i d'orientació. el mètode proposat formula i resol les equacions que determinen les singularitats de posició. Pel que fa a les singularitats d'orientació, es mostra que poden ser evitades sense perdre una quantitat significant de volum de treball, des del punt de vista de la posició.Los robots estén siendo utilizados, cada vez más, en la realización de tareas en la industria. Muchos de ellos también son diseñados pensados para realizar las tareas del hogar. En general, los robots son diseñados para facilitar el día a día de los seres humanos. Pero cuando se trata de obras artíticas, es menos común encontrarse a robots realizándolas. Nosotros pretendemos salirnos de lo común mediante el uso de un robot para pintar un grafiti. La motivación por lograrlo converge en la formulación de dos preguntas: "¿Cuál es el volumen de trabajo de un robot, cuando la orientación de su efector final está fijada?" y "Dado un plano arbitrario, ¿cuál es la mayor área de trabajo libre de singularidades en éste?" Esta tesis propone un método para la obtención de las singularidades de posición en un plano cualquiera de un manipulador serial con una muñeca esférica. El método ha sido obtenido mediante la combinación de un método de determinación de singularidades de posición, el cual está basado en una técnica para el decoplado de manipuladores que presentan una muñeca esférica, y un algoritmo branch-and-prune para la resolución de sistemas de ecuaciones. Se ha obtenido el volumen de trabajo de un manipulador serial de 7 grados de libertad a través de un enfoque de cinemática directa. Se presenta la metodología para obtener el volumen de trabajo del manipulador serial cuando su efector final tiene una orientación constante y se aplica para obtener aproximaciones para el caso de ciertas orientaciones. Se muestra cómo las singularidades pueden ser analizadas a través de separarlas en singularidades de posición y de orientación. El método propuesto formula y resuelve las ecuaciones que determinan las singularidades de posición. En cuanto a las singularidades de orientación, se muestra que pueden ser evitadas sin perder una cantidad significante de volumen de trabajo, desde el punto de vista de la posición.Robots are overtaking every day more tasks in the industry. A lot of them are even designed for performing household chores. In general, robots are designed to facilitate the day-to-day of human beings. But when it comes to artistic tasks, it is less usual to see robots performing them. We pretend to stay out of the crowd by using a robot to paint a graffiti. The motivation to achieve this task converges into the statement of two questions: "What is the workspace of a robot, when the orientation of its end-effector is fixed?" and "For a given plane, what is the largest singularity free surface on it?". This thesis proposes a method for the computation of the position singularities of a wrist-partitioned serial manipulator for a given plane. The method is obtained from the combination of a position singularity determination method, which is based on the decoupling technique of a wrist-partitioned manipulator, and a branch-and-prune algorithm for the resolution of systems of equations. The workspace of a 7-DoF serial manipulator is obtained by a forward kinematics approach. A methodology to obtain the constant orientation workspace of a serial manipulator is presented and applied to get approximations for some specific orientations. It is shown how singularities can be analyzed by decoupling them into position singularities and orientation singularities. The proposed method formulates and solves the equation that determines the position singularities. In the case of the orientation singularities, it is shown that they can be avoided without losing a significant amount of the workspace's volume, from the point of view of the position.Outgoin

Dynamic Active Constraints for Surgical Robots using Vector Field Inequalities

Robotic assistance allows surgeons to perform dexterous and tremor-free procedures, but robotic aid is still underrepresented in procedures with constrained workspaces, such as deep brain neurosurgery and endonasal surgery. In these procedures, surgeons have restricted vision to areas near the surgical tooltips, which increases the risk of unexpected collisions between the shafts of the instruments and their surroundings. In this work, our vector-field-inequalities method is extended to provide dynamic active-constraints to any number of robots and moving objects sharing the same workspace. The method is evaluated with experiments and simulations in which robot tools have to avoid collisions autonomously and in real-time, in a constrained endonasal surgical environment. Simulations show that with our method the combined trajectory error of two robotic systems is optimal. Experiments using a real robotic system show that the method can autonomously prevent collisions between the moving robots themselves and between the robots and the environment. Moreover, the framework is also successfully verified under teleoperation with tool-tissue interactions.Comment: Accepted on T-RO 2019, 19 Page

Parallel Manipulators

In recent years, parallel kinematics mechanisms have attracted a lot of attention from the academic and industrial communities due to potential applications not only as robot manipulators but also as machine tools. Generally, the criteria used to compare the performance of traditional serial robots and parallel robots are the workspace, the ratio between the payload and the robot mass, accuracy, and dynamic behaviour. In addition to the reduced coupling effect between joints, parallel robots bring the benefits of much higher payload-robot mass ratios, superior accuracy and greater stiffness; qualities which lead to better dynamic performance. The main drawback with parallel robots is the relatively small workspace. A great deal of research on parallel robots has been carried out worldwide, and a large number of parallel mechanism systems have been built for various applications, such as remote handling, machine tools, medical robots, simulators, micro-robots, and humanoid robots. This book opens a window to exceptional research and development work on parallel mechanisms contributed by authors from around the world. Through this window the reader can get a good view of current parallel robot research and applications

