Distributed Path Planning Classification with Web-based 3D Visualization using Deep Neural Network for Internet of Robotic Things

Internet of Robotic Things (IoRT) distributes heterogeneous intelligences among devices and platforms. A distributed control of a three-degree-of-freedom (3-DOF) robot manipulator is integrated with web-based 3D visualization. An asynchronous protocol was utilized to broadcast kinematic data of a 3-DOF robot manipulator between platforms. However, kinematic data computed using inverse kinematic equations directly cannot identify the singularity issue of robot manipulator. Singularity avoidance required to prevent robot component or joint from damage. Therefore, this study proposed a deep neural network approach as a classification-based of manipulator robot path planning to avoid singularity issues. Deep neural network (DNN) was trained in 12 minutes, 52 seconds in 500 iterations. Training accuracy measured with value 96,23 percent, validation accuracy measured with value 96,13 percent, and testing accuracy measured with value 96,48 percent Additionally, 3 DOF manipulator robot web-based 3D visualization was made using Web Graphics Library (WebGL). The distributed platform was tested successfully and can distribute and classify 2352 motions per second

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

기구학적 및 동적 제한조건들을 고려한 모바일 매니퓰레이터의 작업 중심 전신 동작 생성 전략

학위논문(박사) -- 서울대학교대학원 : 융합과학기술대학원 융합과학부(지능형융합시스템전공), 2023. 2. 박재흥.모바일 매니퓰레이터는 모바일 로봇에 장착된 매니퓰레이터입니다. 모바일 매니퓰레이터는 고정형 매니퓰레이터에 비해 모바일 로봇의 이동성을 제공받기 때문에 다양하고 복잡한 작업을 수행할 수 있습니다. 그러나 두 개의 서로 다른 시스템을 결합함으로써 모바일 매니퓰레이터의 전신을 계획하고 제어할 때 여러 특징을 고려해야 합니다. 이러한 특징들은 여자유도, 두 시스템의 관성 차이 및 모바일 로봇의 비홀로노믹 제한 조건 등이 있습니다. 본 논문의 목적은 기구학적 및 동적 제한조건들을 고려하여 모바일 매니퓰레이터의 전신 동작 생성 전략을 제안하는 것입니다. 먼저, 모바일 매니퓰레이터가 초기 위치에서 문을 통과하여 목표 위치에 도달하기 위한 전신 경로를 계산하는 프레임워크를 제안합니다. 이 프레임워크는 로봇과 문에 의해 생기는 기구학적 제한조건을 고려합니다. 제안하는 프레임워크는 두 단계를 거쳐 전신의 경로를 얻습니다. 첫 번째 단계에서는 그래프 탐색 알고리즘을 이용하여 모바일 로봇의 자세 경로와 문의 각도 경로를 계산합니다. 특히, 그래프 탐색에서 area indicator라는 정수 변수를 상태의 구성 요소로서 정의하는데, 이는 문에 대한 모바일 로봇의 상대적 위치를 나타냅니다. 두 번째 단계에서는 모바일 로봇의 경로와 문의 각도를 통해 문의 손잡이 위치를 계산하고 역기구학을 활용하여 매니퓰레이터의 관절 위치를 계산합니다. 제안된 프레임워크의 효율성은 비홀로노믹 모바일 매니퓰레이터를 사용한 시뮬레이션 및 실제 실험을 통해 검증되었습니다. 둘 째, 최적화 방법을 기반으로한 전신 제어기를 제안합니다. 이 방법은 등식 및 부등식 제한조건 모두에 대해 가중 행렬을 반영한 계층적 최적화 문제의 해를 계산합니다. 이 방법은 모바일 매니퓰레이터 또는 휴머노이드와 같이 자유도가 많은 로봇의 여자유도를 해결하기 위해 개발되어 작업 우선 순위에 따라 가중치가 다른 관절 동작으로 여러 작업을 수행할 수 있습니다. 제안된 방법은 가중 행렬을 최적화 문제의 1차 최적 조건을 만족하도록 하며, Active-set 방법을 활용하여 등식 및 부등식 작업을 처리합니다. 또한, 대칭적인 영공간 사영 행렬을 사용하여 계산상 효율적입니다. 결과적으로, 제안된 제어기를 활용하는 로봇은 우선 순위에 따라 개별적인 관절 가중치를 반영하여 전신 움직임을 효과적으로 보여줍니다. 제안된 제어기의 효용성은 모바일 매니퓰레이터와 휴머노이드를 이용한 실험을 통해 검증하였습니다. 마지막으로, 모바일 매니퓰레이터의 동적 제한조건들 중 하나로서 자가 충돌 회피 알고리즘을 제안합니다. 제안된 방법은 매니퓰레이터와 모바일 로봇 간의 자가 충돌에 중점을 둡니다. 모바일 로봇의 버퍼 영역을 둘러싸는 3차원 곡면인 distance buffer border의 개념을 정의합니다. 버퍼 영역의 두께는 버퍼 거리입니다. 매니퓰레이터와 모바일 로봇 사이의 거리가 버퍼 거리보다 작은 경우, 즉 매니퓰레이터가 모바일 로봇의 버퍼 영역 내부에 있는 경우 제안된 전략은 매니퓰레이터를 버퍼 영역 밖으로 내보내기 위해 모바일 로봇의 움직임을 생성합니다. 따라서 매니퓰레이터는 미리 정의된 매니퓰레이터의 움직임을 수정하지 않고도 모바일 로봇과의 자가 충돌을 피할 수 있습니다. 모바일 로봇의 움직임은 가상의 힘을 가함으로써 생성됩니다. 특히, 힘의 방향은 차동 구동 이동 로봇의 비홀로노믹 제약 및 조작기의 도달 가능성을 고려하여 결정됩니다. 