In this article, a study of the zeros of the transfer function, between the base torque and the e... more In this article, a study of the zeros of the transfer function, between the base torque and the end-effector displacement, for flexible link manipulators is performed. The analysis is carried out on a single flexible link manipulator with the initial part of the link being rigid. This type of manipulator is referred to as a slewing single rigid—flexible link manipulator (SRFLM). A new method for finding the zeros of the transfer function of an SRFLM without using the corresponding transfer function is introduced. The changes of the locations of the zeros of an SRFLM owing to the changes in all the physical parameters (PPs) are investigated. It is shown that there are PPs where the increase in their values moves the zeros further from the imaginary axis; while by increasing the values of some other PPs the zeros become closer to the imaginary axis. Finally, there are PPs where the locations of the zeros are independent of their values. These findings will be beneficial in the design as well as control of flexible link manipulators and are among the main contributions of this work.
Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B, 2004
ABSTRACT In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by t... more ABSTRACT In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by three base-mounted partial spherical actuators is proposed. The parallel manipulator consists of a base, a moving platform and three connecting legs. Each leg has spherical (S), prismatic (P) and universal (U) joints (SPU) in serial manner. The spherical joints are partially actuated due to the fact that the actuators of each leg are used only to specify its leg’s direction. The inverse and forward pose kinematics as well as the singularity points of the aforementioned mechanism is described in the article. In the inverse pose kinematics, active joint variables could be calculated with no need for the evaluation of passive joint variables. It will be shown that the inverse pose kinematics has sixty-four (64) solutions (64 different configurations exists for the inverse pose problem). In the forward pose kinematics, instead of twelve nonlinear equations derived by equaling the transformation matrices of each leg through Denavit-Hartenberg notation, only three nonlinear equations with less nonlinearity could be solved via numerical method, and therefore the numerical method converges more rapidly to the answer. Finally two different sets of singularity points with different natures are obtained.
ABSTRACT In this paper a new identification method to obtain the friction parameters in the joint... more ABSTRACT In this paper a new identification method to obtain the friction parameters in the joints of robotic manipulators is presented. These parameters are coulomb friction, static friction, Stribeck velocity constant and viscous damping coefficient. The available methods to find these parameters either require the design of a controller or the precise value of system parameters such as mass moment of inertia. In contrast, the new method proposed here finds these parameters by a nonlinear optimization approach which requires neither any knowledge of system’s parameters nor any controller design. The corresponding nonlinear optimization problem is solved using an efficient technique which does not require iteration or any initial estimate of optimization parameters. The new method proposed in this paper was experimentally verified on a robotic manipulator available in the robotics laboratory at the University of Saskatchewan.
Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B, 2010
ABSTRACT In this paper a new identification method to obtain the friction parameters in the joint... more ABSTRACT In this paper a new identification method to obtain the friction parameters in the joints of robotic manipulators is presented. These parameters are coulomb friction, static friction, Stribeck velocity constant and viscous damping coefficient. The available methods to find these parameters either require the design of a controller or the precise value of system parameters such as mass moment of inertia. In contrast, the new method proposed here finds these parameters by a nonlinear optimization approach which requires neither any knowledge of system’s parameters nor any controller design. The corresponding nonlinear optimization problem is solved using an efficient technique which does not require iteration or any initial estimate of optimization parameters. The new method proposed in this paper was experimentally verified on a robotic manipulator available in the robotics laboratory at the University of Saskatchewan.
