Motion equations of cooperative multi flexible mobile manipulator via recursive Gibbs–Appell formulation

In this paper, the developed model of an N-flexible-link mobile manipulator with revolute-prismatic joints is presented for the cooperative flexible multi mobile manipulator. In this model, the deformation of flexible links is calculated by using the assumed modes method. In additions, non-holonomic constraints of the robots’ mobile platforms that bound its locomotion are considered. This limitation is alleviated through the concurrent motion of revolute and prismatic joints, although it results in computational complexity and changes the final motion equations to time-varying form. Not only is the proposed dynamic model implemented for the multi-mobile manipulators with arms having independent motion, but also for multi-mobile manipulators in cooperation after defining gripper's kinematic constraints. These constraints are imported to the dynamic equations by defining Lagrange multipliers. The recursive Gibbs–Appell formulation is preferred over other similar approaches owing to the capability of solving the equations without the need to use Lagrange multipliers for eliminating non-holonomic constraints in addition to the novel optimized process of obtaining system equations. Hence, cumbersome simultaneous computations for eliminating the constraints of platform and arms are circumvented. Therefore, this formulation is improved for the first time by importing Lagrange multipliers for solving kinematic constrained systems. In the simulation section, the results of forward dynamics solution for two flexible single-arm manipulators with revolute-prismatic joints while carrying a rigid object are presented. Inverse dynamics equations of the system are also presented to obtain the maximum dynamic load-carrying capacity of the two-rigid-link mobile manipulators on a predefined path. Two constraints, namely the capacity of joint motors torque and robot motion stability are considered as the limitation criteria. The concluded motion equations are used to accurately control the movement of sensitive bodies, which is not achievable through the use of one platform.     

The motion of wheeled robots

The equations of motion of three-wheeled robots with two drive wheels and one passive caster wheel are derived and investigated. The control of longitudinal motion and turns of such a robot is implemented by appropriate control of the independent motors of the drive wheels. The research is carried out under the assumption that the robot is moving on a horizontal plane surface and that the wheels do not slip. A system of two non-linear equations with two controls is obtained for the non-holonomic system considered. The dependence of the phase portrait on the values of the constant controls and parameters of the system, taking into account the asymmetry of the robot, is investigated. The results obtained are not only of theoretical but also of practical interest.     

Cooperative Sensing and Distributed Control of a Diffusion Process Using Centroidal Voronoi Tessellations

<正>This paper considers how to use a group of robots to sense and control a diffusion process.The diffusion process is modeled by a partial differential equation (PDE),which is a both spatially and temporally variant system.The robots can serve as mobile sensors,actuators,or both.Centroidal Voronoi Tessellations based coverage control algorithm is proposed for the cooperative sensing task.For the diffusion control problem,this paper considers spraying control via a group of networked mobile robots equipped with chemical neutralizers,known as smart mobile sprayers or actuators,in a domain of interest having static mesh sensor network for concentration sensing.This paper also introduces the information sharing and consensus strategy when using centroidal Voronoi tessellations algorithm to control a diffusion process.The information is shared not only on where to spray but also on how much to spray among the mobile actuators.Benefits from using CVT and information consensus seeking for sensing and control of a diffusion process are demonstrated in simulation results.     

Optimal design of a 2 DOF parallel robot

This paper is aimed at presenting a study on the optimization of the Biglide mini parallel robot, which comprises two-degree-of-freedom (DOF) mini parallel robots with constant struts. The robot workspace is characterized and the inverse kinematics equation is obtained. In the paper, design optimization is implemented with Genetic Algorithms (GA) for optimization considering transmission quality index and workspace. Here, intended to show the advantages of using the GA, we applied it to a multicriteria optimization problem of 2 DOF mini parallel robot. Genetic algorithms (GA) are so far generally the best and most robust kind of evolutionary algorithms. A GA has a number of advantages. It can quickly scan a vast solution set. Bad proposals do not affect the end solution negatively as they are simply discarded. The obtained results have shown that the use of GA in such kind of optimization problem enhances the quality of the optimization outcome, providing a better and more realistic support for the decision maker. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling and trajectory planning of mobile manipulators with flexible links and joints

