Dynamic Load-carrying Capacity Research Articles

A New Methodology for Solving Trajectory Planning and Dynamic Load-Carrying Capacity of a Robot Manipulator

A new methodology using a direct method for obtaining the best found trajectory planning and maximum dynamic load-carrying capacity (DLCC) is presented for a 5-degree of freedom (DOF) hybrid robot manipulator. A nonlinear constrained multiobjective optimization problem is formulated with four objective functions, namely, travel time, total energy involved in the motion, joint jerks, and joint acceleration. The vector of decision variables is defined by the sequence of the time-interval lengths associated with each two consecutive via-points on the desired trajectory of the 5-DOF robot generalized coordinates. Then this vector of decision variables is computed in order to minimize the cost function (which is the weighted sum of these four objective functions) subject to constraints on joint positions, velocities, acceleration, jerks, forces/torques, and payload mass. Two separate approaches are proposed to deal with the trajectory planning problem and the maximum DLCC calculation for the 5-DOF robot manipulator using an evolutionary optimization technique. The adopted evolutionary algorithm is the elitist nondominated sorting genetic algorithm (NSGA-II). A numerical application is performed for obtaining best found solutions of trajectory planning and maximum DLCC calculation for the 5-DOF hybrid robot manipulator.

Trajectory planning of parallel kinematic manipulators for the maximum dynamic load-carrying capacity

The objective of this paper is to identify the trajectory that accomplishes the assigned motion with the maximum dynamic load-carrying capacity (DLCC) which is subject to constraints imposed by the kinematics and dynamics of a manipulator structure. In this study, the possible trajectories of the manipulator are modeled using a parametric path representation, the optimal trajectory is then obtained using a two-loop of optimization process, in which the inner-loop optimization process based on the Simplex-type linear programming method is used to determine the dynamic loading at each discrete point along the presumed trajectory and then to formulate the DLCC; the outer-loop optimization process based on the particle swarm optimization algorithm is to solve the controlled points by maximizing the formulated DLCC. The numerical results confirm the feasibility of the optimized trajectories and demonstrate the effectiveness of the proposed algorithm for the maximum dynamic load-carrying trajectory planning of a parallel kinematic manipulator.

Maximum allowable load of very flexible manipulators by using absolute nodal coordinate

The main objective of the present paper is to develop a general formula for finding the Dynamic Load Carrying Capacity (DLCC) of very flexible link manipulators undergoing large deflection. An efficient finite element formulation, absolute nodal coordinate formulation (ANCF) is employed to describe nonlinear modeling for flexible link manipulator with large deflection, in which both the transverse normal strain and the shear strain are considered. In comparison to other large deflection formulations, the motion equations contain constant mass matrix, and also, the Coriolis and centrifugal forces are identically equal to zero because the terms arising from geometric elastic nonlinearity are moved to stiffness, reactive and external forces, which are originally nonlinear. This makes the formulation particularly efficient in computational terms and numerically more stable than alternative geometrically nonlinear formulations based on lower-order terms. In this investigation, the equations of motion are derived taking into account the shear deformable using the ANCF based approaches. Then, a method for determination of the dynamic load carrying capacity (DLCC) for geometrically nonlinear elastic robot is described giving attention to accuracy and actuator constraints. In order to initially check the validity of the dynamic equations, the proposed model has been implemented and tested on a single-link very flexible arm. A simulation study is carried out to verify the effectiveness of the presented algorithm for finding DLCC of very flexible link manipulators. The results illustrate the power and efficiency of the method to overcome the high nonlinearity nature of the problem.

Path planning algorithm in wheeled mobile manipulators based on motion of arms

This work proposes an algorithm besides output feedback linearization method for controlling a wheeled mobile robot with two manipulators. To control such a mobile robot, three desired trajectories (or fixed points for regulation) are needed: two for the arms and one for the base. Improper choice in base path leads to singularity, low performance and failure. To prevent singularities and to attain a smooth motion, an algorithm is introduced as a local path planning process for the base. It consists of two parts which helps the robot to maintain the desired configuration. The first part of the algorithm mainly focuses on the position and orientation of the base in future time based on the arms configuration, and the second part adjusts the movement of the arms for obtaining a consistent motion. This maintenance reduces and preserves the norm of applied torques, which consequently leads to an increase in the performance of the robot and its dynamic load carrying capacity (DLCC). Also, it is no longer required to define a trajectory or an end point for the base movement since they will be calculated automatically by the algorithm.