제안된 알고리즘은 7자유도 로봇팔을 가진 차동 구동 모바일 로봇에 적용하여 다양한 실험 시나리오에서 입증되었습니다.A mobile manipulator is a manipulator mounted on a mobile robot. Compared to a fixed-base manipulator, the mobile manipulator can perform various and complex tasks because the mobility is offered by the mobile robot. However, combining two different systems causes several features to be considered when generating the whole-body motion of the mobile manipulator. The features include redundancy, inertia difference, and non-holonomic constraint. The purpose of this thesis is to propose the whole-body motion generation strategy of the mobile manipulator for considering kinematic and dynamic constraints. First, a planning framework is proposed that computes a path for the whole-body configuration of the mobile manipulator to navigate from the initial position, traverse through the door, and arrive at the target position. The framework handles the kinematic constraint imposed by the closed-chain between the robot and door. The proposed framework obtains the path of the whole-body configuration in two steps. First, the path for the pose of the mobile robot and the path for the door angle are computed by using the graph search algorithm. In graph search, an integer variable called area indicator is introduced as an element of state, which indicates where the robot is located relative to the door. Especially, the area indicator expresses a process of door traversal. In the second step, the configuration of the manipulator is computed by the inverse kinematics (IK) solver from the path of the mobile robot and door angle. The proposed framework has a distinct advantage over the existing methods that manually determine several parameters such as which direction to approach the door and the angle of the door required for passage. The effectiveness of the proposed framework was validated through experiments with a nonholonomic mobile manipulator. Second, a whole-body controller is presented based on the optimization method that can consider both equality and inequality constraints. The method computes the optimal solution of the weighted hierarchical optimization problem. The method is developed to resolve the redundancy of robots with a large number of Degrees of Freedom (DOFs), such as a mobile manipulator or a humanoid, so that they can execute multiple tasks with differently weighted joint motion for each task priority. The proposed method incorporates the weighting matrix into the first-order optimality condition of the optimization problem and leverages an active-set method to handle equality and inequality constraints. In addition, it is computationally efficient because the solution is calculated in a weighted joint space with symmetric null-space projection matrices for propagating recursively to a low priority task. Consequently, robots that utilize the proposed controller effectively show whole-body motions handling prioritized tasks with differently weighted joint spaces. The effectiveness of the proposed controller was validated through experiments with a nonholonomic mobile manipulator as well as a humanoid. Lastly, as one of dynamic constraints for the mobile manipulator, a reactive self-collision avoidance algorithm is developed. The proposed method mainly focuses on self-collision between a manipulator and the mobile robot. We introduce the concept of a distance buffer border (DBB), which is a 3D curved surface enclosing a buffer region of the mobile robot. The region has the thickness equal to buffer distance. When the distance between the manipulator and mobile robot is less than the buffer distance, i.e. the manipulator lies inside the buffer region of the mobile robot, the proposed strategy is to move the mobile robot away from the manipulator in order for the manipulator to be placed outside the border of the region, the DBB. The strategy is achieved by exerting force on the mobile robot. Therefore, the manipulator can avoid self-collision with the