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)     

用旋量方法规划机器人运动轨迹

以姿态旋量描述机器人的位置姿态,在对偶空间中通过姿态旋量映射的点规划机器人的终端轨迹,具有直观、简便的独特优点。规划中直接根据跟踪误差进行收敛,提高了轨迹运行的动态精度,并适合于冗余自由度操作器。     

Learning Robot Force/Position Control for Repetitive High Speed Applications with Unknown Non–Linear Contact Stiffness

This paper proposes a learning robot force/position control for high speed force trajectory following. Following high speed force trajectories in different repetitve robotic applications is a challenging field in robot force control. If the end–effector should provide a contact force while following a position trajectory in the non–force controlled direction a parallel force / position control is suitable. However, when it comes to high speed tasks this force control method reaches its limit. The problem can be solved by using an iterative learning control method in combination with the parallel force/position control. In this paper the learning force control method is introduced and experimental results are presented. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Methods of Analysis of Discrete - Continuous Systems Vibrations and Their Application to Railway Transport Problems

In the paper some aspects of the interaction between the current collector and the overhead equipment have been presented. A model of the system that consists of a discrete subsystem modelling the pantograph and a continuous subsystem modelling the contact wire has been introduced. The dynamic interaction between the discrete oscillator of two degrees of freedom and a continuous string has been studied. At the contact point of the pantograph and the wire a varying component of force appears. It is the source of waves that propagate along the contact wire. There are also two standing sources of wave generation, i.e. varying forces at the points of catenary supports. General results have been illustrated by numerical examples in which the effect of wave propagation is confirmed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Controlled rolling of a disc along a plane curve

The plane-parallel rolling of a disc along a fairly smooth curve under the action of perturbing and controlling forces and moments of forces is investigated. Models of the controlled motion corresponding to an explicit or implicit coordinate specification of the curve are constructed. The requirements imposed on the values of the sliding friction force and the normal pressure force, which ensure that the disc rolls without slipping and without loss of contact are determined. The problem of bringing the disc into the required state of motion in a time-optimal way by the action of the force of gravity and a limited axial moment of forces are considered. The situation when the reference curve contains a linear component (inclined upwards or downwards) and a periodic (wavy) component is investigated. Problems of optimal synthesis for a relatively large and relatively small controlling moment are considered.Investigations of the rolling of bodies of different geometrical shape on surfaces, both flat and curved (see 1, 2, 3, 4, etc.), are important for applications in modern machine construction, transport, mobile robot systems,5, 6, 7 etc. However, there are no results of systematic investigations of the problems of the dynamics and control of rolling of bodies on curved surfaces, including comparatively simple bodies (cylinders, discs and spheres). From the applied point of view, the problem of controlled rolling of a disc under gravitational forces on a curve containing a linear incline and periodic smooth changes in the slope is of interest as a model of the motion of a wheel along a path with a curvilinear profile. The solution of problems of the control of the motion of a disc along a closed curve, for example, inside or outside a circle, surmounting obstacles or “rolling out” from hollows of different shapes etc. is of fundamental importance.     

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.     

Modelling of the robotic Powerball®: a nonholonomic,underactuated and variable structure-type system

The Powerball® is the commercial name for a gyroscopic device that is marketed as a wrist exerciser. The device has a rotor with two underactuated degrees of freedom, which can be actuated by the appropriate motion of human or robot wrist axes. After the initial spin, applying the appropriate motion and torques to the housing leads to a spin-up of the rotor. Finding these torques intuitively is an easy task for human operators, but a complex task for a technical consideration, for example, in robotics.

This article's main contribution is a novel dynamic model that considers friction effects. The presented model includes all three working principles of the device: free rotor mode and both modes of rotor rolling in the housing. The work introduces models with one and two degrees of freedom actuation, both of which are suitable for laboratory control experiments. An estimation of the friction is discussed, and both the simulation and the experimental results are presented to evaluate the models.     

