Poincaré–Cosserat Equations for the Lighthill Three-dimensional Large Amplitude Elongated Body Theory: Application to Robotics

In this article, we describe a dynamic model of the three-dimensional eel swimming. This model is analytical and suited to the online control of eel-like robots. The proposed solution is based on the Large Amplitude Elongated Body Theory of Lighthill and a framework recently presented in Boyer et al. (IEEE Trans. Robot. 22:763–775, 2006) for the dynamic modeling of hyper-redundant robots. This framework was named “macro-continuous” since, at this macroscopic scale, the robot (or the animal) is considered as a Cosserat beam internally (and continuously) actuated. This article introduces new results in two directions. Firstly, it extends the Lighthill theory to the case of a self-propelled body swimming in three dimensions, while including a model of the internal control torque. Secondly, this generalization of the Lighthill model is achieved due to a new set of equations, which are also derived in this article. These equations generalize the Poincaré equations of a Cosserat beam to an open system containing a fluid stratified around the slender beam.     

Analytical solution for the evolution of exit point along the sloping seepage face

This paper developed an analytical solution for the problem of exit point evolution on the seepage face in the unconfined aquifer with sloping interface. A theoretical model for the groundwater drawdown problem in a half‐infinite aquifer with a sloping boundary is built in accordance with the linearized one‐dimensional Boussinesq equation and the Neumann boundary condition at the seepage point. The homotopy analysis method is then adopted for solving this dynamic boundary problem. By constructing two continuous deformations, the original problem could be converted into a group of subproblems with the same physical essence and similar mathematical solutions. To compare this analytical solution, a numerical model based on the finite volume method is developed, which employs adaptive grids to settle the dynamic boundary condition. The comparisons show that the analytical solution agrees with the numerical model well. The results are useful for the quantification of various hydrological problems. The methodology applied in this study is referential for other dynamic boundary problems as well.     

Modelling Flexible Manipulators With Motors at the Joints

A computationally efficient recursive model of a flexible manipulator with motors at the joints is described in this paper. The model adopts a mixed Eulerian and Lagrangian formulation of the equations of a flexible body and exploits the chained structure of the equations for a serial manipulator. The dynamic effects of the motors at the joints, including gyroscopic terms, are fully taken into account. Symbolic manipulation is used in a newly developed package, whose performance in detailed reproduction of the dynamic effects due to the interplay between the motors and the flexible links is assessed through simulation. A comparison between the complete model and a simplified one, where the motors are considered as simple inertias rotating around their own axis, has been carried out, using both a time domain analysis and a frequency domain analysis, in order to show the relevance of gyroscopic effects in modelling flexible robots.     

Modelling and control of two robotic manipulators handling a constrained object

In this paper, the problem of modelling and controlling two manipulators handling a constrained object is addressed. At first, a reduced order dynamic model of the system is derived, and several of its properties are outlined. Using the reduced order model, an adaptive control scheme that guarantees the asymptotic convergence of the position of the object, and the forces acting on the object to their desired values is developed. Simulation results of two planar robots moving an object along a plane illustrate the effectiveness of the proposed control scheme.     

An analytical dynamic model for single-cracked beams including bending,axial stiffness,rotational inertia,shear deformation and coupling effects

This paper develops an analytical dynamic model for cracked beams including bending, axial stiffness, rotational inertia, shear deformation and the coupling of the last two effects. The damage is modelled using a rotational spring that simulates the crack based on fracture mechanics theory. The developed model is used to predict variations on natural frequencies for several crack sites and damage magnitude along the beam. The importance of this work lies in the development of an analytical model that has no approximation due to discretization of the displacement field. This initial theoretical approach describes the expected behaviour for changes in the natural frequencies for simply-supported and clamped-free beams with the precision that only analytical methods allow. The results provide a useful benchmark to compare with approximate numerical methods that can be used to model and analyse the problem. The model showed similar results for long span beams, but the inclusion of rotational inertia and shear deformation effects rendered improvements in the dynamic behaviour mainly in the case of slender and short span beams when compared with the simplified Euler–Bernoulli model.     

Cyclic multiple-robot scheduling with time-window constraints using a critical path approach

An automated production system is considered in which several robots are used for transporting parts between workstations following a given route in a carousel mode. The problem is to maximize the throughput rate. Extending previous works treating scheduling problems for a single robot, we consider a more realistic case in which workstations are served by multiple robots. A graph model of the production process is developed, making it possible to apply PERT–CPM solution techniques. The problem is proved to be solvable in polynomial time.     