mobile robot without modifying the predefined motion of the manipulator in a world Cartesian coordinate frame. In particular, the direction of the force is determined by considering the non-holonomic constraint of the differentially driven mobile robot. Additionally, the reachability of the manipulator is considered to arrive at a configuration in which the manipulator can be more maneuverable. To realize the desired force and resulting torque, an avoidance task is constructed by converting them into the accelerations of the mobile robot and smoothly inserted with a top priority into the controller. The proposed algorithm was implemented on a differentially driven mobile robot with a 7-DOFs robotic arm and its performance was demonstrated in various experimental scenarios.1 INTRODUCTION 1 1.1 Motivation 1 1.2 Contributions of thesis 2 1.3 Overview of thesis 3 2 WHOLE-BODY MOTION PLANNER : APPLICATION TO NAVIGATION INCLUDING DOOR TRAVERSAL 5 2.1 Background & related works 7 2.2 Proposed framework 9 2.2.1 Computing path for mobile robot and door angle - S1 10 2.2.1.1 State 10 2.2.1.2 Action 13 2.2.1.3 Cost 15 2.2.1.4 Search 18 2.2.2 Computing path for arm configuration - S2 20 2.3 Results 21 2.3.1 Application to pull and push-type door 21 2.3.2 Experiment in cluttered environment 22 2.3.3 Experiment with different robot platform 23 2.3.4 Comparison with separate planning by existing works 24 2.3.5 Experiment with real robot 29 2.4 Conclusion 29 3 WHOLE-BODY CONTROLLER : WEIGHTED HIERARCHICAL QUADRATIC PROGRAMMING 31 3.1 Related works 32 3.2 Problem statement 34 3.2.1 Pseudo-inverse with weighted least-squares norm for each task 35 3.2.2 Problem statement 37 3.3 WHQP with equality constraints 37 3.4 WHQP with inequality constraints 45 3.5 Experimental results 48 3.5.1 Simulation experiment with nonholonomic mobile manipulator 48 3.5.1.1 Scenario description 48 3.5.1.2 Task and weighting matrix description 49 3.5.1.3 Results 51 3.5.2 Real experiment with nonholonomic mobile manipulator 53 3.5.2.1 Scenario description 53 3.5.2.2 Task and weighting matrix description 53 3.5.2.3 Results 54 3.5.3 Real experiment with humanoid 55 3.5.3.1 Scenario description 55 3.5.3.2 Task and weighting matrix description 55 3.5.3.3 Results 57 3.6 Discussions and implementation details 57 3.6.1 Computation cost 57 3.6.2 Composite weighting matrix in same hierarchy 59 3.6.3 Nullity of WHQP 59 3.7 Conclusion 59 4 WHOLE-BODY CONSTRAINT : SELF-COLLISION AVOIDANCE 61 4.1 Background & related Works 64 4.2 Distance buffer border and its score computation 65 4.2.1 Identification of potentially colliding link pairs 66 4.2.2 Distance buffer border 67 4.2.3 Evaluation of distance buffer border 69 4.2.3.1 Singularity of the differentially driven mobile robot 69 4.2.3.2 Reachability of the manipulator 72 4.2.3.3 Score of the DBB 74 4.3 Self-collision avoidance algorithm 75 4.3.1 Generation of the acceleration for the mobile robot 76 4.3.2 Generation of the repulsive acceleration for the other link pair 82 4.3.3 Construction of an acceleration-based task for self-collision avoidance 83 4.3.4 Insertion of the task in HQP-based controller 83 4.4 Experimental results 86 4.4.1 System overview 87 4.4.2 Experimental results 87 4.4.2.1 Self-collision avoidance while tracking the predefined trajectory 87 4.4.2.2 Self-collision avoidance while manually guiding the end-effector 89 4.4.2.3 Extension to obstacle avoidance when opening the refrigerator 91 4.4.3 Discussion 94 4.5 Conclusion 95 5 CONCLUSIONS 97 Abstract (In Korean) 113 Acknowlegement 116박