A random forest application to contact‐state classification for robot programming by human demonstration

This paper addresses the non‐parametric estimation of the stochastic process related to the classification problem that arises in robot programming by demonstration of compliant motion tasks. Robot programming by demonstration is a robot programming paradigm in which a human operator demonstrates the task to be performed by the robot. In such demonstration, several observable variables, such as velocities and forces can be modeled, non‐parametrically, in order to classify the current state of a contact between an object manipulated by the robot and the environment in which it operates. Essential actions in compliant motion tasks are the contacts that take place, and therefore, it is important to understand the sequence of contact states made during a demonstration, called contact classification. We propose a contact classification algorithm based on the random forest algorithm. The main advantage of this approach is that it does not depend on the geometric model of the objects involved in the demonstration. Moreover, it does not rely on the kinestatic model of the contact interactions. The comparison with state‐of‐the‐art contact classifiers shows that random forest classifier is more accurate. Copyright © 2015 John Wiley & Sons, Ltd.     

基于冗余任务的轮式机器人巡检方法

针对配电室电力设备智能化巡检工作中,存在巡检方式单一等问题,基于轮式巡检机器人结构及系统、路径优化和通信等关键技术,研究了一种基于冗余任务的轮式机器人巡检方法.针对目前配电室巡检环境和轮式巡检机器人结构及系统特性,建立配电室巡检过程模型.分析顺序巡检方法的速度、位姿和节点关系,建立机器人巡检过程的路程-时间模型和奖惩模...     

Model Based Control of a Parallel Robot – A Comparison of Control Algorithms

In this contribution the control behavior of a special construction of a parallel robot, called multi-axes test facility, is investigated. After a brief discussion of the different tasks of the robot the construction of the robot is briefly presented. To solve the tasks, different control algorithms are derived based on model equations of different complexity of the robot. Depending on the task to be performed by the robot, the controllers compensate the kinematic and/or kinetic coupling of the degrees of freedom of the robot, stabilize the system and achieve the desired spatial motion of each degree of freedom as well as sufficient robustness with respect to parameter uncertainties and load variations. A few results obtained in computer simulations and laboratory experiments are presented and judged with respect to the quality of control, the closeness to reality of the computer simulations, and the amount of costs and work needed to realize the different solutions.     

Control of the spatial motion of a multilink inverted pendulum using a torque applied to the first link

An approach to constructing a control for non-linear mechanical systems in which the number of degrees of freedom exceeds the dimension of the generalized control forces is developed. An n-link pendulum with two-degree-of-freedom joints, controlled by a torque applied to the first link, is considered as an example. Such a pendulum has 2ⁿ different equilibrium positions. A feedback control with an absolute value constraint, which transfers the pendulum from the neighbourhood of an arbitrary equilibrium position to this equilibrium position in a finite time, is constructed. For this purpose, the equations of motion of the pendulum are linearized in the neighbourhood of the equilibrium position under consideration, complete controllability of the linear model is established, and a control is constructed for it using the linear matrix inequality technique. The applicability of the control law obtained to the solution of the problem of controlling a non-linear multilink pendulum is verified. ©2014     

Motion Planning for Multiple Robots

We study the motion-planning problem for pairs and triples of robots operating in a shared workspace containing n obstacles. A standard way to solve such problems is to view the collection of robots as one composite robot, whose number of degrees of freedom is d , the sum of the numbers of degrees of freedom of the individual robots. We show that it is sufficient to consider a constant number of robot systems whose number of degrees of freedom is at most d-1 for pairs of robots, and d-2 for triples. (The result for a pair assumes that the sum of the number of degrees of freedom of the robots constituting the pair reduces by at least one if the robots are required to stay in contact; for triples a similar assumption is made. Moreover, for triples we need to assume that a solution with positive clearance exists.) We use this to obtain an O(n ^d ) time algorithm to solve the motion-planning problem for a pair of robots; this is one order of magnitude faster than what the standard method would give. For a triple of robots the running time becomes O(n ^d-1 ) , which is two orders of magnitude faster than the standard method. We also apply our method to the case of a collection of bounded-reach robots moving in a low-density environment. Here the running time of our algorithm becomes O(n log n) both for pairs and triples. Received August 10, 1998, and in revised form February 17, 1999.     

基于Udwadia-Kalaba方法的并联机器人鲁棒伺服约束控制

针对2自由度冗余驱动并联机器人轨迹跟踪控制问题,提出了一种基于Udwadia-Kalaba方程的鲁棒伺服控制方法.在负载、外部干扰以及制造误差的影响下,无法得到机器人精确、完整的运动模型,导致机器人控制性能变差.为解决这类不确定性带来的影响,提出了一种鲁棒控制方法.该方法通过保证系统的一致有界性和一致最终有界性,使系统能够精确跟踪理想约束轨迹.此外,该方法采用Udwadia-Kalaba方程,求解控制过程中满足系统理想约束所需要的约束力.Udwadia-Kalaba方程不需要Lagrange乘子或伪广义速度等辅助变量,可以同时处理完整约束和非完整约束,且可以获得满足轨迹约束的约束力解析解.利用Lyapunov函数对该鲁棒控制方法的稳定性进行了理论证明,并且通过仿真实验,验证了该鲁棒控制方法能够在非理想条件下实现给定轨迹的高精度跟踪控制.     

