Stabilization of the motion of a spherical robot using feedbacks

The paper is concerned with the problem of stabilizing a spherical robot of combined type during its motion. The focus is on the application of feedback for stabilization of the robot which is an example of an underactuated system. The robot is set in motion by an internal wheeled platform with a rotor placed inside the sphere. The results of experimental investigations for a prototype of the spherical robot are presented.     

Switched control of a nonholonomic mobile robot

We present a switched control algorithm to stabilize a car-like mobile robot which possesses velocity level nonholonomic constraint. The control approach rests on splitting the system into several second-order subsystems and then stabilizing the system sequentially using finite-time controllers, finally resulting in the mobile robot being moved from one point to another point. State dependent switching control is employed in which the controllers switches on a thin surface in the state-space. Robustness analysis is presented by redefining the switching signal using relaxed switching surface. Both, non-robust and robust controllers are validated through numerical simulation.     

Linear stabilization of the programmed motions of non-linear controlled dynamical systems under parametric perturbations

A non-linear controlled dynamical system that describes the dynamics of a broad class of non-linear mechanical and electromechanical systems (in particular, electromechanical robot manipulators) is considered. It is proposed that the real parameter vector of a non-linear controlled dynamical system belongs to an assigned (admissible) constrained closed set and is assumed to be unknown. The programmed motion of the non-linear controlled dynamical system and the programmed control that produces it are assigned (constructed) by using an estimate, that is, the nominal value of the parameter vector of the non-linear controlled dynamical system, which differs from its actual value. A procedure for synthesizing stabilizing control laws with linear feedback with respect to the state that ensure stabilization of the programmed motions of the non-linear controlled dynamical system under parametric perturbations is proposed. A non-singular linear transformation of the coordinates of the state space that transforms the original non-linear controlled dynamical system in deviations (from the programmed motion and programmed control) into a certain non-linear controlled dynamical system of special form, which is convenient for analysing and synthesizing laws for controlling the motion of the system, is constructed. A certain non-linear controlled dynamical system of canonical form is derived in the original non-linear controlled dynamical system in deviations. The transformation of the coordinates of the state space constructed and the Lyapunov function methodology are used to synthesize stabilizing control laws with linear feedback with respect to the state, which ensure asymptotic stability as a whole of the equilibrium position of the non-linear controlled dynamical system of canonical form and dissipativity “in the large” of the non-linear controlled dynamical system of special form and of the original non-linear controlled dynamical system in deviations. In the control laws synthesized, the formulae for the elements of their matrices of the feedback loop gains do not depend on the real parameter vector of the non-linear controlled dynamical system, and they depend solely on the constants from certain estimates that hold for all of its possible values from an assigned set. Estimates of the region of dissipativity “in the large” of the non-linear controlled dynamical system of special form and the original non-linear controlled dynamical system in deviations closed by the stabilizing control laws synthesized are given, and estimates for their limit sets and regions of attraction are presented.     

空间机器人组装超大型结构的动力学分析北大核心CSCD

超大型航天结构具有超大柔性、超低固有频率的特点,空间机器人在轨组装时应尽可能避免激起超大型结构的柔性振动.空间机器人组装超大型结构模块的过程分成抓捕阶段、位姿调整与稳定阶段、安装阶段和爬行阶段.通过对安装阶段的动力学与控制研究,提出共线安装的轨迹规划方法,有效避免了柔性结构振动.首先,采用自然坐标法和绝对节点坐标法建立主结构-空间机器人-待组装结构的在轨组装系统动力学模型.然后,将共线安装的要求转化为空间机器人的轨迹规划约束,要求空间机器人质心到主结构/待组装结构的距离保持不变,实现共线安装的轨迹规划.数值仿真表明:提出的组装方法在组装过程中可有效避免超大型结构的横向运动,降低夹持力矩.最后,分析了系统参数对组装过程动力学响应的影响,为超大型航天器的在轨组装提供了参考.     

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.     

