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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 27 Sep 2020 04:31:35 GMT2020-09-27T04:31:35ZRobot dynamics: A recursive algorithm for efficient calculation of Christoffel symbols
http://hdl.handle.net/10985/17237
Robot dynamics: A recursive algorithm for efficient calculation of Christoffel symbols
SAFEEA, Mohammad; NETO, Pedro; BEAREE, Richard
Christoffel symbols of the first kind are very important in robot dynamics. They are used for tuning various proposed robot controllers, for determining the bounds on Coriolis/Centrifugal matrix, for mathematical formulation of optimal trajectory calculation, among others. In the literature of robot dynamics, Christoffel symbols of the first kind are calculated from Lagrangian dynamics using an off-line generated symbolic formula. In this study we present a novel and efficient recursive, non-symbolic, method where Christoffel symbols of the first kind are calculated on-the-fly based on the inertial parameters of robot’s links and their transformation matrices. The proposed method was analyzed in terms of execution time, computational complexity and numerical error. Results show that the proposed algorithm compares favorably with existing methods.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/172372019-01-01T00:00:00ZSAFEEA, MohammadNETO, PedroBEAREE, RichardChristoffel symbols of the first kind are very important in robot dynamics. They are used for tuning various proposed robot controllers, for determining the bounds on Coriolis/Centrifugal matrix, for mathematical formulation of optimal trajectory calculation, among others. In the literature of robot dynamics, Christoffel symbols of the first kind are calculated from Lagrangian dynamics using an off-line generated symbolic formula. In this study we present a novel and efficient recursive, non-symbolic, method where Christoffel symbols of the first kind are calculated on-the-fly based on the inertial parameters of robot’s links and their transformation matrices. The proposed method was analyzed in terms of execution time, computational complexity and numerical error. Results show that the proposed algorithm compares favorably with existing methods.Efficient Calculation of Minimum Distance Between Capsules and Its Use in Robotics
http://hdl.handle.net/10985/14515
Efficient Calculation of Minimum Distance Between Capsules and Its Use in Robotics
SAFEEA, Mohammad; NETO, Pedro; BEAREE, Richard
The problem of minimum distance calculation between line-segments/capsules, in 3D space, is an important subject in many engineering applications, spanning CAD design, computer graphics, simulation, and robotics. In the latter, the human robot minimum distance is the main input for collision avoidance/detection algorithms to measure collision imminence. Capsules can be used to represent humans and objects, including robots, in a given dynamic environment. In this scenario, it is important to calculate the minimum distance between capsules ef ciently, especially for scenes (situations) that include a high number of capsules. This paper investigates the utilization of QR factorization for performing ef cient minimum distance calculation between capsules. The problem is reformulated as a bounded variable optimization in which an af ne transformation, deduced from QR factorization, is applied on the region of feasible solutions. A geometrical approach is proposed to calculate the solution, which is achieved by computing the point closest to the origin from the transferred region of feasible solutions. This paper is concluded with numerical tests, showing that the proposed method compares favorably with the most ef cient method reported in the literature.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/145152018-01-01T00:00:00ZSAFEEA, MohammadNETO, PedroBEAREE, RichardThe problem of minimum distance calculation between line-segments/capsules, in 3D space, is an important subject in many engineering applications, spanning CAD design, computer graphics, simulation, and robotics. In the latter, the human robot minimum distance is the main input for collision avoidance/detection algorithms to measure collision imminence. Capsules can be used to represent humans and objects, including robots, in a given dynamic environment. In this scenario, it is important to calculate the minimum distance between capsules ef ciently, especially for scenes (situations) that include a high number of capsules. This paper investigates the utilization of QR factorization for performing ef cient minimum distance calculation between capsules. The problem is reformulated as a bounded variable optimization in which an af ne transformation, deduced from QR factorization, is applied on the region of feasible solutions. A geometrical approach is proposed to calculate the solution, which is achieved by computing the point closest to the origin from the transferred region of feasible solutions. This paper is concluded with numerical tests, showing that the proposed method compares favorably with the most ef cient method reported in the literature.Reducing the Computational Complexity of Mass-Matrix Calculation for High DOF Robots
http://hdl.handle.net/10985/17376
Reducing the Computational Complexity of Mass-Matrix Calculation for High DOF Robots
SAFEEA, Mohammad; BEAREE, Richard; NETO, Pedro
Increasingly, robots have more degrees of freedom (DOF), imposing a need for calculating more complex dynamics. As a result, better efficiency in carrying out dynamics computations is becoming more important. In this study, an efficient method for computing the joint space inertia matrix (JSIM) for high DOF serially linked robots is addressed. We call this method the Geometric Dynamics Algorithm for High number of robot Joints (GDAHJ). GDAHJ is non-symbolic, preserve simple formulation, and it is convenient for numerical implementation. This is achieved by simplifying the way to recursively derive the mass-matrix exploiting the unique property of each column of the JSIM and minimizing the number of operations with O(n2) complexity. Results compare favorably with existing methods, achieving better performance over state-of-the-art by Featherstone when applied for robots with more than 13 DOF.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/173762018-01-01T00:00:00ZSAFEEA, MohammadBEAREE, RichardNETO, PedroIncreasingly, robots have more degrees of freedom (DOF), imposing a need for calculating more complex dynamics. As a result, better efficiency in carrying out dynamics computations is becoming more important. In this study, an efficient method for computing the joint space inertia matrix (JSIM) for high DOF serially linked robots is addressed. We call this method the Geometric Dynamics Algorithm for High number of robot Joints (GDAHJ). GDAHJ is non-symbolic, preserve simple formulation, and it is convenient for numerical implementation. This is achieved by simplifying the way to recursively derive the mass-matrix exploiting the unique property of each column of the JSIM and minimizing the number of operations with O(n2) complexity. Results compare favorably with existing methods, achieving better performance over state-of-the-art by Featherstone when applied for robots with more than 13 DOF.On-line collision avoidance for collaborative robot manipulators by adjusting off-line generated paths: An industrial use case