안전한 재구성 로봇 시스템: 설계, 프로그래밍 및 반응형 경로계획

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 기계항공공학부, 2020. 8. 박종우.The next generation of robots are being asked to work in close proximity to humans. At the same time, the robot should have the ability to change its topology to flexibly cope with various tasks. To satisfy these two requirements, we propose a novel modular reconfi gurable robot and accompanying software architecture, together with real-time motion planning algorithms to allow for safe operation in unstructured dynamic environments with humans. Two of the key innovations behind our modular manipulator design are a genderless connector and multi-dof modules. By making the modules connectable regardless of the input/output directions, a genderless connector increases the number of possible connections. The developed genderless connector can transmit as much load as necessary to an industrial robot. In designing two-dof modules, an offset between two joints is imposed to improve the overall integration and the safety of the modules. To cope with the complexity in modeling due to the genderless connector and multi-dof modules, a programming architecture for modular robots is proposed. The key feature of the proposed architecture is that it efficiently represents connections of multi-dof modules only with connections between modules, while existing architectures should explicitly represent all connections between links and joints. The data structure of the proposed architecture contains properties of tree-structured multi-dof modules with intra-module relations. Using the data structure and connection relations between modules, kinematic/dynamic parameters of connected modules can be obtained through forward recursion. For safe operation of modular robots, real-time robust collision avoidance algorithms for kinematic singularities are proposed. The main idea behind the algorithms is generating control inputs that increase the directional manipulability of the robot to the object direction by reducing directional safety measures. While existing directional safety measures show undesirable behaviors in the vicinity of the kinematic singularities, the proposed geometric safety measure generates stable control inputs in the entire joint space. By adding the preparatory input from the geometric safety measure to the repulsive input, a hierarchical collision avoidance algorithm that is robust to kinematic singularity is implemented. To mathematically guarantee the safety of the robot, another collision avoidance algorithm using the invariance control framework with velocity-dependent safety constraints is proposed. When the object approached the robot from a singular direction, the safety constraints are not satis ed in the initial state of the robot and the safety cannot be guaranteed using the invariance control. By proposing a control algorithm that quickly decreases the preparatory constraints below thresholds, the robot re-enters the constraint set and avoids collisions using the invariance control framework. The modularity and safety of the developed reconfi gurable robot is validated using a set of simulations and hardware experiments. The kinematic/dynamic model of the assembled robot is obtained in real-time and used to accurately control the robot. Due to the safe design of modules with o sets and the high-level safety functions with collision avoidance algorithms, the developed recon figurable robot has a broader safe workspace and wider ranger of safe operation speed than those of cooperative robots.다음 세대의 로봇은 사람과 가까이에서 협업할 수 있는 기능을 가져야한다. 그와 동시에, 로봇은 다양하게 변하는 작업에 대해 유연하게 대처할 수 있도록 자신의 구조를 바꾸는 기능을 가져야 한다. 