A comparison study of the numerical integration methods in the trajectory tracking application of redundant robot manipulators

Differential kinematic has a wide range application area in robot kinematics. The main advantage of the differential kinematic is that it can be easily implemented any kind of mechanisms. In differential kinematic method, Jacobian is used as a mapping operator in the velocity space. The joint velocities are required to be integrated to obtain the pose of the robot manipulator. This integration can be evaluated by using numerical integration methods, since the inverse kinematic equations are highly complex and nonlinear. Thus, the performances of the numerical integration methods affect the trajectory tracking application. This paper compares the performances of numerical integration methods in the trajectory tracking application of redundant robot manipulators. Four different and widely used numerical integration methods are implemented to the trajectory tracking application of the 7-DOF redundant robot manipulator named PA-10 and simulation results are given

Contact aware robust semi-autonomous teleoperation of mobile manipulators

In the context of human-robot collaboration, cooperation and teaming, the use of mobile manipulators is widespread on applications involving unpredictable or hazardous environments for humans operators, like space operations, waste management and search and rescue on disaster scenarios. Applications where the manipulator's motion is controlled remotely by specialized operators. Teleoperation of manipulators is not a straightforward task, and in many practical cases represent a common source of failures. Common issues during the remote control of manipulators are: increasing control complexity with respect the mechanical degrees of freedom; inadequate or incomplete feedback to the user (i.e. limited visualization or knowledge of the environment); predefined motion directives may be incompatible with constraints or obstacles imposed by the environment. In the latter case, part of the manipulator may get trapped or blocked by some obstacle in the environment, failure that cannot be easily detected, isolated nor counteracted remotely. While control complexity can be reduced by the introduction of motion directives or by abstraction of the robot motion, the real-time constraint of the teleoperation task requires the transfer of the least possible amount of data over the system's network, thus limiting the number of physical sensors that can be used to model the environment. Therefore, it is of fundamental to define alternative perceptive strategies to accurately characterize different interaction with the environment without relying on specific sensory technologies. In this work, we present a novel approach for safe teleoperation, that takes advantage of model based proprioceptive measurement of the robot dynamics to robustly identify unexpected collisions or contact events with the environment. Each identified collision is translated on-the-fly into a set of local motion constraints, allowing the exploitation of the system redundancies for the computation of intelligent control laws for automatic reaction, without requiring human intervention and minimizing the disturbance of the task execution (or, equivalently, the operator efforts). More precisely, the described system consist in two different building blocks. The first, for detecting unexpected interactions with the environment (perceptive block). The second, for intelligent and autonomous reaction after the stimulus (control block). The perceptive block is responsible of the contact event identification. In short, the approach is based on the claim that a sensorless collision detection method for robot manipulators can be extended to the field of mobile manipulators, by embedding it within a statistical learning framework. The control deals with the intelligent and autonomous reaction after the contact or impact with the environment occurs, and consist on an motion abstraction controller with a prioritized set of constrains, where the highest priority correspond to the robot reconfiguration after a collision is detected; when all related dynamical effects have been compensated, the controller switch again to the basic control mode

Control of Redundant Robots Under Hard Joint Constraints: Saturation in the Null Space

We present an efficient method for addressing online the inversion of differential task kinematics for redundant manipulators, in the presence of hard limits on joint space motion that can never be violated. The proposed SNS (Saturation in the Null Space) algorithm proceeds by successively discarding the use of joints that would exceed their motion bounds when using the minimum norm solution. When processing multiple tasks with priority, the SNS method realizes a preemptive strategy by preserving the correct order of priority in spite of the presence of saturations. In the single- and multi-task case, the algorithm automatically integrates a least possible task scaling procedure, when an original task is found to be unfeasible. The optimality properties of the SNS algorithm are analyzed by considering an associated Quadratic Programming problem. Its solution leads to a variant of the algorithm, which guarantees optimality also when the basic SNS algorithm does not. Numerically efficient versions of these algorithms are proposed. Their performance allows real-time control of robots executing many prioritized tasks with a large number of hard bounds. Experimental results are reported

An experimentally validated technique for the real-time management of wrist singularities in nonredundant anthropomorphic manipulators

