Dynamics and stability of a hybrid serial-parallel mobile robot

Kinematics, dynamics, and stability analysis of a hybrid serial-parallel wheeled mobile robot is detailed in this paper. Privileging the advantages of both serial and parallel robots, the suggested structure will provide higher stability for heavy object manipulation by a mobile robotic system. The proposed system is made of a differentially-driven wheeled platform, a planar parallel manipulator, which is called here as star-triangle (ST) mechanism, and a serial Puma-type manipulator arm. In order to develop a comprehensive kinematics model of the robot; first it is divided into three modules, i.e. a mobile platform, a parallel ST mechanism, and a serial robot. Next, a closed-form dynamics model is derived for the whole hybrid system based on a combined Newton–Euler and Lagrange formulation. Then, a careful validation procedure is presented to verify the obtained dynamics model. Finally, using the new postural stability metric named as moment-height stability (MHS), the important role of the parallel ST mechanism for stabilizing the mobile robotic system is demonstrated. The obtained results show that the proposed hybrid serial–parallel arrangement effectively enhances the tip-over stability of the overall mobile robotic system. Hence, it can be successfully exploited to prevent tip-over instability particularly during heavy object manipulation tasks.     

Recursive Methods in Modeling and Control of Modular Robotic Systems

This paper addresses the dynamical modeling and control of reconfigurable modular robots. The modular actuators (brushless DC motors with Harmonic Drive gears) for the robots under consideration are connected by rigid links. This way the robot can be assembled in different configurations by rearranging these components. For dynamical modeling the Projection Equation in Subsystem representation is used, taking advantage of its modular structure. Due to the lack of position sensors at the gearbox output shaft, deflections caused by the elasticities in the gears can not be compensated by the PD motor joint controller. Therefore, a correction of the motor trajectory is needed, which can be calculated as part of a flatness based feed-forward control using the exact model of the robot. With the recursive approach proposed in this paper the concept of reconfigurability is retained. For validation a redundant articulated robot arm with seven joints is regarded and results are presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Cosserat生长弹性杆动力学的Gauss最小拘束原理

以自然界中具有生长、变形和运动特征的细长体为背景,用经典力学中的Gauss最小拘束原理研究生长弹性杆的动力学建模问题.在为生长弹性杆动力学建模提供新方法的同时,扩大了Gauss原理的应用范围.以Cosserat弹性杆为对象,分析弹性杆生长和变形的几何规则,表明生长应变和弹性应变是非线性耦合的;本构方程给出了截面的内力与弹性变形的线性关系;利用逆并矢,将经典力学中的Gauss原理和Gauss最小拘束原理用于生长弹性杆动力学,得到等价的两种表现形式,反映了时间和弧坐标在表述上的对称性,由此导出了封闭的动力学微分方程.给出了两种形式的最小拘束函数,表明生长弹性杆的实际运动使拘束函数取驻值,且为最小值.最后讨论了生长弹性杆的约束与条件极值等问题.     

机械臂运动路径规划的算法设计

我们对题目中所给的特定的六自由度机械手臂设计一整套通用的算法.让它能够实现点到点移动,有障碍的曲线跟踪,和避障点对点移动三种基本功能.并能自动生成控制台所需要的指令序列.最后我们会对模型的适用范围和准确性进行评价.     

Adaptive control of kinematically redundant robots

A redundant robot has more degrees of freedom than those neededto position the Robert end-effector uniquely. In a usual robotictask, only end-effector position trajectory is specified. Thejoint position trajectory is unknown, and it must be selectedfrom a self-motion manifold for a specified end-effector. Inmany situations, the robot dynamic parameters such as the linkmass, inertia, and joint viscous friction are unknown. The lackof knowledge of the joint trajectory and the dynamic parametersmake it difficult to control redundant robots. In this paper we show, through careful formulation of the problem,that the adaptative control of redundant robots can be addressedas a reference-velocity traking problem in the joint space.A control law ensures bounded estimation of the unknown dynamicparameters of the robot, and the convergence to zero of thevelocity traking error is derived. To ensure the joint motionon the self-motion manifold remains bounded, a homeomorphictransformation is found. This transformation decomposes thedynamics of the velocity tracking error into a cascade systemconsisting of the dynamics in the end-effector error coordinatesand the dynamics on the self-motion manifold. The dynamics onthe self-motion manifold is shown to be related to the conceptof zero dynamics. In the shown that, if the reference jointtrajectory is selected to optimize a certain type of objectivefunction, then stable dynamics on the self-motion manifold result.This ensures the overall stability of the adaptive system. Detailedsimulations are given to test the theoretical developments.The proposed adaptive scheme does not require measurements ofthe joint acceleration or the inversion of the inertia matrixof the robot.     

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.      