Adaptive control of uncertain coupled mechanical systems with application to base-isolated structures

A problem of feedback stabilization is addressed for a class of uncertain nonlinear mechanical systems with n degrees of freedom and n_c < n control inputs. Each system of the class has the structure of two coupled subsystems with n_c and n_r degrees of freedom, respectively, a prototype being an uncertain base isolated building structure with n degrees of freedom actively controlled via actuators applying forces to specific degrees of freedom of the base movement, n_c < n in number. A nonlinear adaptive feedback strategy is described, which, under appropriate assumptions on the system uncertainties, guarantees a form of practical stability of the zero state. Numerical simulations are also presented to illustrate the application of the control strategy to a base isolated building.     

Influence of model reduction techniques on the impact force calculation of two flexible bodies

One important issue for the simulation of flexible multibody systems is the reduction of the flexible body's degrees of freedom. For the reduction process finite element data and user inputs are necessary. The model reduction program for elastic multibody systems MOREMBS, which is developed at the ITM, has an easy-to-use interface and the data can be gained from the programs ABAQUS or ANSYS. In this work, the simulation of a fuel injection process is investigated with MOREMBS. We focus on the interaction between valve and armature. These two bodies impact in every injection circle. The impacting bodies are modeled as flexible and the contact force is calculated by a penalty approach. One essential part of this work is the investigation of the influence of different model reduction techniques on the impact force calculation of the flexible multibody system. The main reduction techniques modal reduction, Krylov-subspace based and Gramian matrix based techniques are compared. The results achieved with modal reduction, the state of the art reduction method, are not acceptable here. Krylov-subspace based techniques are especially well-suited for large sparse systems but are not error controlled. However, by choosing appropriate moment-matching properties the impact force calculation is nearly as good as with a full finite element model. The Gramian matrix based reduction techniques can be fully automated and are error controlled but require high computational effort. Hence, appropriate approximation schemes have to be used for them. With Gramian matrix based methods we can even further reduce the size of the subsystems compared to Krylov-subspace based methods and still have an impact force calculation nearly as good as with finite element results, but we gain a simulation speedup by the factor 4000. In addition, a parameter study of the parameters involved in the model reduction process is presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Aspects Regarding the Conception,Modeling and Implementation of an Articulated Robot in Space with Noises and Vibrations

The authors want to conceive and to model a structure of a 6R serial modular industrial robot with six freedom degrees. Some specific points are followed: the direct geometric modelling of the robot using the matrix of rotation method, the given in 3D modelling of the robot, the presentation of its components having some possible applications in the processes of production in the spaces with noises and vibrations. The direct geometrical modelling will be determinate the relative orientation matrices, which express the position of each system T_i, (i=1-6), according to the system T_i–1, also expressing the vectors of relative position of origin O_i of the systems T_i. They will be expressed the orientation of each system T_i in account to the fixed system T_o attached to the robot base, the set of independent parameters of orientation then are obtained the final equation of the column vector of the generalized coordinates, which express the position and the orientation of the clamping device. The paper presents the two possible applications of the studied robot implementation in a flexible manufacturing cel for the manipulation operations of parts. The robot will be used on the other side for the execution of weld in a points applied to the car carcases. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Ziegler effect in a non-conservative mechanical system

The destabilization of the stable equilibrium of a non-conservative system under the action of an infinitesimal linear viscous friction force is considered. In the case of low friction, the necessary and sufficient conditions for stability of a system with several degrees of freedom and, as a consequence, the conditions for the existence of the destabilization effect (Ziegler's effect) are obtained. Criteria for the stability of the equilibrium of a system with two degrees of freedom, in which the friction forces take arbitrary values, are constructed. The results of the investigation are applied to the problem of the stability of a two-link mechanism on a plane, and the stability regions and Ziegler's areas are constructed in the parameoter space of the problem.