Maximum load of flexible joint manipulators using nonlinear controllers

SUMMARYThe main innovation of this paper is determining the dynamic load carrying capacity (DLCC) of a flexible joint manipulator (FJM) using a closed form nonlinear optimal control approach. The proposed method is compared with two closed loop nonlinear methods that are usually applied to robotic systems. As a new idea, DLCC of the manipulator is considered as a criterion to compare how well controllers perform point to point mission for the FJMs. The proposed method is compared with feedback linearization (FL) and robust sliding mode control (SMC) methods to show better performance of proposed nonlinear optimal control approach. An optimal controller is designed by solving a nonlinear partial differential equation named the Hamilton–Jacobi–Bellman (HJB) equation. This equation is complicated to solve exactly for complex dynamics so it is solved numerically using an iterative approximation combined with the Galerkin method. In the FL method, angular position, velocity, acceleration and jerk of links are considered as new states to linearize the dynamic equations. In the case of SMC, the dynamic equations of manipulator are changed to the standard form then the Slotine method is used to design the sliding mode controller. Two simulations are performed for a planar and a spatial Puma manipulator and performances of controllers are compared. Finally an experimental test is done on 6R manipulator and the Stereo vision method is used to determine the position and orientation of the end-effector.

Evaluation of Dynamic Load-Carrying Capacity for Free-Floating Space Manipulators

Two kinds of dynamic load-carrying capacity (DLCC) evaluation methods for free-floating space manipulators (FFSM) in two typical on-orbit operating missions are proposed in this paper. DLCC evaluation is transformed into nonlinear programming problem (NPP) by introducing load-carrying coefficient to measure DLCC: in point-to-point task, penalty function method is adopted to approach the boundary of feasible region rapidly, then DLCC can be obtained through following iterations; in trajectory tracking task, NPP is solved by using multiple one-dimensional search, the dynamic load-carrying coefficient in discontinuous feasible region can be quickly solved through adjusting the searching boundary constantly. The effectiveness of the mentioned methods is verified by simulations.

Dynamic Load-Carrying Capacity of Multi-arm Cooperating Wheeled Mobile Robots via Optimal Load Distribution Method

In this paper, the dynamic load-carrying capacity (DLCC) of cooperating mobile robots is investigated. The term, cooperating mobile robot, means a wheeled mobile base with multiple arms where end-effectors of the arms are connected to each other for holding and manipulating an object. In order to compute the load capacity of an arm, it is necessary to extract applied torques of motors in the joints. The cooperating feature of multiple manipulators is identified by applying proper constraints on dynamic models of the manipulators. These constraints are used to model the connections between the end-effectors, which imply that all the manipulators should grasp an object simultaneously. In that case, there exists a redundancy in corresponding dynamic equations, which can be solved by introducing new equations from optimal load distribution technique. This optimization is based on Lagrange multipliers method, considering the applied constraints. In this research, by virtue of cooperating models and by deriving the torques equations, the problem of DLCC is extended to multi-arm mobile manipulators. The general modeling is presented for a multi-arm manipulator with m arms where each arm has n degrees of freedom. For appreciating the advantages of the cooperative model, a simplified model of this general formulation is simulated and the results are discussed. Moreover, the cooperating model of the problem is simulated and conferred with an alternative model. The alternative model is called “free”, in a sense that it does not contain the constraints on the end-effectors for simultaneous grasping. The corresponding results prove the improvement in DLCC for systems with constraints and additional internal forces induced by it.

