Bipedal Hopping: Reduced-order Model Embedding via Optimization-based Control

This paper presents the design and validation of controlling hopping on the 3D bipedal robot Cassie. A spring-mass model is identified from the kinematics and compliance of the robot. The spring stiffness and damping are encapsulated by the leg length, thus actuating the leg length can create and control hopping behaviors. Trajectory optimization via direct collocation is performed on the spring-mass model to plan jumping and landing motions. The leg length trajectories are utilized as desired outputs to synthesize a control Lyapunov function based quadratic program (CLF-QP). Centroidal angular momentum, taking as an addition output in the CLF-QP, is also stabilized in the jumping phase to prevent whole body rotation in the underactuated flight phase. The solution to the CLF-QP is a nonlinear feedback control law that achieves dynamic jumping behaviors on bipedal robots with compliance. The framework presented in this paper is verified experimentally on the bipedal robot Cassie.Comment: 8 pages, 7 figures, accepted by IROS 201

로봇 시스템의 설계 및 동작 동시 최적화

학위논문 (석사) -- 서울대학교 대학원 : 공과대학 기계공학부, 2020. 8. 박종우.A robot design has the potential for numerous combinations of the components such as the actuators, links, joints, etc. Therefore, a process of finding a good design is a challenging problem even for the robot experts. To overcome this difficulty, we present an optimization framework for the morphological shape of a robot, considering its motion. Both the design and motion parameters can be simultaneously optimized for specific tasks by our methodology. In the space where the design and motion parameters are combined, our framework seeks the steepest direction that reduces the objective function on the constraint manifold. To overcome the flaws of the previous studies, we utilize the recently discovered recursive differential dynamics, which informs of the analytic relationship between the variation of joint torques and design parameters, thus our framework brings faster and more accurate optimization results. We validate our optimization framework through two numerical experiments: the 2-R planar manipulator with a given end-effector trajectory and the quadruped robot with a locomotion task.로봇 디자인에는 액츄에이터, 링크, 관절 등과 같은 구성요소의 수많은 조합 가능성이 존재한다. 따라서, 좋은 로봇 디자인을 찾는 과정은 전문가에게도 어려운 문제이다. 위 문제점을 극복하기 위해 로봇의 동작을 고려하여 형태를 최적화하는 방법론을 제시한다. 제시된 방법론을 통해 특정 작업을 위한 로봇 형태 및 동작의 동시 최적화가 가능하다. 위 방법론은 형태 및 동작 변수가 결합된 공간 상에서 목적함수를 가장 많이 감소시키는 구속조건 매니폴드 상에서의 방향을 찾아 최적화를 진행한다. 이전 연구들의 결점을 극복하기 위해 우리는 최근 개발된 반복 미분 동역학(recursive differential dynamics) 알고리즘을 사용한다. 이 알고리즘을 통해 관절 토크 변화와 형태 변화 사이의 해석적 관계를 계산할 수 있다. 따라서, 제시된 방법론을 사용하면 더욱 빠르고 정확한 최적화 결과를 도출할 수 있다. 총 두 가지 수치적 실험을 통해 위 최적화 방법론을 검증하였다: 엔드이펙터가 주어진 궤적을 추종하는 2축 평면 매니퓰레이터, 4족로봇의 보행작업.1 Introduction 1 1.1 Design Optimization of Robotic Devices 1 1.2 Limitations of Previous Works 4 1.3 Main Contributions of This Thesis 5 2 Preliminaries 7 2.1 Lie Group Theory 7 2.1.1 SO(3) and SE(3) 8 2.1.2 Twists and Wrenches 10 2.1.3 Adjoint Mappings 10 2.2 Rigid Body Dynamics 11 2.2.1 Dynamics of a Single Rigid Body 11 2.2.2 Dynamics of Open Chains 12 2.2.3 Dynamics of Floating Bodies 14 2.3 Recursive Differential Dynamics 15 3 Simultaneous Design and Motion Optimization 18 3.1 Problem Definition 18 3.2 Optimization Parameters 20 3.2.1 Design Parameters 20 3.2.2 Motion Parameters 23 3.2.3 Constraints 24 3.2.4 Inertial Changes 26 3.3 Optimization Algorithm Description 27 4 Numerical Experiments31 4.1 2-R Planar Manipulator 31 4.1.1Experimental Settings 31 4.1.2Optimization Results 33 4.2 Quadruped Robot 36 4.2.1Experimental Settings 37 4.2.2Optimization Results 39 5 Conclusion 44 A Appendix 46 A.1 Local parametrization of the design 46 A.2 Design rule for the link 48 A.3 Derivative of the constraints 51 A.3.1 End-effector trajectory 51 A.3.2 Equations of motion of the base for quadruped robots 52 A.4 Laikago Specification 53 Bibliography 55 국문초록 60Maste