The automatic management of kinematic singularities, which are typical for trajectories planned in the operational space, is arousing a renewed interest among the scientific community because the most recent strategies make it possible their real-time management. The approach described in this paper allows executing trajectories in the operational space which pass through wrist singularities. It introduces several novelties w.r.t. known alternative strategies. First of all, it is conceived for trajectories which are planned on-the-fly. Secondly, singularities are avoided by changing slightly the tool-frame orientation while strictly preserving both the assigned Cartesian path and time-law. Finally, the approach is effective also for manipulators moving at standard operative speeds and it explicitly handles given limits on joint velocities and accelerations. In this paper an approach proposed in early works is revised in order to make it ready for an industrial implementation. In particular a procedural method is proposed for the tuning of the algorithm, so as to make it more deterministic and to increase the success rates. Furthermore, the singularity avoidance problem is theoretically analyzed in order to devise a necessary condition for the the existence of a solution. Results are experimentally validated through an anthropomorphic industrial manipulator

Redundancy analysis of cooperative dual-arm manipulators

This paper presents the redundancy analysis of two cooperative manipulators, showing how they can be considered as a single redundant manipulator through the use of the relative Jacobian matrix. In this way, the kinematic redundancy can be resolved by applying the principal local optimization techniques used in the single manipulator case. We resolve the redundancy by using the Jacobian null space technique, which permits us to perform several tasks with different execution priority levels at the same time; this is a useful feature, especially when the manipulators are to be mounted on and cooperate with a mobile platform. As an illustrative example, we present a case study consisting of two planar manipulators mounted on a smart wheelchair, whose degrees of redundancy are employed to move an object along a pre-defined path, while avoiding an obstacle in the manipulator's workspace at the same time

Intuitive Telemanipulation of Hyper-Redundant Snake Robots within Locomotion and Reorientation using Task-Priority Inverse Kinematics

Snake robots offer considerable potential for endoscopic interventions due to their ability to follow curvilinear paths. Telemanipulation is an open problem due to hyper-redundancy, as input devices only allow a specification of six degrees of freedom. Our work addresses this by presenting a unified telemanipulation strategy which enables follow-the-leader locomotion and reorientation keeping the shape change as small as possible. The basis for this is a novel shape-fitting approach for solving the inverse kinematics in only a few milliseconds. Shape fitting is performed by maximizing the similarity of two curves using Fréchet distance while simultaneously specifying the position and orientation of the end effector. Telemanipulation performance is investigated in a study in which 14 participants controlled a simulated snake robot to locomote into the target area. In a final validation, pivot reorientation within the target area is addressed.© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

