High speed precision motion strategies for lightweight structures

Work during the recording period proceeded along the lines of the proposal, i.e., three aspects of high speed motion planning and control of flexible structures were explored: fine motion control, gross motion planning and control, and automation using light weight arms. In addition, modeling the large manipulator arm to be used in experiments and theory has lead to some contributions in that area. These aspects are reported below. Conference, workshop and journal submissions, and presentations related to this work were seven in number, and are listed. Copies of written papers and abstracts are included

Multiobjective control of a four-link flexible manipulator: A robust H∞ approach

Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper presents an approach to robust H∞ control of a real multilink flexible manipulator via regional pole assignment. We first show that the manipulator system can be approximated by a linear continuous uncertain model with exogenous disturbance input. The uncertainty occurring in an operating space is assumed to be norm-bounded and enter into both the system and control matrices. Then, a multiobjective simultaneous realization problem is studied. The purpose of this problem is to design a state feedback controller such that, for all admissible parameter uncertainties, the closed-loop system simultaneously satisfies both the prespecified H∞ norm constraint on the transfer function from the disturbance input to the system output and the prespecified circular pole constraint on the closed-loop system matrix. An algebraic parameterized approach is developed to characterize the existence conditions as well as the analytical expression of the desired controllers. Third, by comparing with the traditional linear quadratic regulator control method in the sense of robustness and tracking precision, we provide both the simulation and experimental results to demonstrate the effectiveness and advantages of the proposed approach

Modeling and Control of Flexible Link Manipulators

Autonomous maritime navigation and offshore operations have gained wide attention with the aim of reducing operational costs and increasing reliability and safety. Offshore operations, such as wind farm inspection, sea farm cleaning, and ship mooring, could be carried out autonomously or semi-autonomously by mounting one or more long-reach robots on the ship/vessel. In addition to offshore applications, long-reach manipulators can be used in many other engineering applications such as construction automation, aerospace industry, and space research. Some applications require the design of long and slender mechanical structures, which possess some degrees of flexibility and deflections because of the material used and the length of the links. The link elasticity causes deflection leading to problems in precise position control of the end-effector. So, it is necessary to compensate for the deflection of the long-reach arm to fully utilize the long-reach lightweight flexible manipulators. This thesis aims at presenting a unified understanding of modeling, control, and application of long-reach flexible manipulators. State-of-the-art dynamic modeling techniques and control schemes of the flexible link manipulators (FLMs) are discussed along with their merits, limitations, and challenges. The kinematics and dynamics of a planar multi-link flexible manipulator are presented. The effects of robot configuration and payload on the mode shapes and eigenfrequencies of the flexible links are discussed. A method to estimate and compensate for the static deflection of the multi-link flexible manipulators under gravity is proposed and experimentally validated. The redundant degree of freedom of the planar multi-link flexible manipulator is exploited to minimize vibrations. The application of a long-reach arm in autonomous mooring operation based on sensor fusion using camera and light detection and ranging (LiDAR) data is proposed.publishedVersio

Hybrid Data-Driven and Analytical Model for Kinematic Control of a Surgical Robotic Tool

Accurate kinematic models are essential for effective control of surgical robots. For tendon driven robots, which is common for minimally invasive surgery, intrinsic nonlinearities are important to consider. Traditional analytical methods allow to build the kinematic model of the system by making certain assumptions and simplifications on the nonlinearities. Machine learning techniques, instead, allow to recover a more complex model based on the acquired data. However, analytical models are more generalisable, but can be over-simplified; data-driven models, on the other hand, can cater for more complex models, but are less generalisable and the result is highly affected by the training dataset. In this paper, we present a novel approach to combining analytical and data-driven approaches to model the kinematics of nonlinear tendon-driven surgical robots. Gaussian Process Regression (GPR) is used for learning the data-driven model and the proposed method is tested on both simulated data and real experimental data

Studies on Trajectory Tracking of Two Link Planar Manipulator

In robotic manipulator control situations, high accuracy trajectory tracking is one of the challenging aspects. This is due to nonlinearities in dynamics and input coupling present in the robotic arm. In the present work, a two link planar manipulator revolving in a horizontal plane is considered. Its kinematics, Jacobian analysis, dynamic equations are obtained from modelling. It is proposed to use this manipulator for following a desired trajectory by using an effective control method. Initially, computed torque control scheme is used to obtain the end effector motions. The dynamic equations are solved by numerical method and the joint space results are used to obtain the error and its derivative. This linearized error dynamic control uses constant gains and an attempt is made to obtain a correct set of gains in each error cycle to refine the control performance. A scaled prototype is made with aluminium links and joint servos. A mechatronic system with an arduino microcontroller board is employed to drive the servos in incremental fashion as per the tracking point and its inverse kinematics. The computer results are shown for two trajectories namely a straight line and spline. The errors are reported as a function of time and the corresponding joint torques computed in each time step are plotted. Finally to illustrate the mechatronic control system on the prototype, a path containing three points is considered and corresponding errors and repeatability are presented