Hierarchical Constraint-Based Singularity Avoidance for Multi-Axis Robots

A generalized reflexive approach for Hierarchical Constraint-Based Singularity Avoidance (HCB-SA) is proposed and demonstrated for the multi-axis robot control of a six Degrees Of Freedom (DOF) hybrid manipulator system. The concept utilizes a dynamic adaptation of virtual constraints by introducing virtual damped actuation on the velocity control level and an anisotropic reflexive trajectory deflection depending on the robot constraints on the position control level. Redundant or low priority DOFs can be used to minimize the pose error in the more important DOFs reflexively without calculating new trajectories. Accordingly, the end-effector can be safely controlled in the vicinity of singularities and all constraints in the task and joint space can be surely hold. Furthermore, the proposed cascaded feedback control with the generalized HCB-SA algorithm is able to react on the presence of external disturbances which is validated using software-in-the-loop simulation on the real-time control system. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computed torque control of an under-actuated service robot platform modeled by natural coordinates

The paper investigates the motion planning of a suspended service robot platform equipped with ducted fan actuators. The platform consists of an RRT robot and a cable suspended swinging actuator that form a subsequent parallel kinematic chain and it is equipped with ducted fan actuators. In spite of the complementary ducted fan actuators, the system is under-actuated. The method of computed torques is applied to control the motion of the robot.The under-actuated systems have less control inputs than degrees of freedom. We assume that the investigated under-actuated system has desired outputs of the same number as inputs. In spite of the fact that the inverse dynamical calculation leads to the solution of a system of differential–algebraic equations (DAE), the desired control inputs can be determined uniquely by the method of computed torques.We use natural (Cartesian) coordinates to describe the configuration of the robot, while a set of algebraic equations represents the geometric constraints. In this modeling approach the mathematical model of the dynamical system itself is also a DAE.The paper discusses the inverse dynamics problem of the complex hybrid robotic system. The results include the desired actuator forces as well as the nominal coordinates corresponding to the desired motion of the carried payload. The method of computed torque control with a PD controller is applied to under-actuated systems described by natural coordinates, while the inverse dynamics is solved via the backward Euler discretization of the DAE system for which a general formalism is proposed. The results are compared with the closed form results obtained by simplified models of the system. Numerical simulation and experiments demonstrate the applicability of the presented concepts.     

Motion planning for planar bipeds using flatness: the single support phase

Trajectory planning and control of planar motions of biped robots is considered. The robot is modeled as a hierarchical structure of rigid links with rotational joints, which may be seen as a pendulum tree. Motors are available at all rotational joints. However, by the absence of control torques at the contact points with the ground, the system is underactuated. It is shown how differential flatness and time scaling can be helpful for the design of walking motions. Emphasis is put on the single support phase, when the robot touches the floor at a single point. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adaptive anti control of chaos for robot manipulators with experimental evaluations

Roughly speaking, anti control of chaos consists in injecting a chaotic behavior to a system by means of a control scheme. This note introduces a new scheme to solve the anti control of chaos for robot manipulators. The proposed controller uses an adaption law to estimate the robot parameters on line. Thus, the controller does not require any knowledge of the physical parameters of the manipulator, such as masses, lengths of the links, moments of inertia, etc. The new scheme is based in the velocity field control paradigm, hence the specification of a chaotic system to define a desired velocity field is required. Experimental results in a two degrees-of-freedom direct-drive robot illustrate the practical feasibility of the introduced theory. In order to achieve anti control of chaos of our experimental system, two different chaotic attractors are used: the Genesio-Tesi system and a Jerk-type system. Results showed that the controller is able to inject the chaotic behavior to the robot while the robot parameters are estimated on line.     

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.     

Variable structure control of linear time invariant fractional order systems using a finite number of state feedback law

In this paper, an approach based on the variable structure control is proposed for stabilization of linear time invariant fractional order systems (LTI-FOS) using a finite number of available state feedback controls, none of which is capable of stabilizing the LTI-FOS by itself. First, a system with integer order derivatives is defined and its existence is proved, which has stability equivalent properties with respect to the fractional system. This makes it possible to use Lyapunov function and convex analysis in order to define the sliding sector and develop a variable structure control which enables the switching between available control gains and stabilizing the fractional order system.     

一类超混沌离散系统的控制

研究一类超混沌离散系统的控制问题.基于局部线性化建立了时变线性反馈控制律.采用Liapunov直接法估计了控制律可以有效作用的邻域范围.分别给出了应用该控制律解决不稳定周期轨道的镇定问题和任意给定周期轨道的追踪问题的算例.     

On asympotic behavior of solutions to several classes of discrete dynamical systems

In this paper, a new complete and simplified proof for the Husainov-Nikiforova Theorem is given. Then this theorem is generalized to the case where the coefficients may have different signs as well as nonlinear systems. By these results, the robust stability and the bound for robustness for high-order interval discrete dynamical systems are studied, which can be applied to designing stable discrete control system as well as stabilizing a given unstable control system.     

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.     