Volume 8: Dynamic Systems and Control, Parts A and B, 2010
ABSTRACT A temporal planning algorithm that is implemented on a wheeled mobile robot is presented... more ABSTRACT A temporal planning algorithm that is implemented on a wheeled mobile robot is presented. This algorithm has two parts: the first part is developed to control the motion of the mobile robot, and the second part is designed to control a 6-degrees-of-freedom (DOF) arm attached to the robot. In most robotic applications, it is necessary for the mobile robot to plan and follow a desired path. It may also be necessary for the robot to follow a given velocity profile, which is known as temporal planning. The advantage of temporal planning method in this paper is in its simplicity and its computational efficiency. A rudimentary trajectory is first created by assigning an arbitrary time to each segment of the path. This trajectory is made feasible by applying a number of constraints and using a linear scaling technique. When a velocity profile is given, a nonlinear time scaling technique is used to fit the mobile robot’s linear velocity to the given velocity profile. A method for avoiding moving obstacles is also implemented. Simulation and experimental results showed good agreement with each other. A novelty of this paper is in developing and implementing a new method for control of a 6-DOF arm attached to the mobile robot. Two methods have been proposed and tested for position control of the robot arm; i) linear end-effector increment (LEI), and ii) linear joints increment (LJI). It is shown that LEI is more precise than LJI in trajectory tracking of robot arm; however, the singularity of Denavit-Hartenberg (DH) transformations matrix limits the application of this method for specific trajectories. The LJI is developed to avoid the singularity in DH transformation matrix. The experimental results for four different paths show the effectiveness of the LJI approach. The successful experimental results of path and temporal planning of a wheeled mobile robot and motion control of its industrial arm is reported.
Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B, 2005
ABSTRACT In this article kinematic analysis of a 3 Leg-Spherically Actuated (3SA) parallel manipu... more ABSTRACT In this article kinematic analysis of a 3 Leg-Spherically Actuated (3SA) parallel manipulator will be addressed. Since each leg has a spherical actuator (three inputs for each leg) and manipulator has three legs; totally, there are nine inputs. Due to the fact that the manipulator has six degree of freedom, only six independent inputs are needed. Thus actuation could be done in different ways. If the triangles representing base and platform are equilateral, there are twenty different ways of actuation that should be studied during forward kinematic analysis. Rather than adopting the standard Denavit-Hartenberg approach, a simple method for forward kinematic analysis for all these different ways of twenty ways has been introduced. Considering all these ways, it will be shown that at least two and at most six nonlinear algebraic equations should be solved during forward kinematic analysis, while choosing the standard approach twelve nonlinear equations should be solved for each way of actuation. A unique inverse kinematic method has been presented. The singularly analysis for all these different ways of actuation has also been studied. For two out of the twenty different ways, closed form solutions for the singularity analysis have been obtained, for other ways; conditions which result in singularity configuration has been presented and simulation justified the proposed criteria.
Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007
New methods for the inverse and forward kinematic analysis of the novel six degrees of freedom (6... more New methods for the inverse and forward kinematic analysis of the novel six degrees of freedom (6DOF) parallel manipulator which has only two legs are presented. The actuation of the new mechanism is through two base-mounted spherical actuators. In the inverse pose kinematic, active joint variables are directly calculated with no need for the evaluation of passive joint variables. In the forward pose kinematic, closed form solution adopting a new approach is presented. It is shown that the inverse and forward pose kinematic have sixteen and four different solutions, respectively. Moreover, closed form equations for the rate kinematic analysis are proposed. Finally, two different categories of the singularity points for the new mechanism with their geometrical interpretation are introduced. In one category the mechanism loses one or more DOF while in the other one it gains one or more DOF.
ABSTRACT A new controller for the end-effector trajectory tracking (EETT) of a class of flexible ... more ABSTRACT A new controller for the end-effector trajectory tracking (EETT) of a class of flexible link manipulators which consists of a chain of rigid links with a flexible end-link (CRFE) is introduced. To design this new controller, a dynamic model of the CRFE is expressed in the singularly perturbed form; that is, decomposed into slow and fast subsystems. The states of the slow subsystem are the joints’ rotations and their time derivative, while the states of the fast subsystem are the flexible variables, which model the lateral deflection of the end-link, and their time derivative. For the slow subsystem, the new controller requires only ‘‘one’’ corrective torque in addition to the computed torque command of the rigid link counterpart of the CRFE for the reduction of the EETT error. This corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. The need for only one corrective torque and its derivation are among the contributions of the new controller. To stabilize the fast subsystem, an observer-based controller is designed according to the gain-scheduling technique. Due to the application of the observer-based controller there is no need for the measurement of the time derivative of the flexible link’s lateral deflection, in which its measurement is difficult if not impossible in practice. This feature of the new controller is an advantage for it. To facilitate the derivation and implementation of this controller, several properties of the matrices in the dynamic model of the CRFE are introduced and used which are other contributions of this research. The effectiveness and feasibility of the new controller are shown by simulation and experimental studies.