This paper is concerned with mathematical modeling and optimal motion designing of flexible mobile manipulators. The system is composed of a multiple flexible links and flexible revolute joints manipulator mounted on a mobile platform. First, analyzing on kinematics and dynamics of the model is carried out then; open-loop optimal control approach is presented for optimal motion designing of the system. The problem is known to be complex since combined motion of the base and manipulator, non-holonomic constraint of the base and highly non-linear and complicated dynamic equations as a result of the flexible nature of both links and joints are taken into account. In the proposed method, the generalized coordinates and additional kinematic constraints are selected in such a way that the base motion coordination along the predefined path is guaranteed while the optimal motion trajectory of the end-effector is generated. This method by using Pontryagin’s minimum principle and deriving the optimality conditions converts the optimal control problem into a two point boundary value problem. A comparative assessment of the dynamic model is validated through computer simulations, and then additional simulations are done for trajectory planning of a two-link flexible mobile manipulator to demonstrate effectiveness and capability of the proposed approach.     

On quadratic stage costs for mobile robots in model predictive control

We consider nonholonomic mobile robots. Since the system is finite time controllable, it is stabilizable by a receding horizon control scheme with purely quadratic stage costs if an infinite optimization horizon is employed. However, due to the so called short-sightedness of model predictive control, these stability properties are not preserved if the control problem is only optimized on a truncated and, thus, finite prediction horizon — even if an arbitrarily large terminal weight is added. Hence, it is necessary to either incorporate structurally different terminal costs or use non-quadratic stage costs to appropriately penalize the deviation from the desired set point. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robotic disassembly line balancing problem: A mathematical model and ant colony optimization approach

The use of robots is significantly increasing day by day in manufacturing systems, and especially improving the efficiency of the lines. Robots can be used to complete disassembly tasks, and each of the robots can need different operation times to perform the tasks. In this paper, the balancing of the robotic disassembly line problem has been studied to develop efficient solution techniques. Firstly, a mixed-integer linear mathematical model is proposed to determine and solve the problem optimally. A case study from literature is addressed to assess and show the efficiency and effectiveness of the model to minimize cycle time. Secondly, a heuristic algorithm based on ant colony optimization is also proposed to discover a solution for especially the large-size test problems due to the complexity of the problem. The performance of the proposed heuristic algorithm is verified and compared with the different heuristic on data sets. The computational results indicate that the proposed mathematical model and the algorithms are promising for the small and large-size test problems, respectively. Finally, it should be stated that robots have great potential to use in the area of disassembly line and useful solutions provide according to test results.     

Bio-inspired optimization of fuzzy logic controllers for robotic autonomous systems with PSO and ACO

In this paper we describe the use of bio-inspired optimization techniques, such as ant colony optimization and particle swarm optimization, for the design of optimal fuzzy logic controllers of autonomous wheeled mobile robots. The results obtained by the simulations with ant colony optimization and particle swarm optimization are statistically compared with previous optimization results obtained with genetic algorithms in order to find out the best optimization technique for a particular robotics problem.     

Experimental and theoretical investigation of creep groan of brakes through minimal models

Creep groan of brake systems is a low frequency vibration phenomenon occurring at low speeds which can make passengers feel uncomfortable. This phenomenon is caused by the stick-slip-effect resulting in limit cycle oscillations with frequencies lower than 200 Hz. For the experimental investigation of this problem, an idealized brake test rig is designed concentrating on the investigation of the frictional contact by realizing low damping and small disturbances in the system. Different sensors are utilized in the test rig. Limit cycles and bifurcation effects can be observed in the experimental results. With respect to modeling, a one degree-of-freedom (DOF) model using Coulomb's friction law and a two DOF model using the bristle friction law are considered. In a comparative study of experimental and simulation results, the parameters of both friction laws can be identified from the dynamic experimental results, such as the static and dynamic friction coefficients, contact stiffness and Stribeck velocity. Experimental and theoretical results show a very good concordance. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Integral estimation and adaptive stabilization of non-holonomic controlled systems

A method for the programmed stabilization of non-holonomic dynamic systems is proposed. The original problem is reduced to a constrained adaptive control problem with unknown perturbations, which are represented by the reactions of linear (not necessarily ideal) non-holonomic constraints. Effective control and parameter estimation algorithms are constructed for the exponential stabilization of the system. The method can be extended to non-holonomic systems whose parameters are not known in advance or undergo an unknown bounded drift with time.     