이러한 두 가지 요구조건을 만족시키기 위해, 본 논문에서는 새로운 모듈라 로봇 시스템과 프로그래밍 아키텍쳐를 제시하고, 사람이 존재하는 동적 환경에서 안전한 로봇의 운용을 위한 실시한 경로 계획 알고리즘을 제시한다. 개발된 모듈라 로봇의 두 가지 핵심적인 혁신성은 무성별 커넥터와 다자유도 모듈에서 찾을 수 있다. 입력/출력 방향에 상관 없이 모듈이 연결될 수 있도록 함으로써, 무성별 커넥터는 결합 가능한 경우의 수를 늘릴 수 있다. 개발된 무성별 커넥터는 산업용 로봇에서 요구되는 충분한 부하를 견딜 수 있도록 설계되었다. 2 자유도 모듈의 설계에서 두 축 사이에 오프셋을 가지도록 함으로써 전체적인 완성도 및 안전도를 증가시켰다. 무성별 커넥터와 다자유도 모듈로 인한 모델링의 복잡성에 대응하기 위해, 일반적인 모듈라 로봇을 위한 소프트웨어 아키텍쳐를 제안하였다. 기존 모듈라 로봇의 연결을 나타내는 방법이 모든 링크와 조인트 사이의 연결 관계를 별도로 나타내야하는 것과 다르게, 제안된 아키텍쳐는 모듈들 사이의 연결관계만을 나타냄으로써 효율적인 다자유도 모듈의 연결관계를 나타낼 수 있다는 것을 특징으로 한다. 이를 위해 트리 구조를 가지는 일반적인 다자유도 모듈의 성질을 나타내는 데이터 구조를 정의하였다. 모듈들 사이의 연결관계 및 데이터 구조를 이용하여, 정확한 기구학/동역학 모델 파라미터를 얻어내는 순방향 재귀 알고리즘을 구현하였다. 모듈라 로봇의 안전한 운용을 위해, 기구학적 특이점에 강건한 실시간 충돌회피 알고리즘을 제안하였다. 방향성 안전도를 줄이는 방향의 제어 입력을 생성하여 물체 방향으로의 로봇 방향성 매니퓰러빌리티를 증가시키는 것이 제안한 알고리즘의 핵심이다. 기존의 방향성 안전도가 기구학적 특이점 근처에서 원하지 않는 성질을 가지는 것과는 반대로, 제안한 기하학적 안전도는 전체 조인트 공간에서 안정적인 제어 입력을 생성한다. 이 기하학적 안전도를 이용하여, 기구학적 특이점에 강건한 계층적 충돌회피 알고리즘을 구현하였다. 수학적으로 로봇의 안전도를 보장하기 위해, 상대속도에 종속적인 안전 제약조건을 가지는 불변 제어 프레임워크을 이용하여 또 하나의 충돌 회피 알고리즘을 제안하였다. 물체가 특이점 방향으로부터 로봇에 접근할 때, 로봇의 초기 상태에서 안전 제약조건을 만족시키지 못하게 되어 불변제어를 적용할 수 없게 된다. 준비 제약조건을 빠르게 임계점 아래로 감소시키는 알고리즘을 적용함으로써, 로봇은 제약조건 집합에 다시 들어가고 불변 제어 방법을 이용하여 충돌을 회피할 수 있게 된다. 개발된 재구성 로봇의 모듈라리티와 안전도는 일련의 시뮬레이션과 하드웨어 실험을 통해 검증되었다. 실시간으로 조립된 로봇의 기구학/동역학 모델을 얻어내 정밀 제어에 사용하였다. 안전한 모듈 디자인과 충돌 회피 등의 고차원 안전 기능을 통하여, 개발된 재구성 로봇은 기존 협동로봇보다 넓은 안전한 작업공간과 작업속도를 가진다.1 Introduction 1 1.1 Modularity and Recon gurability 1 1.2 Safe Interaction 4 1.3 Contributions of This Thesis 9 1.3.1 A Recon gurable Modular Robot System with Bidirectional Modules 9 1.3.2 A Modular Robot Software Programming Architecture 10 1.3.3 Anticipatory Collision Avoidance Planning 11 1.4 Organization of This Thesis 14 2 Design and Prototyping of the ModMan 17 2.1 Genderless Connector 18 2.2 Modules for ModMan 21 2.2.1 Joint Modules 21 2.2.2 Link and Gripper Modules 25 2.3 Experiments 26 2.3.1 System Setup 26 2.3.2 Repeatability Comparison with Non-recon gurable Robot Manipulators 28 2.3.3 E ect of the O set in Two-dof Modules 30 2.4 Conclusion 32 3 A Programming Architecture for Modular Recon gurable Robots 33 3.1 Data Structure for Multi-dof Joint Modules 34 3.2 Automatic Kinematic Modeling 37 3.3 Automatic Dynamic Modeling 40 3.4 Flexibility in Manipulator 42 3.5 Experiments 45 3.5.1 System Setup 46 3.5.2 Recon gurability 46 3.5.3 Pick-and-Place with Vision Sensors 48 3.6 Conclusion 49 4 A Preparatory Safety Measure for Robust Collision Avoidance 51 4.1 Preliminaries on Manipulability and Safety 52 4.2 Analysis on Reected Mass 56 4.3 Manipulability Control on S+(1;m) 60 4.3.1 Geometry of the Group of Positive Semi-de nite Matrices 60 4.3.2 Rank-One Manipulability Control 63 4.4 Collision Avoidance with Preparatory Action 65 4.4.1 Repulsive and Preparatory Potential Functions 65 4.4.2 Hierarchical Control and Task Relaxation 67 4.5 Experiments 70 4.5.1 Manipulability Control 71 4.5.2 Collision Avoidance 75 4.6 Conclusion 82 5 Collision Avoidance with Velocity-Dependent Constraints 85 5.1 Input-Output Linearization 87 5.2 Invariance Control 89 5.3 Velocity-Dependent Constraints for Robot Safety 90 5.3.1 Velocity-Dependent Repulsive Constraints 90 5.3.2 Preparatory Constraints 92 5.3.3 Corrective Control for Dangerous Initial State 93 5.4 Experiment 95 5.5 Conclusion 98 6 Conclusion 101 6.1 Overview of This Thesis 101 6.2 Future Work 104 Appendix A Appendix 107 A.1 Preliminaries on Graph Theory 107 A.2 Lie-Theoretic Formulations of Robot Kinematics and Dynamics 108 A.3 Derivatives of Eigenvectors and Eigenvalues 110 A.4 Proof of Proposition Proposition 4.1 111 A.5 Proof of Triangle Inequality When p = 1 114 A.6 Detailed Conditions for a Danger Field 115 Bibliography 117 Abstract 127Docto