A Maple Toolchain for Rigid Body Dynamics of Serial, Hybrid and Parallel Robots

A new Maple toolchain for generating rigid body dynamics in symbolic form for robot manipulators is presented. The peculiarity compared to existing tools lies in the framework of Bash scripts controlling the full workflow of the toolchain with a high degree of automation. The optimized Matlab code generated by Maple is automatically converted to function files with proper documentation and input assertions. This renders manual post-processing of the results unnecessarily. The focus of the paper is on the implemented unit-testing framework according to the method of test-driven development. By providing the test framework together with the generated code in a stand-alone version, a good test coverage and a good software quality can be achieved. The results of the open source project provide a basis for dynamics simulations for robot dimensional synthesis or in model-based control of robot manipulators in research or in industrial context. The general software approach can be applied to other fields where theoretical models are derived with Maple

Design, analysis and kinematic control of highly redundant serial robotic arms

The use of robotic manipulators in industry has grown in the last decades to improve and speed up industrial processes. Industrial manipulators started to be investigated for machining tasks since they can cover larger workspaces, increasing the range of achievable operations and improving flexibility. The company Nimbl’Bot developed a new mechanism, or module, to build stiffer flexible serial modular robots for machining applications. This manipulator is a kinematic redundant robot with 21 degrees of freedom. This thesis thoroughly analysis the Nimbl’Bot robot features and is divided into three main topics. The first topic regards using a task priority kinematic redundancy resolution algorithm for the Nimbl’Bot robot tracking trajectory while optimizing its kinetostatic performances. The second topic is the kinematic redundant robot design optimization with respect to a desired application and its kinetostatic performance. For the third topic, a new workspace determination algorithm is proposed for kinematic redundant manipulators. Several simulation tests are proposed and tested on some Nimbl’Bot robot designs for each subjects

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

Geometric origin of mechanical properties of granular materials

Some remarkable generic properties, related to isostaticity and potential energy minimization, of equilibrium configurations of assemblies of rigid, frictionless grains are studied. Isostaticity -the uniqueness of the forces, once the list of contacts is known- is established in a quite general context, and the important distinction between isostatic problems under given external loads and isostatic (rigid) structures is presented. Complete rigidity is only guaranteed, on stability grounds, in the case of spherical cohesionless grains. Otherwise, the network of contacts might deform elastically in response to load increments, even though grains are rigid. This sets an uuper bound on the contact coordination number. The approximation of small displacements (ASD) allows to draw analogies with other model systems studied in statistical mechanics, such as minimum paths on a lattice. It also entails the uniqueness of the equilibrium state (the list of contacts itself is geometrically determined) for cohesionless grains, and thus the absence of plastic dissipation. Plasticity and hysteresis are due to the lack of such uniqueness and may stem, apart from intergranular friction, from small, but finite, rearrangements, in which the system jumps between two distinct potential energy minima, or from bounded tensile contact forces. The response to load increments is discussed. On the basis of past numerical studies, we argue that, if the ASD is valid, the macroscopic displacement field is the solution to an elliptic boundary value problem (akin to the Stokes problem).Comment: RevTex, 40 pages, 26 figures. Close to published paper. Misprints and minor errors correcte

Appropriate Design of Parallel Manipulators

International audienceAlthough parallel structures have found a niche market in many applications such as machine tools, telescope positioning or food packaging, they are not as successful as expected. The main reason of this relative lack of success is that the study and hardware of parallel structures have clearly not reached the same level of completeness than the one of serial structures. Among the main issues that have to be addressed, the design problem is crucial. Indeed, the performances that can be expected from a parallel robot are heavily dependent upon the choice of the mechanical structure and even more from its dimensioning. In this chapter, we show that classical design methodologies are not appropriate for such closed-loop mechanism and examine what alternatives are possible