Configuration control of seven-degree-of-freedom arms

A seven degree of freedom robot arm with a six degree of freedom end effector is controlled by a processor employing a 6 by 7 Jacobian matrix for defining location and orientation of the end effector in terms of the rotation angles of the joints, a 1 (or more) by 7 Jacobian matrix for defining 1 (or more) user specified kinematic functions constraining location or movement of selected portions of the arm in terms of the joint angles, the processor combining the two Jacobian matrices to produce an augmented 7 (or more) by 7 Jacobian matrix, the processor effecting control by computing in accordance with forward kinematics from the augmented 7 by 7 Jacobian matrix and from the seven joint angles of the arm a set of seven desired joint angles for transmittal to the joint servo loops of the arm. One of the kinematic functions constraints the orientation of the elbow plane of the arm. Another one of the kinematic functions minimizes a sum of gravitational torques on the joints. Still another kinematic function constrains the location of the arm to perform collision avoidance. Generically, one kinematic function minimizes a sum of selected mechanical parameters of at least some of the joints associated with weighting coefficients which may be changed during arm movement. The mechanical parameters may be velocity errors or gravity torques associated with individual joints

Efficient Learning of Fast Inverse Kinematics with Collision Avoidance

Fast inverse kinematics (IK) is a central component in robotic motion planning. For complex robots, IK methods are often based on root search and non-linear optimization algorithms. These algorithms can be massively sped up using a neural network to predict a good initial guess, which can then be refined in a few numerical iterations. Besides previous work on learning-based IK, we present a learning approach for the fundamentally more complex problem of IK with collision avoidance. We do this in diverse and previously unseen environments. From a detailed analysis of the IK learning problem, we derive a network and unsupervised learning architecture that removes the need for a sample data generation step. Using the trained network's prediction as an initial guess for a two-stage Jacobian-based solver allows for fast and accurate computation of the collision-free IK. For the humanoid robot, Agile Justin (19 DoF), the collision-free IK is solved in less than 10 milliseconds (on a single CPU core) and with an accuracy of 10^-4 m and 10^-3 rad based on a high-resolution world model generated from the robot's integrated 3D sensor. Our method massively outperforms a random multi-start baseline in a benchmark with the 19 DoF humanoid and challenging 3D environments. It requires ten times less training time than a supervised training method while achieving comparable results.Comment: Presented at the 2023 IEEE-RAS International Conference on Humanoid Robot

Recurrent Neural Networks-Based Collision-Free Motion Planning for Dual Manipulators Under Multiple Constraints

Dual robotic manipulators are robotic systems that are developed to imitate human arms, which shows great potential in performing complex tasks. Collision-free motion planning in real time is still a challenging problem for controlling a dual robotic manipulator because of the overlap workspace. In this paper, a novel planning strategy under physical constraints of dual manipulators using dynamic neural networks is proposed, which can satisfy the collision avoidance and trajectory tracking. Particularly, the problem of collision avoidance is first formulated into a set of inequality formulas, whereas the robotic trajectory is then transformed into an equality constraint by introducing negative feedback in outer loop. The planning problem subsequently becomes a Quadratic Programming (QP) problem by considering the redundancy, the boundaries of joint angles and velocities of the system. The QP is solved using a convergent provable recurrent neural network that without calculating the pseudo-inversion of the Jacobian. Consequently, numerical experiments on 8-DoF modular robot and 14-DoF Baxter robot are conducted to show the superiority of the proposed strategy