Geometry-aware Manipulability Learning, Tracking and Transfer

Body posture influences human and robots performance in manipulation tasks, as appropriate poses facilitate motion or force exertion along different axes. In robotics, manipulability ellipsoids arise as a powerful descriptor to analyze, control and design the robot dexterity as a function of the articulatory joint configuration. This descriptor can be designed according to different task requirements, such as tracking a desired position or apply a specific force. In this context, this paper presents a novel \emph{manipulability transfer} framework, a method that allows robots to learn and reproduce manipulability ellipsoids from expert demonstrations. The proposed learning scheme is built on a tensor-based formulation of a Gaussian mixture model that takes into account that manipulability ellipsoids lie on the manifold of symmetric positive definite matrices. Learning is coupled with a geometry-aware tracking controller allowing robots to follow a desired profile of manipulability ellipsoids. Extensive evaluations in simulation with redundant manipulators, a robotic hand and humanoids agents, as well as an experiment with two real dual-arm systems validate the feasibility of the approach.Comment: Accepted for publication in the Intl. Journal of Robotics Research (IJRR). Website: https://sites.google.com/view/manipulability. Code: https://github.com/NoemieJaquier/Manipulability. 24 pages, 20 figures, 3 tables, 4 appendice

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

Robustness to external disturbances for legged robots using dynamic trajectory optimisation

In robotics, robustness is an important and desirable attribute of any system, from perception to planning and control. Robotic systems need to handle numerous factors of uncertainty when they are deployed, and the more robust a method is, the fewer chances there are of something going wrong. In planning and control, being robust is crucial to deal with uncertain contact timings and positions, mismatches in the dynamics model of the system, noise in the sensor readings and communication delays. In this thesis, we focus on the problem of dealing with uncertainty and external disturbances applied to the robot. Reactive robustness can be achieved at the control stage using a variety of control schemes. For example, model predictive control approaches are robust against external disturbances thanks to the online high-frequency replanning of the motion being executed. However, taking robustness into account in a proactive way, i.e., during the planning stage itself, enables the adoption of kinematic configurations that allow the system as a whole to better deal with uncertainty and disturbances. To this end, we propose a novel trajectory optimisation framework for robotic systems, ranging from fixed-base manipulators to legged robots, such as humanoids or quadrupeds equipped with arms. We tackle the problem from a first-principles perspective, and define a robustness metric based on the robot’s capabilities, such as the torques available to the system (considering actuator torque limits) and contact stability constraints. We compare our results with other existing approaches and, through simulation and experiments on the real robot, we show that our method is able to plan trajectories that are more robust against external disturbances

Geometry-aware Tracking of Manipulability Ellipsoids

Body posture can greatly influence human performance when carrying out manipulation tasks. Adopting an appropriate pose helps us regulate our motion and strengthen our capability to achieve a given task. This effect is also observed in robotic manipulation where the robot joint configuration affects not only the ability to move freely in all directions in the workspace, but also the capability to generate forces along different axes. In this context, manipulability ellipsoids arise as a powerful descriptor to analyze, control and design the robot dexterity as a function of the articulatory joint configuration. This paper presents a new tracking control scheme in which the robot is requested to follow a desired profile of manipulability ellipsoids, either as its main task or as a secondary objective. The proposed formulation exploits tensor-based representations and takes into account that manipulability ellipsoids lie on the manifold of symmetric positive definite matrices. The proposed mathematical development is compatible with statistical methods providing 4th-order covariances, which are here exploited to reflect the tracking precision required by the task. Extensive evaluations in simulation and two experiments with a real redundant manipulator validate the feasibility of the approach, and show that this control formulation outperforms previously proposed approaches