Investigation of the mobile platform motion optimal control at energy performance index

The paper presents a method of optimal control of the mobile robot on example of the 2-wheel mobile platform. The robot investigated has non-holonomic constraints. Mathematical model of 2-wheel mobile platform is characterized by finite number of nonlinear differential equations. The presented method of control is minimizing velocity and position errors. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Neuro-fuzzy technique for navigation of multiple mobile robots

In this paper, navigation techniques for several mobile robots are investigated in a totally unknown environment. In the beginning, Fuzzy logic controllers (FLC) using different membership functions are developed and used to navigate mobile robots. First a fuzzy controller has been used with four types of input members, two types of output members and three parameters each. Next two types of fuzzy controllers have been developed having same input members and output members with five parameters each. Each robot has an array of sensors for measuring the distances of obstacles around it and an image sensor for detecting the bearing of the target. It is found that the FLC having Gaussian membership function is best suitable for navigation of multiple mobile robots. Then a hybrid neuro-fuzzy technique has been designed for the same problem. The neuro-fuzzy technique being used here comprises a neural network, which is acting as a pre processor for a fuzzy controller. The neural network considered for neuro-fuzzy technique is a multi-layer perceptron, with two hidden layers. These techniques have been demonstrated in simulation mode, which depicts that the robots are able to avoid obstacles and reach the targets efficiently. Amongst the techniques developed neuro-fuzzy technique is found to be most efficient for mobile robots navigation. Experimental verifications have been done with the simulation results to prove the authenticity of the developed neuro-fuzzy technique.     

On the model of non-holonomic billiard

In this paper we develop a new model of non-holonomic billiard that accounts for the intrinsic rotation of the billiard ball. This model is a limit case of the problem of rolling without slipping of a ball without slipping over a quadric surface. The billiards between two parallel walls and inside a circle are studied in detail. Using the three-dimensional-point-map technique, the non-integrability of the non-holonomic billiard within an ellipse is shown.     

Controllability and stabilization of programmed motions of an automobile-type transport robot

A non-linear model of the motion of an automobile-type transport robot (TR) with absolutely rigid wheels, a steering device and actuators based on DC motors, is considered. Such a model for TR motion is a non-holonomic electromechanical system and, if the dynamics of the actuators and the steering device (forces of elasticity and attenuation in its elements) is ignored, corresponds to the model of automobile motion devised by Lineikin [1]. Non-linear canonical transformations of the state and control space coordinates are constructed which reduce the initial equations of motion of the TR to a simpler canonical form, convenient for the analysis and synthesis of control systems for the TR. These transformations are used to find the conditions for the controllability of the TR as a controlled object. Algorithms are given for constructing programmed controls and programmed motions of the TR. Stabilizing control laws are synthesized that make the programmed motions of the TR asymptotically stable and guarantee that the transients will have preassigned properties     

Shaking table tests of a model-scale building with 2DOF pendulum mass damper

In this paper, the numerical and experimental studies of a tall building's model with 2DOF pendulum mass damper (PMD) are considered. It is assumed that the model excitation is in the form of horizontal and/or torsional motion of the ground caused by earthquake. The construction consists of the main system (tall building's model) and a double pendulum mass damper, which is attuned to the first (bending) and the second (torsional) eigenfrequencies of the main structure. The analysis focuses on reduction of structure vibration caused by horizontal or torsional component of ground motions. Therefore, results presented in this work show efficiency of 2DOF PMD for vibration reduction. The numerical analysis of the problem is performed with using COSMOS/M system (a FEM numerical model is defined), while experimental analysis is carried out on a physical model-scale building with 2DOF PMD. Model consists of twenty five recurrent storeys (height 2.5m) with a PMD located on the highest one. Shaking table device is used to simulate an earthquake excitation in horizontal and torsional component, independently. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A social approach for target localization: simulation and implementation in the marXbot robot