Redundant Unilaterally Actuated Kinematic Chains: Modeling and Analysis

Unilaterally Actuated Robots (UAR)s are a class of robots defined by an actuation that is constrained to a single sign. Cable robots, grasping, fixturing and tensegrity systems are certain applications of UARs. In recent years, there has been increasing interest in robotic and other mechanical systems actuated or constrained by cables. In such systems, an individual constraint is applied to a body of the mechanism in the form of a pure force which can change its magnitude but cannot reverse its direction. This uni-directional actuation complicates the design of cable-driven robots and can result in limited performance. Cable Driven Parallel Robot (CDPR)s are a class of parallel mechanisms where the actuating legs are replaced by cables. CDPRs benefit from the higher payload to weight ratio and increased rigidity. There is growing interest in the cable actuation of multibody systems. There are potential applications for such mechanisms where low moving inertia is required. Cable-driven serial kinematic chain (CDSKC) are mechanisms where the rigid links form a serial kinematic chain and the cables are arranged in a parallel configuration. CDSKC benefits from the dexterity of the serial mechanisms and the actuation advantages of cable-driven manipulators. Firstly, the kinematic modeling of CDSKC is presented, with a focus on different types of cable routings. A geometric approach based on convex cones is utilized to develop novel cable actuation schemes. The cable routing scheme and architecture have a significant effect on the performance of the robot resulting in a limited workspace and high cable forces required to perform a desired task. A novel cable routing scheme is proposed to reduce the number of actuating cables. The internal routing scheme is where, in addition to being externally routed, the cable can be re-routed internally within the link. This type of routing can be considered as the most generalized form of the multi-segment pass-through routing scheme where a cable segment can be attached within the same link. Secondly, the analysis for CDSKCs require extensions from single link CDPRs to consider different routings. The conditions to satisfy wrench-closure and the workspace analysis of different multi-link unilateral manipulators are investigated. Due to redundant and constrained actuation, it is possible for a motion to be either infeasible or the desired motion can be produced by an infinite number of different actuation profiles. The motion generation of the CDSKCs with a minimal number of actuating cables is studied. The static stiffness evaluation of CDSKCs with different routing topologies and isotropic stiffness conditions were investigated. The dexterity and wrench-based metrics were evaluated throughout the mechanism's workspace. Through this thesis, the fundamental tools required in studying cable-driven serial kinematic chains have been presented. The results of this work highlight the potential of using CDSKCs in bio-inspired systems and tensegrity robots

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

Dynamics and control of flexible manipulators

Flexible link manipulators (FLM) are well-known for their light mass and small energy consumption compared to rigid link manipulators (RLM). These advantages of FLM are even of greater importance in applications where energy efficiency is crucial, such as in space applications. However, RLM are still preferred over FLM for industrial applications. This is due to the fact that the reliability and predictability of the performance of FLM are not yet as good as those of RLM. The major cause for these drawbacks is link flexibility, which not only makes the dynamic modeling of FLM very challenging, but also turns its end-effector trajectory tracking (EETT) into a complicated control problem. The major objectives of the research undertaken in this project were to develop a dynamic model for a FLM and model-based controllers for the EETT. Therefore, the dynamic model of FLM was first derived. This dynamic model was then used to develop the EETT controllers. A dynamic model of a FLM was derived by means of a novel method using the dynamic model of a single flexible link manipulator on a moving base (SFLMB). The computational efficiency of this method is among its novelties. To obtain the dynamic model, the Lagrange method was adopted. Derivation of the kinetic energy and the calculation of the corresponding derivatives, which are required in the Lagrange method, are complex for the FLM. The new method introduced in this thesis alleviated these complexities by calculating the kinetic energy and the required derivatives only for a SFLMB, which were much simpler than those of the FLM. To verify the derived dynamic model the simulation results for a two-link manipulator, with both links being flexible, were compared with those of full nonlinear finite element analysis. These comparisons showed sound agreement. A new controller for EETT of FLM, which used the singularly perturbed form of the dynamic model and the integral manifold concept, was developed. By using the integral manifold concept the links’ lateral deflections were approximately represented in terms of the rotations of the links and input torques. Therefore the end-effector displacement, which was composed of the rotations of the links and links’ lateral deflections, was expressed in terms of the rotations of the links and input torques. The input torques were then selected to reduce the EETT error. The originalities of this controller, which was based on the singularly perturbed form of the dynamic model of FLM, are: (1) it is easy and computationally efficient to implement, and (2) it does not require the time derivative of links’ lateral deflections, which are impractical to measure. The ease and computational efficiency of the new controller were due to the use of the several properties of the dynamic model of the FLM. This controller was first employed for the EETT of a single flexible link manipulator (SFLM) with a linear model. The novel controller was then extended for the EETT of a class of flexible link manipulators, which were composed of a chain of rigid links with only a flexible end-link (CRFE). Finally it was used for the EETT of a FLM with all links being flexible. The simulation results showed the effectiveness of the new controller. These simulations were conducted on a SFLM, a CRFE (with the first link being rigid and second link being flexible) and finally a two-link manipulator, with both links being flexible. Moreover, the feasibility of the new controller proposed in this thesis was verified by experimental studies carried out using the equipment available in the newly established Robotic Laboratory at the University of Saskatchewan. The experimental verifications were performed on a SFLM and a two-link manipulator, with first link being rigid and second link being flexible.Another new controller was also introduced in this thesis for the EETT of single flexible link manipulators with the linear dynamic model. This controller combined the feedforward torque, which was required to move the end-effector along the desired path, with a feedback controller. The novelty of this EETT controller was in developing a new method for the derivation of the feedforward torque. The feedforward torque was obtained by redefining the desired end-effector trajectory. For the end-effector trajectory redefinition, the summation of the stable exponential functions was used. Simulation studies showed the effectiveness of this new controller. Its feasibility was also proven by experimental verification carried out in the Robotic Laboratory at the University of Saskatchewan