Search

In this article a method for determining the admissible acceleration of the end-effector is presented for the suspended cable robot in the different points of the workspace. The presented acceleration analysis is different with the dynamic work space. Indeed, the dynamic work space is defined as the set of all end-effector poses satisfying the acceleration conditions. While in the proposed analysis in this paper, the allowable acceleration range of the end-effector in each direction is obtained for any point of the workspace. To this end, after deriving the kinematic equations of the four-cable suspended robot, its dynamic equations are derived using the Lagrange method. Then, on the base of the positive tension constraint in the cables and the torque constraint of the actuators, the obtained equations are simplified to obtain the simple relation between the constrains and the end-effector acceleration in such a way that the lower and upper limit of the admissible acceleration is obtained. Some simulations are done in order to present the admissible acceleration in different point of the workspace. The simulation results show that the acceleration range is in the form of the pyramid with the rhomboid base. So the allowable range of the acceleration is changed in different direction. The results obtained in this paper can be used for online trajectory planning in high speed motion of cable robot.

In the dynamic manipulation of objects, the aim is to throw an object by a robot to the desired target even outside the reachable workspace. In this paper, the concept of the throw-able workspace or dynamic manipulation workspace is defined as a set of points which the robot is able to throw the object at them. Thus, in order to obtain the maximum dynamic manipulation workspace which means the farthest points that object can be manipulated, it is necessary to solve the optimal throwing problem. To this end, the optimal throwing problem is defined as the optimal control problem solved using the indirect solution method based on the fundamental theorem of the calculus of variations. By applying the throwing equation as a moving boundary condition, the derived optimality conditions construct a two-point boundary value problem which its solution results in the optimal throwing. Finally, an algorithm is presented to calculate the maximum dynamic manipulation workspace. Then, simulation results are presented for a single link robot in order to evaluate the defined concept as well as the effectiveness of the proposed method for problem-solving.

In this paper, optimal swing up of a double inverted pendulum (DIP) with two underactuated degrees of freedom (DOFs) is solved using the indirect solution of optimal control problem. Unlike the direct method that leads to an approximate solution, the proposed indirect method results in an exact solution of the optimal control problem, but suffers from its limited convergence domain which makes it difficult to solve. In order to overcome this problem, an inversion-based method is used to obtain the required initial solution for the indirect method. In the proposed methodology, dynamic equations are derived for a general inverted pendulum using Euler-Lagrange formulation. Then the necessary optimality conditions are derived for a DIP on the cart using the Pontryagin’s maximum principle (PMP). The obtained equations establish a two-point boundary value problem (TPBVP) which solution results in optimal trajectories of the cart and pendulums. In order to demonstrate the applicability of the presented method, a simulation study is performed for a DIP. The simulation results confirm the superiority of the proposed method in terms of reduced effort.

In this paper, a method based on the indirect solution of optimal control problem is presented to specify the optimal trajectory of spatially suspended cable robot in point to point motion with considering the counterweights. In fact, an optimal trajectory planning problem is outlined in which states, controls and the values of counterweights must be calculated simultaneously in order to minimize the given performance index. The value of the pulley torques is considered for the performance index (objective function). Using the fundamental theorem of a calculus of variations, the necessary conditions for optimality of cable robot are achieved. For the three-cable spatial robot, a two-point boundary value problem is achieved which can be solved with bvp4c command in MATLAB. The obtained results show that optimal balancing in comparison with the unbalancing method can reduce the performance index significantly.

The purpose of this article is finding the optimal path with minimum effort to move the end-effector of the three cable spatial robot in work space. For this work, first, kinematic and dynamic modeling is done of the three cable spatial robot. Then simulation and results extraction are done by both direct and indirect methods. Based on of indirect solution method is the calculus of variations. Optimality necessary condition is given in order to minimize the torque between the two points and is extracted using the pontryagin minimum principle. This optimality condition is formed a boundary value problem of two-point, which can be solved using numerical algorithms. Direct method is created by combining a metaheuristic optimization method, a polynomial interpolation and the robot equations. This article is used the metaheuristic method of triangular optimizer algorithm and the polynomial interpolation of four degree. This new combination created with the polynomial of four degree, instead of using the intermediate values of the path as design variables, specified constants of polynomial puts the design variable in order to path optimization. The indirect method gives the exact response, but extraction of optimality condition its, is the difficult in terms of calculations mathematical. While the direct method gives the approximate response without algebraic calculations. Finally, two examples are done with direct method and indirect method. The results comparisons are show the appropriate efficiency of the suggested direct method.