ABSTRACT A new control strategy for the end- effector trajectory tracking (EETT) of a single flex... more ABSTRACT A new control strategy for the end- effector trajectory tracking (EETT) of a single flexible link manipulator (SFLM) is introduced. The linear dynamic model of the SFLM is expressed in the singularly perturbed form. To reduce the EETT error, a corrective torque is added to the "computed torque control" command of the rigid link counterpart of the SFLM. This corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. It is proven that the EETT error is a function of the fundamental natural frequency of the SFLM. That is, the order of the EETT error, after employing 3 2 this new method, is greater than epsiv3 and smaller than epsiv2 , where epsiv = 1(2pif) and f is the fundamental natural frequency of the SFLM. The implementation of the introduced technique does not require the full state measurements, since by designing an observer; the rate of the change of the flexible variables with respect to time is estimated. Thus only the measurements of the joint rotation, joint velocity, and flexible variables are required. The proof of the stability, based on the Lyapunov criteria, is given. The results of the simulation and experimental studies are also included. Making the error of the EETT smaller and reducing the number of state measurements are the main contributions of this work.
ABSTRACT In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by t... more ABSTRACT In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by three base-mounted partial spherical actuators is proposed. The parallel manipulator consists of a base, a moving platform and three connecting legs. Each leg has spherical (S), prismatic (P) and universal (U) joints (SPU) in serial manner. The spherical joints are partially actuated due to the fact that the actuators of each leg are used only to specify its leg’s direction. The inverse and forward pose kinematics as well as the singularity points of the aforementioned mechanism is described in the article. In the inverse pose kinematics, active joint variables could be calculated with no need for the evaluation of passive joint variables. It will be shown that the inverse pose kinematics has sixty-four (64) solutions (64 different configurations exists for the inverse pose problem). In the forward pose kinematics, instead of twelve nonlinear equations derived by equaling the transformation matrices of each leg through Denavit-Hartenberg notation, only three nonlinear equations with less nonlinearity could be solved via numerical method, and therefore the numerical method converges more rapidly to the answer. Finally two different sets of singularity points with different natures are obtained.
In this article, a study of the zeros of the transfer function, between the base torque and the e... more In this article, a study of the zeros of the transfer function, between the base torque and the end-effector displacement, for flexible link manipulators is performed. The analysis is carried out on a single flexible link manipulator with the initial part of the link being rigid. This type of manipulator is referred to as a slewing single rigid—flexible link manipulator (SRFLM). A new method for finding the zeros of the transfer function of an SRFLM without using the corresponding transfer function is introduced. The changes of the locations of the zeros of an SRFLM owing to the changes in all the physical parameters (PPs) are investigated. It is shown that there are PPs where the increase in their values moves the zeros further from the imaginary axis; while by increasing the values of some other PPs the zeros become closer to the imaginary axis. Finally, there are PPs where the locations of the zeros are independent of their values. These findings will be beneficial in the design as well as control of flexible link manipulators and are among the main contributions of this work.
Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B, 2004
ABSTRACT In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by t... more ABSTRACT In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by three base-mounted partial spherical actuators is proposed. The parallel manipulator consists of a base, a moving platform and three connecting legs. Each leg has spherical (S), prismatic (P) and universal (U) joints (SPU) in serial manner. The spherical joints are partially actuated due to the fact that the actuators of each leg are used only to specify its leg’s direction. The inverse and forward pose kinematics as well as the singularity points of the aforementioned mechanism is described in the article. In the inverse pose kinematics, active joint variables could be calculated with no need for the evaluation of passive joint variables. It will be shown that the inverse pose kinematics has sixty-four (64) solutions (64 different configurations exists for the inverse pose problem). In the forward pose kinematics, instead of twelve nonlinear equations derived by equaling the transformation matrices of each leg through Denavit-Hartenberg notation, only three nonlinear equations with less nonlinearity could be solved via numerical method, and therefore the numerical method converges more rapidly to the answer. Finally two different sets of singularity points with different natures are obtained.