구조로봇을 위한 강건한 계층적 동작 계획 및 제어

학위논문(박사) -- 서울대학교대학원 : 공과대학 기계항공공학부, 2021.8. 박종우.Over the last several years, robotics has experienced a striking development, and a new generation of robots has emerged that shows great promise in being able to accomplish complex tasks associated with human behavior. Nowadays the objectives of the robots are no longer restricted to the automaton in the industrial process but are changing into explorers for hazardous, harsh, uncooperative, and extreme environments. As these robots usually operate in dynamic and unstructured environments, they should be robust, adaptive, and reactive under various changing operation conditions. We propose online hierarchical optimization-based planning and control methodologies for a rescue robot to execute a given mission in such a highly unstructured environment. A large number of degrees of freedom is provided to robots in order to achieve diverse kinematic and dynamic tasks. However, accomplishing such multiple objectives renders on-line reactive motion planning and control problems more difficult to solve due to the incompatible tasks. To address this problem, we exploit a hierarchical structure to precisely resolve conflicts by creating a priority in which every task is achieved as much as possible according to the levels. In particular, we concentrate on the reasoning about the task regularization to ensure the convergence and robustness of a solution in the face of singularity. As robotic systems with real-time motion planners or controllers often execute unrehearsed missions, a desired task cannot always be driven to a singularity free configuration. We develop a generic solver for regularized hierarchical quadratic programming without resorting to any off-the-shelf QP solver to take advantage of the null-space projections for computational efficiency. Therefore, the underlying principles are thoroughly investigated. The robust optimal solution is obtained under both equality and inequality tasks or constraints while addressing all problems resulting from the regularization. Especially as a singular value decomposition centric approach is leveraged, all hierarchical solutions and Lagrange multipliers for properly handling the inequality constraints are analytically acquired in a recursive procedure. The proposed algorithm works fast enough to be used as a practical means of real-time control system, so that it can be used for online motion planning, motion control, and interaction force control in a single hierarchical optimization. Core system design concepts of the rescue robot are presented. The goals of the robot are to safely extract a patient and to dispose a dangerous object instead of humans. The upper body is designed humanoid in form with replaceable modularized dual arms. The lower body is featured with a hybrid tracked and legged mobile platform to simultaneously acquire versatile manipulability and all-terrain mobility. Thus, the robot can successfully execute a driving task, dangerous object manipulation, and casualty extraction missions by changing the pose and modularized equipments in an optimized manner. Throughout the dissertation, all proposed methods are validated through extensive numerical simulations and experimental tests. We highlight precisely how the rescue robot can execute a casualty extraction and a dangerous object disposal mission both in indoor and outdoor environments that none of the existing robots has performed.최근에 등장한 새로운 세대의 로봇은 기존에는 인간만이 할 수 있었던 복잡한 일을 로봇 또한 수행할 수 있음을 보여주었다. 