Pathplanning and control of an autonomous robot vehicle with a manipulator

An autonomous mobile robot is presented. It consists of two parts: a mobile vehicle underneath a robotarm with DOF 5. These two are a nonholomic (the mobile vehicle) and a holonomic subsystem (the robotarm). To give the robot orders or tasks to accomplish this can be done from an external controlsoftware via TCP–IP to the controlsoftware of the robot. An embedded system involves chart creation, pathplanning (global, local), evaluation of sensorsignals, object– and/or marker–detection and a controlled movement. Futhermore it communicates over FIFOs with an nonrealtime–task which allows a communication via TCP–IP. Several sensors are implemented, e.g. infrared–/ ultrasonic–range sensors connected via CAN to the embedded board, as well as the control boards for each engine. A Laserscanner is installed in front of the robot to detect edges and obstacles. For marker–tracking and object recognition an USB–Webcam is added on the robotarm. For avoidance of collisions between the robotarm and the mobile robot a repeller is introduced. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robust Optimal Trajectory Planning for Robots by Stochastic Optimization

In the optimal control of industrial, field or service robots, the standard procedure is to determine first offline a reference trajectory and a feedforward control, based on some selected nominal values of the unknown stochastic model parameters, and to correct then the inevitable and increasing deviation of the state or performance of the robot from the prescribed state or performance of the system by online measurement and control actions. Due to the stochastic variations of the model parameters, increasing measurement and correction actions are needed during the process. By optimal stochastic trajectory planning (OSTP), based on stochastic optimization methods, the available a priori and sample information about the robot and its working environment is incorporated into the control process. Consequently, more robust reference trajectories and feedforward controls are obtained which cause much less online control actions. In order to maintain a high quality of the guiding functions, the reference trajectory and the feedforward control can be updated at some later time points such that additional information about the control process is available. After the presentation of the Adaptive Optimal Stochastic Trajectory Planning (AOSTP) procedure based on stochastic optimization methods, several numerical techniques for the computation of robust reference trajectories and feedforward controls under real-time conditions are presented. Additionally, numerical examples for a Manutec r3 industrial robot are discussed. The first one demonstrates real-time solutions of (OSTP) based on a sensitivity analysis of a before-hand calculated reference trajectory. The second shows the differences between reference trajectories based on deterministic methods and the stochastic methods introduced in this paper. Based on simulations of the robots behavior, the increased robustness of stochastic reference trajectories is demonstrated.     

Robot learning schemes that trade motion accuracy for command simplification

This study was inspired by the human motor control system in its ability to accommodate a wide variety of motions. By contrast, the biologically inspired robot learning controller usually encounters huge learning space problems in many practical applications. A hypothesis for the superiority of the human motor control system is that it may have simplified the motion command at the expense of motion accuracy. This tradeoff provides an insight into how fast and simple control can be achieved when a robot task does not demand high accuracy. Two motion command simplification schemes are proposed in this paper based on the equilibrium-point hypothesis for human motion control. Investigation into the tradeoff between motion accuracy and command simplification reported in this paper was conducted using robot manipulators to generate signatures. Signature generation involves fast handwriting, and handwriting is a human skill acquired via practice. Because humans learn how to sign their names after they learn how to write, in the second learning process, they somehow learn to trade motion accuracy for motion speed and command simplicity, since signatures are simplified forms of original handwriting. Experiments are reported that demonstrate the effectiveness of the proposed schemes.     

Conditions for stability and stabilization of systems of neutral type with nonmonotone Lyapunov functionals

We suggest new tests for the stability and uniform asymptotic stability of an equilibrium in systems of neutral type. By using these tests, we prove conditions for optimal stabilization and derive new estimates for perturbations that can be countered by a system closed by an optimal control. We show that, by using nonmonotone sign-indefinite functionals as Lyapunov functionals, one can obtain conditions for uniform asymptotic stability that do not contain the a priori requirement of stability of the difference operator and do not imply the boundedness of the right-hand side of the system. When studying the action of perturbations on the stabilized systems, these conditions permit one to obtain new estimates of perturbations preserving the stabilizing properties of optimal controls. The obtained estimates do not imply any constraint on the value of perturbations in some domains of the phase space that are defined when constructing an optimal stabilizing control. Some examples are considered.     

Stabilization of the equilibria of dynamical systems

Based on Rumyantsev's method, a procedure is developed for stabilizing stable and unstable equilibria of dynamical systems by continuous and modulus-constrained control actions. It is shown that, when modulus constraints are imposed on the controls, and when the quadratic-form coefficients are reduced in modulus, the optimal stabilization, in terms of this method, approximates to time-optimal stabilization. A solution is obtained of the problem of stabilizing unstable equilibrium positions at which the potential energy of the system has neither a maximum nor a minimum (or, in particular, at which the potential energy is identically equal to zero).