Control Strategy of Hardware-in-the-Loop Simulator EPOS 2.0 for Autonomous Docking Verification

This paper briefly describes the hybrid simulator system called European Proximity Operation Simulator (EPOS 2.0) and the development of the hardware-in-the-loop (HIL) docking simulation concept. A critical requirement for the docking simulation of this HIL simulator is that the 6-DOF robots in the loop have to exactly mimic the dynamic response of the two satellites during a contact operation. The main challenges to meet this requirement are in the stiffness of the robots, which is unlike that of the satellites, as well as the time delay in the HIL simulator. The paper mainly presents the impedance parameter identification concept for matching the impedance between the satellites impact model and the EPOS robots. Finally it presents the preliminary results and future work. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A coupled model for train-track-bridge stochastic analysis with consideration of spatial variation and temporal evolution

Due to random characteristics of system parameters and excitations, the dynamic assessment and prediction for the train-track-bridge interaction systems become rather complex issues needing to be addressed, especially considering the longitudinal inhomogeneity and uncertainty of dynamic properties in physics and correspondingly their temporal evolutions. In this paper, a temporal-spatial coupled model is developed to fully deal with the deterministically/non-deterministically computational and analytical matters in the train-track-bridge interactions with a novelty, where a train-track-bridge interaction model is newly developed by effectively coupling the three-dimensional nonlinear wheel-rail contact model and the finite element theory, moreover, the Monte-Carlo method (MCM) and Karhunen–Loève expansion (KLE) are effectively united to model the random field of track-bridge systems, and a spectral evolution method accompanied by a track irregularity probabilistic model are introduced to select the most representative track irregularity sets and to characterize their random evolutions in temporal dimension. In terms of random vibration analysis, the high-efficiency and effectiveness of this developed model is validated by comparing to a robust method, i.e., MCM. Apart from validations, multi-applications of the temporal-spatial coupled model from aspects of deterministic computation, random vibration, resonant analysis and long-term dynamic prediction, etc., have been fully presented to illustrate the universality of the proposed model.     

System dynamic modelling and simulation of hydrodynamic machines

A graph-theoretic framework for the dynamic simulation of hydrodynamic (both axial and radial flow) machines is presented in this article. The physics based analytical models are developed by considering the dynamics of the hydraulic fluid flow and its interaction with the mechanical components. A linear graph is used to capture the topology of the system and the interconnection of the constituent components. Using the graph-theoretic framework, a dynamic model of an automotive hydrodynamic torque converter is developed to simulate its behaviour under different flow conditions. The ability of the model to capture different features of the torque converter will also be demonstrated by simulation. The simulation results are compared with and validated by experimental results in the literature.     

Uncertainty finite element dynamic analysis

An inference-dynamic model is developed based on a model dynamic analysis using a moving boundary condition. The uncertainty of the physical parameters is implemented in the model using an inference scheme coupled with a perturbation technique. Finally, the first two statistical moments of the displacements and the stress field are estimated according to the proposed analytical scheme and are in good agreement with the initially assumed fields.     

Robust position/force control of multiple robots using neural networks

The control of multiple redundant robots, whose end-effectors grasp an object, involves complex control tasks. First, the multiple robotic system, for a cooperative task, forms closed kinematic chains that impose additional kinematic and dynamic constraints. Second, the interactive actions among the robots through the object lead to the essential need to control position and interactive force, simultaneously. Finally, the structured and unstructured uncertainties of the system may cause the system to be unstable. In this paper, a robust controller, which compensates the uncertainties of the dynamic system of the multiple robotic system, is presented in order to obtain good tracking performance of position and force, simultaneously, while satisfying the constraint conditions among the robots. A neural network architecture is proposed as one approach to the design and implementation of the robust controller. In particular, an on-line learning rule is provided for reportedly assigned tasks so that the system is robust to the structured/unstructured uncertainties; and the controller adjusts itself repeatedly to improve the performance progressively for each repeated task.     

A simple model for clock-actuated legged locomotion

The spring-loaded inverted pendulum (SLIP) model describes well the steady-state center-of-mass motions of a diverse range of walking and running animals and robots. Here we ask whether the SLIP model can also explain the dynamic stability of these gaits, and we find that it cannot do so in many physically-relevant parameter ranges. We develop an actuated, lossy, clock-torqued SLIP, or CT-SLIP, with more realistic hip-motor torque inputs, that can capture the robust stability properties observed in most animals and some legged robots. Variations of CT-SLIP at a similar level of detail and complexity may also be appropriate for capturing the whole-system center-of-mass dynamics of locomotion of legged animals and robots varying widely in size and morphology. This paper contributes to a broader program to develop mathematical models, at varied levels of detail, that capture the dynamics of integrated organismal systems exhibiting integrated whole-body motion.      