Optimal path planning of a cable-suspended robot with moving boundary using optimal feedback linearization approach

In this paper, the optimal path of a cable-suspended robot between two boundaries is assessed subject to its maximum load, while the initial and target points are moving boundary. Considering the fact that the most important application of cable robots is load carrying between two boundaries, planning the optimal path in which the heaviest load can be carried is extremely applicable. A closed loop optimal path planning algorithm is proposed in this paper for non-linear dynamic of a cable robots based on optimal feedback linearization. This method not only produces the optimal path of the end-effector, but also is robust to external disturbances and parametric uncertainties as a result of its closed loop nature. Moreover, considering the fact that in many automation applications the target of load handling is a sort of moving boundary like conveyors, finding the optimal point of this boundary which produces the optimal path with the maximum dynamic load carrying capacity (DLCC) amongst the other points of the boundary is obviously a useful study. Therefore, an online solution, based on variational algorithm is proposed here to solve the moving boundary problem which is compatible with the presented closed loop optimal path planning. This method is developed for both the initial and final moving boundaries. Finally maximum DLCC is obtained using an iterative method to check the optimality of the proposed method. The efficiency of the proposed algorithm is verified at the end by the aid of some simulation scenarios performed on a spatial six DOFs cable robot with six cables. The motors’ torque, motors’ speed, and resultant DLCCs are calculated for both simple optimal path and moving boundary cases and comparison of the results proves the mentioned claims based on superiority of the proposed algorithm of moving boundary in saving the energy and increasing the DLCC. All simulation results are supported by conducting an experimental study on the cable robot of IUST (ICaSbot) for regulation movement of the end-effector with moving boundary.

Dynamic load-carrying capacity of a novel redundantly actuated parallel conveyor

Conveyors are important equipment in the painting shop. Conveyors with cantilever beams have low load-carrying capacity and can carry small cars. To solve this problem, this paper presents a novel conveyor that uses redundantly actuated parallel manipulators. A method is proposed to obtain the maximum dynamic load-carrying capacity of the conveyor by optimizing the internal forces of the redundantly actuated parallel manipulators. To improve the dynamic load-carrying capacity, approaches using counterweights are utilized and compared. Furthermore, the maximum dynamic load-carrying capacity of the redundant parallel manipulator is compared with that of its nonredundant counterpart.

Optimal regulation of a cable robot in presence of obstacle using optimal adaptive feedback linearization approach

SUMMARYOptimal path planning of a closed loop cable robot, between two predefined points in presence of obstacles is the goal of this paper. This target is met by proposing a new method of optimal regulation for non linear systems while Dynamic Load Carrying Capacity (DLCC) of the robot is supposed as the related cost function. Feedback linearization is used to linearize the system while Linear Quadratic Regulator (LQR) is employed to optimize the DLCC of the system based on torque and error constraints. Obstacle avoidance for both the end-effector and cables is also considered by the aid of designing an adaptive local obstacle avoidance controller. As a result of linearized nature of the proposed optimal regulation and obstacle avoidance, fast calculation for real time applications is possible. Therefore, formulation of the optimal feedback linearization, together with calculating the DLCC of the robot based on the presented constraints is derived. Finally, a simulation study is performed to study the optimal dynamics and also the maximum DLCC of the cable robot in presence of obstacles. Simulation results are eventually compared with experimental tests conducted on IUST Cable Suspended Robot (ICaSbot) to verify the validity and efficiency of the proposed optimal controllers.

Compensating the flexibility uncertainties of a cable suspended robot using SMC approach

SUMMARYA sliding mode controller is designed to compensate for the flexibility uncertainties of a cable robot and improve its tracking performance. Of the most significant sources of these uncertainties are the elasticity of the cables and the flexibility of the joints. A favorable approach to improve the accuracy of the system is first to model the cable and joint flexibilities and then convert the model uncertainties into parametric uncertainties. Parametric uncertainties are the product of imprecise flexibility coefficients and are finally neutralized by a sliding mode controller. The flexibility in cables is modeled by considering the longitudinal vibration of the time-varying length cables. A simulation study is carried out to confirm the presented model and the positive effect of the designed controller. Then the impact of these uncertainties on the dynamic load carrying capacity (DLCC) of the robot is examined and compared for different cases. Finally, experimental tests are conducted on the IUST (Iran University of Science and Technology) cable-suspended robot to validate the presented theories and simulation results.

New optimization method to solve motion planning of dynamic systems: application on mechanical manipulators

In this paper, a new method is proposed to solve a nonlinear optimal control problem and determine the Dynamic Load-Carrying Capacity (DLCC) of fixed and mobile manipulators in point-to-point motion. Solution methods for designing nonlinear optimal controller in closed loop form are usually based on indirect methods, but the proposed method is a combination of direct and indirect methods. The optimal control law with state feedback form, for nonlinear dynamic systems, is given by the solution to the nonlinear Hamilton–Jacobi–Bellman (HJB) equation. The Galerkin procedure and a nonlinear optimization algorithm are used to solve this equation numerically. Another innovation of this paper is optimal trajectory planning, which is done simultaneously with the controller design procedure. Finally, a new algorithm is developed to find DLCC of manipulators and the related optimal trajectory using proposed method. The validity of the method is demonstrated via simulation and experimental tests for a fixed manipulator and two-link wheeled mobile manipulator named Scout.