Dynamical stability of mobile robots becomes important and it should be discussed when there is a need of high speed motions. This problem can be solved by appropriate design of control signal with stability constraints. But, actually this is, in many cases, impossible or at least unbearable. In this paper, we have noticed balancing approach for this problem to significant reduction of control effort. Based on fixed-point approach the values of counterweights are computed and finally this iterative method drives the mobile robot through a stable trajectory. This novel method is called iterative balancing of mobile robots and final stable trajectory has very low pay-off in compare of unbalanced constrained one. The results are investigated by simulating of open loop control of mobile robot.

In this article, triangular optimizer algorithm optimization method is presented for minimizing the weight of the truss structures. Triangular optimizer algorithm is a new metaheuristic method which is inspired of triangle. In this method, the initial vector of design variables is considered as the base of the triangle (first row). Then the objective functions are calculated and the best and the worst response are identified. The worst response is removed from the current population and the remaining population after some modifications is defined the second row. This process continues till reaching the apex of triangle, the optimal solution of this triangle. In the second iteration (second triangle), a certain number of the initial design variables are retrieved by the optimal solution of the previous triangle and the remaining of this population are created in the initial interval for escape from local optimums. So base of the second optimal triangle is formed. Then the mentioned algorithm is performed until optimum response of second triangle is achieved. These operations are continued until the convergence condition being satisfied. To prove the capabilities of the proposed algorithm shaping and sizing-shaping optimization of four truss structures are considered. The obtained statistical results of truss structures optimization show that the TOA is able to managed to achieve better optimal solutions compared to different optimization techniques.

Finding optimal trajectory is critical in several applications of robot manipulators. This paper is applied the open-loop optimal control approach for generating the optimal trajectory of the flexible mobile manipulators in point-to-point motion. This method is based on the Pontryagin's minimum principle that by providing a two-point boundary value problem is solved the problem. This problem is known to be complex in particular when combined motion of the base and manipulator, nonholonomic constraint of the base and highly non-linear and complicated dynamic equations as a result of flexible nature of links are taken into account. The study emphasizes on modeling of the complete optimal control problem by remaining all nonlinear state and costate variables as well as control constraints. In this method, designer can compromise between different objectives by considering the proper penalty matrices and it yields to choose the proper trajectory among the various paths. The effectiveness and capability of the proposed approach are demonstrated through simulation studies. Finally, to verify the proposed method, the simulation results obtained from the model are compared with the results of those available in the literature.

Abstract  In this paper we extend the work done by Chen et al. (IEEE Trans Ind Electron 47(4):932–938, 2000) which proposed a nonlinear disturbance observer for two-link robot manipulators to n-link robot manipulators. A general form of dynamic equations of serial n-link robot manipulator is considered, and the stability analysis of the proposed observer is performed by using Lyapunov’s direct method. Although it seems that the formulation of disturbance observer is easy to derive, choosing the disturbance observer gain to guarantee stability is really hard. In this paper it is shown that the design parameter can be selected depends on the maximum velocity and physical parameters of robot manipulator to guarantee the global asymptotic stability of the disturbance observer. Using this nonlinear disturbance observer, no accurate dynamic model is required to achieve high precision motion control, because it makes the system robust against internal disturbances such as unmodeled dynamics and external disturbances such as friction in joints. The effectiveness of the proposed observer is investigated by numerical simulation for three-Dofs robot manipulator. In fact, controller with disturbance observer has more superior tracking performance, with a wide range of payloads and in the presence of friction in joints. It is also found that, although the proposed observer is designed for slow varying disturbances, it can estimate rapid time varying disturbances very well. [ABSTRACT FROM AUTHOR]