Agent-based modeling and simulation of community collective efficacy

Community collective efficacy is an important concept in studying various community problems and in developing community well-beings. While existing research on collective efficacy mainly focuses on building analytical or statistical models from informant survey data, this paper develops a complexity science-informed agent-based model to study the dynamic process of collective efficacy formation in a community. We model the individual level cognitive process for participating in community tasks and simulate the emergent spatial patterns of agents’ collective efficacies in a community. The developed model is based on the self-efficacy theory and Theory of Planned Behavior. Interesting patterns such as spatial segregation has been observed through simulations, and an application of the developed model is presented.     

Stability and vibrations of an all-terrain vehicle subjected to nonlinear structural deformation and resistance

This study intends to investigate the dynamic behaviour of an all-terrain vehicle travelling on rough terrains. A nonlinear analytical model is established for quantifying the response of the vehicle with spring and damping nonlinearities to various operation and terrain conditions. Focus of the study is on the motion characteristics of the vehicle operating on rough terrains. Stability analyses are performed for the all-terrain vehicles under the operation of surmounting large obstacles and the operation of the vehicle on rough terrain surfaces. Stability conditions are provided and stable and unstable region diagrams are plotted and analyzed with the analytical model developed. Analytical solutions are provided for weakly nonlinear dynamic systems. Numerical simulations for the motion of the all-terrain vehicle are also presented.     

A cellular automata ant memory model of foraging in a swarm of robots

This study proposes a cellular automata ant memory model (CAAM) that controls a robot swarm when undertaking the foraging task in a previously known environment with nests. The floor field is well known to all robots, which share the same environment, communicating through the inverted pheromone. This substance is deposited by each swarm robot over every step in searching, which results in a repulsive force between team members. Besides, a short-term memory inspired by Tabu Search is applied to enable robots to remember their last positions and to avoid useless explorations. On the other hand, homing is based on the behavior observed in pedestrian evacuation, resulting in an attractive force through the nests. Moreover, a dynamic information is used to avoid queues of robots and bottlenecks next to the nests. Each robot step is a first choice movement with a stochastic conflict solver, which results in a non-deterministic characteristic to the model. The proposed model was implemented and submitted to several simulations to evaluate its resultant behavior. Different environmental conditions were employed to refine its intrinsic parameters. The results shown that the proposed model is able to perform the foraging task in a competitive way: in searching the swarm perform a good environment coverage and in homing robots are able to find the most adequate nests.     

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 a bi-dimensional dynamic alternative routing method

The analysis of a bi-dimensional dynamic routing model for alternative routing telecommunication networks led to the identification of an instability problem in the synchronous path selection associated with the complex interdependencies among the coefficients of the objective functions and the computed paths for every node pair. In this paper an analytical model enabling to make explicit this problem and evaluate its effects in terms of two global network criteria, is presented. Also a heuristic procedure dedicated to overcome this instability problem and select “good” compromise solutions in terms of network performance is developed. Finally the performance of the proposed routing method using the heuristic is compared by recurring to discrete-event simulation with a reference dynamic routing method (Real Time Network Routing) for some test networks.     

Multiphase Jet Flow in Abrasive Water Jet Cutting

A numerical model for ultra-high velocity abrasive water jets (AWJ) is developed and jet dynamic characteristics are calculated under steady-state, turbulent, compressible, multi-phase flow conditions. The model is tested by comparison with analytical solutions for related theoretical problems, generally with very good agreement. Simulations of more realistic flows produce the expected values and behavior. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Trajectory planning based on non-convex global optimization for serial manipulators

To perform specific tasks in dynamic environments, robots are required to rapidly update trajectories according to changing factors. A continuous trajectory planning methodology for serial manipulators based on non-convex global optimization is presented in this paper. First, a kinematic trajectory planning model based on non-convex optimization is constructed to balance motion rapidity and safety. Then, a model transformation method for the non-convex optimization model is presented. In this way, the accurate global solution can be obtained with an iterative solver starting from arbitrary initializations, which can greatly improve the computational accuracy and efficiency. Furthermore, an efficient initialization method for the iterative solver based on multivariable-multiple regression is presented, which further speeds up the solution process. The results show that trajectory planning efficiency is significantly enhanced by model transformation and initialization improvement for the iterative solver. Consequently, real-time continuous trajectory planning for serial manipulators with many degrees of freedom can be achieved, which lays a basis for performing dynamic tasks in complex environments.