Trajectory planning of mobile manipulators using dynamic programming approach

SUMMARYThis paper presents a solution for optimal trajectory planning problem of robotic manipulators with complicated dynamic equations. The main goal is to find the optimal path with maximum dynamic load carrying capacity (DLCC). Proposed method can be implemented to problems of both motion along a specified path and point-to-point motion. Dynamic Programming (DP) approach is applied to solve optimization problem and find the positions and velocities that minimize a pre-defined performance index. Unlike previous attempts, proposed method increases the speed of convergence by using the sequential quadratic programming (SQP) formulation. This formulation is used for solving problems with nonlinear constraints. Also, this paper proposes a new algorithm to design optimal trajectory with maximum DLCC for both fixed and mobile base mechanical manipulators. Algorithms for DLCC calculations in previous works were based on indirect optimization method or linear programming approach. The proposed trajectory planning method is applied to a linear tracked Puma and the mobile manipulator named Scout. Application of this algorithm is confirmed and simulation results are compared with experimental results for Scout robot. In experimental test, results are obtained using a new stereo vision system to determine the position of the robot end-effector.

Optimal Path Planning of Spatial Cable Robot Using Optimal Sliding Mode Control

This paper proposes a control strategy for a cable-suspended robot based on an optimal sliding mode approach confronted by external disturbances and parametric uncertainties. This control algorithm is based on the Lyapunov technique, which is not only able to provide the stability of the end-effector with an acceptable precision but also provides the optimal path in which the maximum load can be carried along. In addition, the optimization of the robot is performed based on an optimal sliding mode (SMC) approach. Tracking a predefined trajectory, path planning and the calculation of its relevant Dynamic Load Carrying Capacity (DLCC) is done based on the motors' torque and accuracy constraints. Optimal SMC, as a robust control algorithm, is used for controlling the stability of the system, while the Linear Quadratic Regulator (LQR) optimization tool is employed in order to optimize the controller gains. The main contribution of the paper is in calculating the DLCC of the cable robot. Finally, the efficiency of the proposed method is illustrated by performing some simulation studies on the ICaSbot (IUST Cable-suspended Robot), which supports six DOFs using six actuating cables, and experimental results confirm the validity of the authors' claim.

Quasi-static and dynamic compressive mechanical properties of engineered cementitious composite incorporating ground granulated blast furnace slag

The ground granulated blast-furnace slag (GGBS) has been widely used as a supplementary cementitious material in concrete production due to its lower heat of hydration, ability to gain strength over a longer period, superior performance against chemical attacks, and lower environmental impact. Four Engineered Cementitious Composite (ECC) mixtures with 50%, 60%, 70% and 80% substitution amounts of GGBS were prepared and their dynamic compressive mechanical behavior had been investigated by using a split Hopkinson pressure bar (SHPB) system at strain rates ranging from 84.8 to 184.6s−1. The corresponding quasi-static compressive responses of GGBS–ECC were also studied experimentally for contrasting with their dynamic tests. The objective of using GGBS to replace fly ash in ECC was to obtain higher quasi-static compressive strength and dynamic load-carrying capacity. The dynamic compressive stress–strain curves did not show residual strength behavior as that in the quasi-static stress–strain curves. ECC incorporating GGBS exhibited strain rate dependence. The peak stress increased and the peak strain decreased with the increase of strain rates. The toughness ratio under quasi-static compression was lower than that of dynamic compression according to the proposed method in this study. The toughness ratio under dynamic compression showed a slight increase with the GGBS content increasing. The strain rate had little influence on the toughness ratio.