특히 DARPA Robotics Challenge를 통해 이러한 사실을 잘 확인할 수 있으며, 이 로봇들은 공장과 같은 정형화된 환경에서 자동화된 일을 반복적으로 수행하던 임무에서 더 나아가 극한의 환경에서 인간을 대신하여 위험한 임무를 수행할 수 있는 방향으로 발전하고 있다. 그래서 사람들은 재난환경에서 안전하고 시의 적절하게 대응할 수 있는 여러 가지 대안 중에서 실현 가능성이 높은 대처 방안으로 로봇을 생각하게 되었다. 하지만 이러한 로봇은 동적으로 변화하는 비정형 환경에서 임무를 수행할 수 있어야 하기 때문에 불확실성에 대해 강건해야하고, 다양한 환경 조건에서 능동적으로 반응을 할 수 있어야 한다. 본 학위논문에서는 로봇이 비정형 환경에서 강건하면서도 적응적으로 동작할 수 있는 실시간 최적화 기반의 동작 계획 및 제어 방법과 구조 로봇의 설계 개념을 제안하고자 한다. 인간은 많은 자유도를 가지고 있으며, 하나의 전신 동작을 생성할 때 다양한 기구학 혹은 동역학적 특성을 가지는 세부 동작 혹은 작업을 정의하고, 이를 효과적으로 종합할 수 있다. 그리고 학습을 통해 각 동작 요소들을 최적화할 뿐만 아니라 상황 에 따라 각 동작 요소에 우선순위를 부여하여 이를 효과적으로 결합하거나 분리하여 실시간으로 최적의 동작을 생성하고 제어한다. 즉, 상황에 따라 중요한 동작요소를 우선적으로 수행하고 우선순위가 낮은 동작요소는 부분 혹은 전체적으로 포기하기도 하면서 매우 유연하게 전체 동작을 생성하고 최적화 한다. 인간과 같이 다자유도를 보유한 로봇 또한 기구학과 동역학적 특성을 가지는 다양한 세부 동작 혹은 작업을 작업공간(task space) 혹은 관절공간(configuration space)에서 정의할 수 있으며, 우선순위에 따라 이를 효과적으로 결합하여 전체 동작을 생 성하고 제어할 수 있다. 서로 양립하기 어려운 로봇의 동작 문제를 해결하기 위해 동작들 사이에 우선순위를 부여하여 계층을 생성하고, 이에 따라 로봇의 전신 동작을 구현하는 방법은 오랫동안 연구가 진행되어 왔다. 이러한 계층적 최적화를 이용하면 우선순위가 높은 동작부터 순차적으로 실행하지만, 우선순위가 낮은 동작요소들도 가능한 만족시키는 최적의 해를 찾을 수 있다. 하지만 관절의 구동 범위와 같은 부등식의 조건이 포함된 계층적 최적화 문제에서 특이점에 대한 강건성까지 확보할 수 있는 방법에 대해서는 아직까지 많은 부분이 밝 혀진 바가 없다. 따라서 본 학위논문에서는 등식과 부등식으로 표현되는 구속조건 혹은 동작요소를 계층적 최적화에 동시에 포함시키고, 특이점이 존재하더라도 강건성과 수렴성을 보장하는 관절공간에서의 최적해를 확보하는데 집중한다. 왜나하면 비정형 임무를 수행하는 로봇은 사전에 계획된 동작을 수행하는 것이 아닌 변화하는 환경조건에 따라 실시간으로 동작을 계획하고 제어해야 하기 때문에 특이점이 없는 자세로 로봇을 항상 제어하기가 어렵다. 그리고 이렇게 특이점을 회피하는 방향으로 로봇을 제어하는 것은 로봇의 운용성을 심각하게 저해시킬 수 있다. 특이점 근방에서의 해의 강건성이 보장되지 않으면 로봇 관절에 과도한 속도 혹은 토크가 발생하여 로봇의 임무 수행이 불가능하거나 환경과 로봇의 손상을 초래할 수 있으며, 나아가 로봇과 함께 임무를 수행하는 사람에게 상해를 가할 수도 있다. 특이점에 대한 강건성을 확보하기 위해 우선순위 기반의 계층적 최적화와 정규화 (regularization)를 통합하여 정규화된 계층적 최적화 (RHQP: Regularized Hierarchical Quadratic Program) 문제를 다룬다. 부등식이 포함된 계층적 최적화에 정규화를 동시에 고려함으로써 야기되는 많은 문제점들을 해결하고 해의 최적성과 강건성을 확보할 수 있는 방법을 제안한다. 특히 외부의 최적화 프로그램을 사용하지 않고 수치적 최적화 (numerical optimization) 이론과 우선순위에 기반을 두는 여유자유도 로봇의 해석 기법을 이용하여 계산의 효율성을 극대화할 수 있는 이차 프로그램(quadratic programming)을 제안한다. 또한 이와 동시에 정규화된 계층적 최적화 문제의 이론적 구조를 철저하게 분석한다. 특히 특이값 분해 (singular value decomposition)를 통해 최적해와 부등식 조건을 처리하는데 필요한 라그랑지 승수를 재귀적인 방법으로 해석적 형태로 구함으로써 계산의 효율성을 증대시키고 동시에 부등식의 조건을 오류 없이 정확하게 처리할 수 있도록 하였다. 그리고 정규화된 계층적 최적화를 힘제어까지 확장하여 환경과 로봇의 안전한 상호작용을 보장하여 로봇이 적절한 힘으로 환경과 접촉할 수 있도록 하였다. 불확실성이 존재하는 비정형 환경에서 비정형 임무를 수행할 수 있는 구조로봇의 핵심 설계 개념을 제시한다. 비정형 환경에서의 조작 성능과 이동 성능을 동시에 확보할 수 있는 형상으로 로봇을 설계하여 구조 로봇으로 하여금 최종 목적으로 설정된 인간을 대신하여 부상자를 구조하고 위험물을 처리하는 임무를 효과적으로 수행할 수 있도록 한다. 구조 로봇에 필요한 매니퓰레이터는 부상자 구조 임무와 위험물 처리 임무에 따라 교체 가능한 모듈형으로 설계하여 각각의 임무에 따라 최적화된 매니퓰 레이터를 장착하여 임무를 수행할 수 있다. 하체는 트랙과 관절이 결합된 하이브리드 형태를 취하고 있으며, 주행 임무와 조작임무에 따라 형상을 변경할 수 있다. 형상 변경과 모듈화된 매니퓰레이터를 통해서조작 성능과 험한 지형에서 이동할 수 있는 주행 성능을 동시에 확보하였다. 최종적으로 구조로봇의 설계와 실시간 계층적 제어를 이용하여 비정형 실내외 환경에서 구조로봇이 주행임무, 위험물 조작임무, 부상자 구조 임무를 성공적으로 수 행할 수 있음을 해석과 실험을 통하여 입증함으로써 본 학위논문에서 제안한 설계와 정규화된 계층적 최적화 기반의 제어 전략의 유용성을 검증하였다.1 Introduction 1 1.1 Motivations 1 1.2 Related Works and Research Problems for Hierarchical Control 3 1.2.1 Classical Approaches 3 1.2.2 State-of-the-Art Strategies 4 1.2.3 Research Problems 7 1.3 Robust Rescue Robots 9 1.4 Research Goals 12 1.5 Contributions of ThisThesis 13 1.5.1 Robust Hierarchical Task-Priority Control 13 1.5.2 Design Concepts of Robust Rescue Robot 16 1.5.3 Hierarchical Motion and ForceControl 17 1.6 Dissertation Preview 18 2 Preliminaries for Task-Priority Control Framework 21 2.1 Introduction 21 2.2 Task-Priority Inverse Kinematics 23 2.3 Recursive Formulation of Null Space Projector 28 2.4 