Foraging is a common benchmark problem in collective robotics in which a robot (the forager) explores a given environment while collecting items for further deposition at specific locations. A typical real-world application of foraging is garbage collection where robots collect garbage for further disposal in pre-defined locations. This work proposes a method to cooperatively perform the task of finding such locations: instead of using local or global localization strategies relying on pre-installed infrastructure, the proposed approach takes advantage of the knowledge gathered by a population about the localization of the targets. In our approach, robots communicate in an intrinsic way the estimation about how near they are from a target; these estimations are used by neighbour robots for estimating their proximity, and for guiding the navigation of the whole population when looking for these specific areas. We performed several tests in a simulator, and we validated our approach on a population of real robots. For the validation tests we used a mobile robot called marXbot. In both cases (i.e., simulation and implementation on real robots), we found that the proposed approach efficiently guides the robots towards the pre-specified targets while allowing the modulation of their speed.     

Motion control of mobile wheeled robots

A vector-matrix formalism of nonholonomic mechanics is set up, which is used to construct mathematical models of mobile wheeled robots. The properties of free (ballistic) motions of mobile robots, which can be the basis of natural motion control modes, are studied. The analysis of uncontrollable motions is carried out, taking transients in circuits of the electric drive into consideration. The problem of determining voltages supplied to drives of the robot that ensure implementation of program motions is discussed. One candidate solution of a problem of planning a pathway of the robot in an ordered medium is presented. A mobile single-wheeled robot with a gyroscopic stabilization system is described—the “Gyrowheel” robot, capable of moving autonomously along a straight-line (rectilinear motion), as well as along a curvilinear pathway. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 8, pp. 29–80, 2005.     

Distributed adaptive formation tracking using quantized feedback communication for networked mobile robots with unknown wheel slippage

In this study, we consider a quantized-feedback-communication-based control design problem for the distributed adaptive formation tracking of multiple nonholonomic mobile robots with unknown slippage constraints under capacity-limited network control environments. Uniform-hysteretic quantizers are employed to quantize all the inputs and states of robots and the quantized position information of each robot is only transmitted to neighboring robots through directed networks. Compared with existing literature related to the robot formation, the primary contribution of this paper lies in establishing a novel local adaptive control design methodology to deal with the discontinuity problem caused by using the quantized states of each follower and the quantized position communication of neighboring robots. In the proposed strategy, the communication of the orientations and velocities of neighboring robots is not required for the local control design of follower robots. Moreover, quantized-states-based adaptive compensation schemes are constructed for the effects of signal quantization and wheel slippage. Based on the analysis of quantization errors, the practical stability strategy of the overall closed-loop formation system is derived with the convergence of local tracking errors. Simulation results clarify the proposed formation strategy.     

Asymptotic stability and associated problems of dynamics of falling rigid body

We consider two problems from the rigid body dynamics and use new methods of stability and asymptotic behavior analysis for their solution. The first problem deals with motion of a rigid body in an unbounded volume of ideal fluid with zero vorticity. The second problem, having similar asymptotic behavior, is concerned with motion of a sleigh on an inclined plane. The equations of motion for the second problem are non-holonomic and exhibit some new features not typical for Hamiltonian systems. A comprehensive survey of references is given and new problems connected with falling motion of heavy bodies in fluid are proposed.      

A genetic algorithm for robotic assembly line balancing

Flexibility and automation in assembly lines can be achieved by the use of robots. The robotic assembly line balancing (RALB) problem is defined for robotic assembly line, where different robots may be assigned to the assembly tasks, and each robot needs different assembly times to perform a given task, because of its capabilities and specialization. The solution to the RALB problem includes an attempt for optimal assignment of robots to line stations and a balanced distribution of work between different stations. It aims at maximizing the production rate of the line. A genetic algorithm (GA) is used to find a solution to this problem. Two different procedures for adapting the GA to the RALB problem, by assigning robots with different capabilities to workstations are introduced: a recursive assignment procedure and a consecutive assignment procedure. The results of the GA are improved by a local optimization (hill climbing) work-piece exchange procedure. Tests conducted on a set of randomly generated problems, show that the Consecutive Assignment procedure achieves, in general, better solution quality (measured by average cycle time). Further tests are conducted to determine the best combination of parameters for the GA procedure. Comparison of the GA algorithm results with a truncated Branch and Bound algorithm for the RALB problem, demonstrates that the GA gives consistently better results.