Modeling of Reconfigurable Modular Redundant Robotic Systems

This paper deals with the dynamical modeling and control of modular redundant robots. The robots under consideration consist of modular actuators (brushless DC motors with Harmonic Drive gears) connected by rigid links. Different configurations can be designed by rearranging these subsystems. In order to fulfill the requirement for an efficient dynamical modeling, the Projection Equation in subsystem representation is used. The subsystems are connected via the kinematical chain. The Projection Equation offers the possibility to calculate the minimal accelerations recursively, leading to an O(n) computational effectiveness. To validate the proposed method, the model of an articulated robot arm with seven joints is considered. Simulation results are compared to measurements. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

柔性杆柔性铰机器人动力学分析

研究由N柔性杆和N柔性铰组成的空间机器人的动力学问题．把柔性铰简化成一个线性扭转弹簧,采用假设模态法表示杆件的弹性变形,运用Kane方法对全柔机器人进行动力学建模,推导出完整的系统动力学方程组．通过一个数值仿真算例,验证所做工作的可行性,并分析了柔性效应对机器人动力学响应的影响．     

A Prediction Model for State Observation and Model Predictive Control of Biped Robots

Biped walking robots present a class of mechanical systems with many different challenges such as nonlinear multi-body dynamics, a large number of degrees of freedom and unilateral contacts. The latter impose constraints for physically feasible motions and in stabilization methods as the robot can only interact due to pressure forces with the environment. This limitation can cause the system to fall under unknown disturbances such as pushing or uneven terrain. In order to face such problems, an accurate and fast model of the robot to observe the current state and predict the state evolution into the future has to be used. This work presents a nonlinear prediction model with two passive degrees of freedom (dof), point masses and compliant unilateral contacts. We show that the model is applicable for real-time model predictive optimization of the robot's motion. Experiments on the biped robot LOLA [1] underline the effectiveness of the proposed model to increase the system's long term stability under large unknown disturbances. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

AIS Based Distributed Wireless Sensor Network for Mobile Search and Rescue Robot Tracking

This research presents the implementation of GSCF, an AIS-based control framework, on a distributed wireless sensor network for tracking search and rescue robots in open fields. The General Suppression Control Framework (GSCF) is a framework inspired by the suppression hypothesis of the immune discrimination theory. The framework consists of five distinct components; each carries a specific function that can generate long-term and short-term influences to other components by the use of humoral and cellular signals. The goal of the research is to develop mathematical models that can assist the control and analyses of robots behavior through the use of Suppressor Cells in the Suppression Modulator. Acquire data from the physical robot will be used as simulation parameters in future search and rescue research.     

The limits of hamiltonian structures in three-dimensional elasticity,shells, and rods

Summary This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material andderive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to the well-known Euler elastica if one adds an additional single constraint that the director lines up with the Frenet frame. This paper is dedicated to the memory of Juan C. Simo This paper was solicited by the editors to be part of a volume dedicated to the memory of Juan Simo.     

Model-based and model-free control of flexible-link robots: A comparison between representative methods

The paper presents a comparative study on representative methods for model-based and model-free control of flexible-link robots. Model-based techniques for the control of flexible-link robots can come up against limitations when an accurate model is unavailable, due to parameters uncertainty or truncation of high order vibration modes. On the other hand, several research papers argue that suitable model-free control methods result in satisfactory performance of flexible-link robots. In this paper two model-free approaches of flexible-link robot control are examined: (i) energy-based control, and (ii) neural adaptive control. The performance of the aforementioned methods is compared to the inverse dynamics model-based control, in a simulation case study for planar 2-DOF manipulators.     

Efficient reconfiguration of lattice-based modular robots

Modular robots consist of many identical units (or atoms) that can attach together and perform local motions. By combining such motions, one can achieve a reconfiguration of the global shape of a robot. The term modular comes from the idea of grouping together a fixed number of atoms into a metamodule, which behaves as a larger individual component. Recently, a fair amount of research has focused on algorithms for universal reconfiguration using Crystalline and Telecube metamodules, which use expanding/contracting cubical atoms.From an algorithmic perspective, this work has achieved some of the best asymptotic reconfiguration times under a variety of different physical models. In this paper we show that these results extend to other types of modular robots, thus establishing improved upper bounds on their reconfiguration times. We describe a generic class of modular robots, and we prove that any robot meeting the generic class requirements can simulate the operation of a Crystalline atom by forming a six-arm structure. Previous reconfiguration bounds thus transfer automatically by substituting the six-arm structures for the Crystalline atoms. We also discuss four prototyped robots that satisfy the generic class requirements: M-TRAN, SuperBot, Molecube, and RoomBot.     

Kinematic and dynamic analysis of the Gantry-Tau,a 3-DoF translational parallel manipulator

This paper deals with the mathematical modeling of kinematics and dynamics of the 3-degrees-of-freedom Gantry-Tau manipulator. Compared to many other parallel robots, Gantry-Tau offers a large accessible workspace and high stiffness. The kinematics of Gantry-Tau is presented which includes inverse kinematics formulation for the position, velocity and acceleration of the mechanism. Also, based on the obtained Jacobin matrices, singular configurations of the robot are studied. Afterwards, the equations of the inverse dynamic model of the Gantry-Tau are obtained through two different methods, i.e., virtual work and Newton–Euler. Finally, a case study is performed to verify the correctness of the derived models and investigate their computational efficiency.     