ABSTRACT In this paper a new identification method to obtain the friction parameters in the joint... more ABSTRACT In this paper a new identification method to obtain the friction parameters in the joints of robotic manipulators is presented. These parameters are coulomb friction, static friction, Stribeck velocity constant and viscous damping coefficient. The available methods to find these parameters either require the design of a controller or the precise value of system parameters such as mass moment of inertia. In contrast, the new method proposed here finds these parameters by a nonlinear optimization approach which requires neither any knowledge of system’s parameters nor any controller design. The corresponding nonlinear optimization problem is solved using an efficient technique which does not require iteration or any initial estimate of optimization parameters. The new method proposed in this paper was experimentally verified on a robotic manipulator available in the robotics laboratory at the University of Saskatchewan.
Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B, 2010
ABSTRACT In this paper a new identification method to obtain the friction parameters in the joint... more ABSTRACT In this paper a new identification method to obtain the friction parameters in the joints of robotic manipulators is presented. These parameters are coulomb friction, static friction, Stribeck velocity constant and viscous damping coefficient. The available methods to find these parameters either require the design of a controller or the precise value of system parameters such as mass moment of inertia. In contrast, the new method proposed here finds these parameters by a nonlinear optimization approach which requires neither any knowledge of system’s parameters nor any controller design. The corresponding nonlinear optimization problem is solved using an efficient technique which does not require iteration or any initial estimate of optimization parameters. The new method proposed in this paper was experimentally verified on a robotic manipulator available in the robotics laboratory at the University of Saskatchewan.
Volume 8: Dynamic Systems and Control, Parts A and B, 2010
ABSTRACT A temporal planning algorithm that is implemented on a wheeled mobile robot is presented... more ABSTRACT A temporal planning algorithm that is implemented on a wheeled mobile robot is presented. This algorithm has two parts: the first part is developed to control the motion of the mobile robot, and the second part is designed to control a 6-degrees-of-freedom (DOF) arm attached to the robot. In most robotic applications, it is necessary for the mobile robot to plan and follow a desired path. It may also be necessary for the robot to follow a given velocity profile, which is known as temporal planning. The advantage of temporal planning method in this paper is in its simplicity and its computational efficiency. A rudimentary trajectory is first created by assigning an arbitrary time to each segment of the path. This trajectory is made feasible by applying a number of constraints and using a linear scaling technique. When a velocity profile is given, a nonlinear time scaling technique is used to fit the mobile robot’s linear velocity to the given velocity profile. A method for avoiding moving obstacles is also implemented. Simulation and experimental results showed good agreement with each other. A novelty of this paper is in developing and implementing a new method for control of a 6-DOF arm attached to the mobile robot. Two methods have been proposed and tested for position control of the robot arm; i) linear end-effector increment (LEI), and ii) linear joints increment (LJI). It is shown that LEI is more precise than LJI in trajectory tracking of robot arm; however, the singularity of Denavit-Hartenberg (DH) transformations matrix limits the application of this method for specific trajectories. The LJI is developed to avoid the singularity in DH transformation matrix. The experimental results for four different paths show the effectiveness of the LJI approach. The successful experimental results of path and temporal planning of a wheeled mobile robot and motion control of its industrial arm is reported.
Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B, 2005
ABSTRACT In this article kinematic analysis of a 3 Leg-Spherically Actuated (3SA) parallel manipu... more ABSTRACT In this article kinematic analysis of a 3 Leg-Spherically Actuated (3SA) parallel manipulator will be addressed. Since each leg has a spherical actuator (three inputs for each leg) and manipulator has three legs; totally, there are nine inputs. Due to the fact that the manipulator has six degree of freedom, only six independent inputs are needed. Thus actuation could be done in different ways. If the triangles representing base and platform are equilateral, there are twenty different ways of actuation that should be studied during forward kinematic analysis. Rather than adopting the standard Denavit-Hartenberg approach, a simple method for forward kinematic analysis for all these different ways of twenty ways has been introduced. Considering all these ways, it will be shown that at least two and at most six nonlinear algebraic equations should be solved during forward kinematic analysis, while choosing the standard approach twelve nonlinear equations should be solved for each way of actuation. A unique inverse kinematic method has been presented. The singularly analysis for all these different ways of actuation has also been studied. For two out of the twenty different ways, closed form solutions for the singularity analysis have been obtained, for other ways; conditions which result in singularity configuration has been presented and simulation justified the proposed criteria.
Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007
New methods for the inverse and forward kinematic analysis of the novel six degrees of freedom (6... more New methods for the inverse and forward kinematic analysis of the novel six degrees of freedom (6DOF) parallel manipulator which has only two legs are presented. The actuation of the new mechanism is through two base-mounted spherical actuators. In the inverse pose kinematic, active joint variables are directly calculated with no need for the evaluation of passive joint variables. In the forward pose kinematic, closed form solution adopting a new approach is presented. It is shown that the inverse and forward pose kinematic have sixteen and four different solutions, respectively. Moreover, closed form equations for the rate kinematic analysis are proposed. Finally, two different categories of the singularity points for the new mechanism with their geometrical interpretation are introduced. In one category the mechanism loses one or more DOF while in the other one it gains one or more DOF.
ABSTRACT A new controller for the end-effector trajectory tracking (EETT) of a class of flexible ... more ABSTRACT A new controller for the end-effector trajectory tracking (EETT) of a class of flexible link manipulators which consists of a chain of rigid links with a flexible end-link (CRFE) is introduced. To design this new controller, a dynamic model of the CRFE is expressed in the singularly perturbed form; that is, decomposed into slow and fast subsystems. The states of the slow subsystem are the joints’ rotations and their time derivative, while the states of the fast subsystem are the flexible variables, which model the lateral deflection of the end-link, and their time derivative. For the slow subsystem, the new controller requires only ‘‘one’’ corrective torque in addition to the computed torque command of the rigid link counterpart of the CRFE for the reduction of the EETT error. This corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. The need for only one corrective torque and its derivation are among the contributions of the new controller. To stabilize the fast subsystem, an observer-based controller is designed according to the gain-scheduling technique. Due to the application of the observer-based controller there is no need for the measurement of the time derivative of the flexible link’s lateral deflection, in which its measurement is difficult if not impossible in practice. This feature of the new controller is an advantage for it. To facilitate the derivation and implementation of this controller, several properties of the matrices in the dynamic model of the CRFE are introduced and used which are other contributions of this research. The effectiveness and feasibility of the new controller are shown by simulation and experimental studies.
ABSTRACT A new control strategy for the end- effector trajectory tracking (EETT) of a single flex... more ABSTRACT A new control strategy for the end- effector trajectory tracking (EETT) of a single flexible link manipulator (SFLM) is introduced. The linear dynamic model of the SFLM is expressed in the singularly perturbed form. To reduce the EETT error, a corrective torque is added to the "computed torque control" command of the rigid link counterpart of the SFLM. This corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. It is proven that the EETT error is a function of the fundamental natural frequency of the SFLM. That is, the order of the EETT error, after employing 3 2 this new method, is greater than epsiv3 and smaller than epsiv2 , where epsiv = 1(2pif) and f is the fundamental natural frequency of the SFLM. The implementation of the introduced technique does not require the full state measurements, since by designing an observer; the rate of the change of the flexible variables with respect to time is estimated. Thus only the measurements of the joint rotation, joint velocity, and flexible variables are required. The proof of the stability, based on the Lyapunov criteria, is given. The results of the simulation and experimental studies are also included. Making the error of the EETT smaller and reducing the number of state measurements are the main contributions of this work.
ABSTRACT In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by t... more ABSTRACT In this paper, a novel six degrees-of-freedom (6-DOF) parallel manipulator actuated by three base-mounted partial spherical actuators is proposed. The parallel manipulator consists of a base, a moving platform and three connecting legs. Each leg has spherical (S), prismatic (P) and universal (U) joints (SPU) in serial manner. The spherical joints are partially actuated due to the fact that the actuators of each leg are used only to specify its leg’s direction. The inverse and forward pose kinematics as well as the singularity points of the aforementioned mechanism is described in the article. In the inverse pose kinematics, active joint variables could be calculated with no need for the evaluation of passive joint variables. It will be shown that the inverse pose kinematics has sixty-four (64) solutions (64 different configurations exists for the inverse pose problem). In the forward pose kinematics, instead of twelve nonlinear equations derived by equaling the transformation matrices of each leg through Denavit-Hartenberg notation, only three nonlinear equations with less nonlinearity could be solved via numerical method, and therefore the numerical method converges more rapidly to the answer. Finally two different sets of singularity points with different natures are obtained.
Uploads
Papers by Mohammad Vakil