Reconfiguration of a parallel kinematic manipulator for the maximum dynamic load-carrying capacity

In determining the maximum dynamic load-carrying capacity (DLCC) of reconfigurable motor-driven parallel kinematic manipulators (PKM), the objective is to identify the optimal configuration which accomplishes the assigned motion for the maximum DLCC subject to the constraints imposed by the kinematics and dynamics of the manipulator structure. In this study, the maximum DLCC problem of a reconfigurable PKM is formulated using the structured Boltzmann–Hamel–d'Alembert formulism, and then the optimal reconfiguration is obtained using a two-level of optimization process, in which the particle swarm optimization (PSO) algorithm is for the higher-level optimization and the Simplex-type linear programming (LP) method is for the lower-level optimization, such that the reconfiguration is achieved by re-locating the base points along linear guideways. The numerical results present the effects of the base locations on the DLCC and the corresponding kinematics and dynamics along the prescribed trajectory.

Analytical design of optimal trajectory with dynamic load-carrying capacity for cable-suspended manipulator

This paper describes the development of an approach for trajectory planning of cable-suspended parallel robots using optimal control approach. A prototype has been built, and tests have been carried out to verify the theoretical results. This paper briefly illustrates this device and presents some initial tests. The final dynamic equations are organized in a closed form similar to serial manipulator equations. Dynamic load-carrying capacity problem is converted into a trajectory optimization problem which is fundamentally a constrained nonlinear optimization problem. The problem is formulated using optimal control theory, and the ideas are analyzed using Pontryagin’s minimum principle. The optimal solutions are found by solving the corresponding nonlinear two-point boundary value problems. The main objective is to find the manipulator load-carrying capacity in point-to-point task by considering actuator torque while cable forces are positive.

Load maximization of flexible joint mechanical manipulator using nonlinear optimal controller

In this paper, a closed loop nonlinear optimal control approach is investigated for flexible joint manipulators (FJM). The dynamic load carrying capacity (DLCC) of these manipulators is obtained via this approach. The state-dependent Riccati equation (SDRE) technique is used for solving nonlinear optimal control problem. This method uses special parameterization to develop the nonlinear system to a linear structure having state-dependent coefficient matrices. The Taylor series numerical method is addressed by approximating the solution to the SDRE. Simulations for FJM are provided to illustrate the effectiveness of this approach for designing nonlinear feedback controllers and computing DLCC of these manipulators. Also effects of change in spring factors of manipulator and control parameters on resulted trajectory of manipulator are considered. DLCC is calculated subject to the limits in actuators and tracking accuracy. Finally the results are checked by comparison with experimental results.

Maximum DLCC of Spatial Cable Robot for a Predefined Trajectory Within the Workspace Using Closed Loop Optimal Control Approach

One of the most important applications of cable robots is load carrying along a specific path. Control procedure of cable robots is more challenging compared to linkage robots since cables can't afford pressure. Meanwhile carrying the heaviest possible payload for this kind of robots is desired. In this paper a nonlinear optimal control is proposed in order to control the end-effector within a predefined trajectory while the highest Dynamic Load Carrying Capacity (DLCC) can be carried. This purpose is met by applying optimum torque distribution among the motors with acceptable tracking accuracy. Besides, other algorithms are applied to make sure that the allowable workspace constraint is also satisfied. Since the dynamics of the robot is nonlinear, feedback linearization approach is employed in order to control the end-effector on its desirable path in a closed loop way while Linear Quadratic Regulator (LOR) method is used in order to optimize its controlling gains since the state space is linearized by the feedback linearization. The proposed algorithm is supported by doing some simulation studies on a two Degrees of Freedom (DOF) constrained planar cable robot as well as a six DOFs under constrained cable suspended robot and their DLCCs are calculated by satisfying the motor torque, tracking error and allowable workspace constraints. The results including the angular velocity, motors' torque, actual tracking of the end-effector and the DLCC of the robot are calculated and verified using experimental tests done on the cable robot. Comparison of the results of open loop simulation results, closed loop simulation results and experimental tests, shows that the results are improved by applying the proposed algorithm. This is the result of tuning the motors' torque and accuracy in a way that the highest DLCC can be achieved.

Positioning of shale-shaker drive with an assigned vibration trajectory

The position of the drive system of a shale shaker with two unbalanced vibration exciters and a given vibration trajectory is determined using systems of motion equations. This drive system is analyzed for an industrial prototype of shale shaker. The result is adjusted for the constraint of the dynamic load-carrying capacity of the bearings in a Russian-built shaker.