http://hdl.handle.net/10985/17378
On-line collision avoidance for collaborative robot manipulators by adjusting off-line generated paths: An industrial use case
SAFEEA, Mohammad; NETO, Pedro; BEAREE, Richard
Human–robot collision avoidance is a key in collaborative robotics and in the framework of Industry 4.0. It plays an important role for achieving safety criteria while having humans and machines working side-by-side in unstructured and time-varying environment. This study introduces the subject of manipulator’s on-line collision avoidance into a real industrial application implementing typical sensors and a commonly used collaborative industrial manipulator, KUKA iiwa. In the proposed methodology, the human co-worker and the robot are represented by geometric primitives (capsules). The minimum distance and relative velocity between them is calculated, when human/obstacles are nearby the concept of hypothetical repulsion and attraction vectors is used. By coupling this concept with a mathematical representation of robot’s kinematics, a task level control with collision avoidance capability is achieved. Consequently, the off-line generated nominal path of the industrial task is modified on-the-fly so the robot is able to avoid collision with the co-worker safely while being able to fulfill the industrial operation. To guarantee motion continuity when switching between different tasks, the notion of repulsion-vector-reshaping is introduced. Tests on an assembly robotic cell in automotive industry show that the robot moves smoothly and avoids collisions successfully by adjusting the off-line generated nominal paths.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/173782019-01-01T00:00:00ZSAFEEA, MohammadNETO, PedroBEAREE, RichardHuman–robot collision avoidance is a key in collaborative robotics and in the framework of Industry 4.0. It plays an important role for achieving safety criteria while having humans and machines working side-by-side in unstructured and time-varying environment. This study introduces the subject of manipulator’s on-line collision avoidance into a real industrial application implementing typical sensors and a commonly used collaborative industrial manipulator, KUKA iiwa. In the proposed methodology, the human co-worker and the robot are represented by geometric primitives (capsules). The minimum distance and relative velocity between them is calculated, when human/obstacles are nearby the concept of hypothetical repulsion and attraction vectors is used. By coupling this concept with a mathematical representation of robot’s kinematics, a task level control with collision avoidance capability is achieved. Consequently, the off-line generated nominal path of the industrial task is modified on-the-fly so the robot is able to avoid collision with the co-worker safely while being able to fulfill the industrial operation. To guarantee motion continuity when switching between different tasks, the notion of repulsion-vector-reshaping is introduced. Tests on an assembly robotic cell in automotive industry show that the robot moves smoothly and avoids collisions successfully by adjusting the off-line generated nominal paths.Collision Avoidance of Redundant Robotic Manipulators Using Newton’s Method
http://hdl.handle.net/10985/18196
Collision Avoidance of Redundant Robotic Manipulators Using Newton’s Method
SAFEEA, Mohammad; BÉARÉE, Richard; NETO, Pedro
This study investigates the application of Newton method to the problems of collision avoidance and path planning for robotic manipulators, especially robots with high Degrees of Freedom (DOF). The proposed algorithm applies to the potential fields method, where the Newton technique is used for performing the optimization. As compared to classical gradient descent method this implementation is mathematically elegant, enhances the performance of motion generation, eliminates oscillations, does not require gains tuning, and gives a faster convergence to the solution. In addition, the paper presents a computationally efficient symbolic formula for calculating the Hessian with respect to joint angles, which is essential for achieving realtime performance of the algorithm in high DOF configuration spaces. The method is validated successfully in simulation environment. Results for different methods (Newton, gradient descent and gradient descent with momentum) are compared in terms of quality of the path generated, oscillations, minimum distance to obstacles and convergence rate.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/181962020-01-01T00:00:00ZSAFEEA, MohammadBÉARÉE, RichardNETO, PedroThis study investigates the application of Newton method to the problems of collision avoidance and path planning for robotic manipulators, especially robots with high Degrees of Freedom (DOF). The proposed algorithm applies to the potential fields method, where the Newton technique is used for performing the optimization. As compared to classical gradient descent method this implementation is mathematically elegant, enhances the performance of motion generation, eliminates oscillations, does not require gains tuning, and gives a faster convergence to the solution. In addition, the paper presents a computationally efficient symbolic formula for calculating the Hessian with respect to joint angles, which is essential for achieving realtime performance of the algorithm in high DOF configuration spaces. The method is validated successfully in simulation environment. Results for different methods (Newton, gradient descent and gradient descent with momentum) are compared in terms of quality of the path generated, oscillations, minimum distance to obstacles and convergence rate.