Conclusion 31 3 Robust Hierarchical Task-Priority Control 33 3.1 Introduction 33 3.1.1 Motivations 35 3.1.2 Objectives 36 3.2 Task Function Approach 37 3.3 Regularized Hierarchical Optimization with Equality Tasks 41 3.3.1 Regularized Hierarchical Optimization 41 3.3.2 Optimal Solution 45 3.3.3 Task Error and Hierarchical Matrix Decomposition 49 3.3.4 Illustrative Examples for Regularized Hierarchical Optimization 56 3.4 Regularized Hierarchical Optimization with Inequality Constraints 60 3.4.1 Lagrange Multipliers 61 3.4.2 Modified Active Set Method 66 3.4.3 Illustrative Examples of Modified Active Set Method 70 3.4.4 Examples for Hierarchical Optimization with Inequality Constraint 72 3.5 DLS-HQP Algorithm 79 3.6 Concluding Remarks 80 4 Rescue Robot Design and Experimental Results 83 4.1 Introduction 83 4.2 Rescue Robot Design 85 4.2.1 System Design 86 4.2.2 Variable Configuration Mobile Platform 92 4.2.3 Dual Arm Manipulators 95 4.2.4 Software Architecture 97 4.3 Performance Verification for Hierarchical Motion Control 99 4.3.1 Real-Time Motion Generation 99 4.3.2 Task Specifications 103 4.3.3 Singularity Robust Task Priority 106 4.3.4 Inequality Constraint Handling and Computation Time 111 4.4 Singularity Robustness and Inequality Handling for Rescue Mission 117 4.5 Field Tests 122 4.6 Concluding Remarks 126 5 Hierarchical Motion and Force Control 129 5.1 Introduction 129 5.2 Operational Space Control 132 5.3 Acceleration-Based Hierarchical Motion Control 134 5.4 Force Control 137 5.4.1 Force Control with Inner Position Loop 141 5.4.2 Force Control with Inner Velocity Loop 144 5.5 Motion and Force Control 145 5.6 Numerical Results for Acceleration-Based Motion and Force Control 148 5.6.1 Task Specifications 150 5.6.2 Force Control Performance 151 5.6.3 Singularity Robustness and Inequality Constraint Handling 155 5.7 Velocity Resolved Motion and Force Control 160 5.7.1 Velocity-Based Motion and Force Control 161 5.7.2 Experimental Results 163 5.8 Concluding Remarks 167 6 Conclusion 169 6.1 Summary 169 6.2 Concluding Remarks 173 A Appendix 175 A.1 Introduction to PID Control 175 A.2 Inverse Optimal Control 176 A.3 Experimental Results and Conclusion 181 Bibliography 183 Abstract 207박

A General Framework for Hierarchical Redundancy Resolution Under Arbitrary Constraints

The increasing interest in autonomous robots with a high number of degrees of freedom for industrial applications and service robotics demands control algorithms to handle multiple tasks as well as hard constraints efficiently. This paper presents a general framework in which both kinematic (velocity- or acceleration-based) and dynamic (torque-based) control of redundant robots are handled in a unified fashion. The framework allows for the specification of redundancy resolution problems featuring a hierarchy of arbitrary (equality and inequality) constraints, arbitrary weighting of the control effort in the cost function and an additional input used to optimize possibly remaining redundancy. To solve such problems, a generalization of the Saturation in the Null Space (SNS) algorithm is introduced, which extends the original method according to the features required by our general control framework. Variants of the developed algorithm are presented, which ensure both efficient computation and optimality of the solution. Experiments on a KUKA LBRiiwa robotic arm, as well as simulations with a highly redundant mobile manipulator are reported.Comment: 19 pages, 19 figures, submitted to the IEE