First steps toward formal controller synthesis for bipedal robots with experimental implementation

Bipedal robots are prime examples of complex cyber–physical systems (CPSs). They exhibit many of the features that make the design and verification of CPS so difficult: hybrid dynamics, large continuous dynamics in each mode (e.g., 10 or more state variables), and nontrivial specifications involving nonlinear constraints on the state variables. In this paper, we propose a two-step approach to formally synthesize controllers for bipedal robots so as to enforce specifications by design and thereby generate physically realizable stable walking. In the first step, we design outputs and classical controllers driving these outputs to zero. The resulting controlled system evolves on a lower dimensional manifold and is described by the hybrid zero dynamics governing the remaining degrees of freedom. In the second step, we construct an abstraction of the hybrid zero dynamics that is used to synthesize a controller enforcing the desired specifications to be satisfied on the full order model. Our two step approach is a systematic way to mitigate the curse of dimensionality that hampers the applicability of formal synthesis techniques to complex CPS. Our results are illustrated with simulations showing how the synthesized controller enforces all the desired specifications and offers improved performance with respect to a classical controller. The practical relevance of the results is illustrated experimentally on the bipedal robot AMBER 3.     

A Note on a Nonlinear Model of a Piezoelectric Rod

If piezoceramics are excited by weak electric fields a nonlinear behavior can be observed, if the excitation frequency is close to a resonance frequency of the system. To derive a theoretical model nonlinear constitutive equations are used, to describe the longitudinal oscillations of a slender piezoceramic rod near the first resonance frequency. Hamilton's principle is used to receive a variational principle for the piezoelectric rod. Introducing a Rayleigh Ritz ansatz with the eigenfunctions of the linearized system to approximate the exact solution leads to nonlinear ordinary differential equations. These equations are approximated with the method of harmonic balance. Finally it is possible to calculate the amplitudes of the displacements numerically. As a result it is shown, that the Duffing type nonlinearities found in measurements can be described with this model.     

Mathematical modeling and computer simulation of a robotic rat pup

In this paper, we describe the mathematics and computer implementation of a robotic rat pup simulation. Our goal is to understand neurobehavioral principles in a mammalian model organism—the Norway rat pup (Rattus norvegicus). Our approach is unique in that animal, simulation, and robot studies occur in parallel and inform each other. Behavior is dependent on the nervous system, body morphology, physiology, environment, and the interactions among these elements. Autonomous robotics hardware models and their associated simulations allow the possibility of systematically manipulating variables in each of these elements in ways that would be impossible using live animals. Specifically, we describe the development and validation of a Newtonian-dynamics-based simulation of a robotic rat pup, including mathematical formulation and computer implementation. The computer simulation consists of three distinct components that interact to simulate robotic behavior: (1) dynamics of the robotic rat pup itself, including sensors and actuators, (2) environmental coupling dynamics of the robot arena with the robotic rat pup, and (3) the robot control algorithms as implemented on the physical robot. The mathematical formulation, software implementation, model identification, model validation, and an application example are all described.     

Topology and the robot arm

A robot arm is in effect a smooth function from the space of positions of the arm to the space of positions of a coordinate frame attached to the end of the arm. For the most common robots built today, this means a map f: T ⁿ R ³×SO ₃. We describe the singularities of this map. The set of rotational singularities is the set of arm positions where the axes of the links are parallel to a plane. Thus, it is always two-dimensional. Also, we show that f is homotopic to a map which factors through a circle, and represents the generator of ₁(SO ₃). The engineering implication of these statements are discussed.     

Optimization of the Internal Dynamics of Underactuated Robots

A robot is underactuated if it possesses less control inputs than degrees of freedom, e.g. due to passive joints. The analysis of the mechanical design of these kinds of underactuated robots often shows that they are non-minimum phase, i.e. they have an internal dynamic which is not asymptotically stable. Therefore, feedback linearization is not possible, and output trajectory tracking becomes a very challenging task. It is shown that through an optimization procedure the mechanical design of an underactuated robot can be altered in such a way that the internal dynamics becomes stable. Thus feedback linearization of the underactuated robot becomes possible. In the optimization procedure, the design parameters are additional masses which are added to defined locations at different un-actuated links of the robot. The optimization criteria is two-stage and firstly requires that all eigenvalues of the linearized zero-dynamics are in the left half-plane and secondly that initial errors in the zero-dynamics decay rapidly. Due to the two-stage criteria computation the optimization problem is discontinuous. Also there might be many local minima. Therefore a particle swarm optimization procedure is used. The efficiency of this optimization approach is demonstrated by simulation of an underactuated robot. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)