A stochastic prey-predator system in a polluted environment with Beddington-DeAngelis functional response is proposed and analyzed. Firstly, for the system with white noise perturbation, by analyzing the limit system, the existence of boundary periodic solutions and positive periodic solutions is proved and the sufficient conditions for the existence of boundary periodic solutions and positive periodic solutions are derived. And then for the stochastic system, by introducing Markov regime switching, the sufficient conditions for extinction or persistence of such system are obtained. Furthermore, we proved that the system is ergodic and has a stationary distribution when the concentration of toxicant is a positive constant. Finally, two examples with numerical simulations are carried out in order to illustrate the theoretical results.

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In this paper, two stochastic SIRS epidemic models with standard incidence were proposed and investigated. For the non-autonomous periodic model, the sufficient criteria for extinction of the disease are obtained firstly. Then we show that the stochastic system has at least one nontrivial positive T-periodic solution under some conditions. For the model that are both disturbed by the white noise and telephone noise, we construct a suitable Lyapunov functions to verify the existence of a unique ergodic stationary distribution. Meanwhile, the sufficient condition for the extinction of the disease is also established. Finally, examples are introduced to illustrate the theoretical analysis. MSC: 60H10; 65C30; 91B70

Purpose The purpose of this paper is to present a method which enables a robot to learn both motion skills and stiffness profiles from humans through kinesthetic human-robot cooperation. Design Methodology Approach Admittance control is applied to allow robot-compliant behaviors when following the reference trajectories. By extending the dynamical movement primitives (DMP) model, a new concept of DMP and stiffness primitives is introduced to encode a kinesthetic demonstration as a combination of trajectories and stiffness profiles, which are subsequently transferred to the robot. Electromyographic signals are extracted from a human’s upper limbs to obtain target stiffness profiles. By monitoring vibrations of the end-effector velocities, a stability observer is developed. The virtual damping coefficient of admittance controller is adjusted accordingly to eliminate the vibrations. Findings The performance of the proposed methods is evaluated experimentally. The result shows that the robot can perform tasks in a variable stiffness mode as like the human dose in the teaching phase. Originality Value DMP has been widely used as a teaching by demonstration method to represent movements of humans and robots. The proposed method extends the DMP framework to allow a robot to learn not only motion skills but also stiffness profiles. Additionally, the authors proposed a stability observer to eliminate vibrations when the robot is disturbed by environment.

Purpose The purpose of this paper is to eliminate instability which may occur when a human stiffens his arms in physical human–robot interaction by estimating the human hand stiffness and presenting a modified vibration index. Design/methodology/approach Human hand stiffness is first estimated in real time as a prior indicator of instability by capturing the arm configuration and modeling the level of muscle co-contraction in the human’s arms. A time-domain vibration index based on the interaction force is then modified to reduce the delay in instability detection. The instability is confirmed when the vibration index exceeds a given threshold. The virtual damping coefficient in admittance controller is adjusted accordingly to ensure stability in physical human–robot interaction. Findings By estimating the human hand stiffness and modifying the vibration index, the instability which may occur in stiff environment in physical human–robot interaction is detected and eliminated, and the time delay is reduced. The experimental results demonstrate significant improvement in stabilizing the system when the human operator stiffens his arms. Originality/value The originality is in estimating the human hand stiffness online as a prior indicator of instability by capturing the arm configuration and modeling the level of muscle co-contraction in the human’s arms. A modification of the vibration index is also an originality to reduce the time delay of instability detection.

Purpose The purpose of this paper is to enable robots to intelligently adapt their damping characteristics and motions in a reactive fashion toward human inputs and task requirements during physical human–robot interaction. Design/methodology/approach This paper exploits a combination of the dynamical system and the admittance model to create robot behaviors. The reference trajectories are generated by dynamical systems while the admittance control enables robots to compliantly follow the reference trajectories. To determine how control is divided between the two models, a collaborative arbitration algorithm is presented to change their contributions to the robot motion based on the contact forces. In addition, the authors investigate to model the robot’s impedance characteristics as a function of the task requirements and build a novel artificial damping field (ADF) to represent the virtual damping at arbitrary robot states. Findings The authors evaluate their methods through experiments on an UR10 robot. The result shows promising performances for the robot to achieve complex tasks in collaboration with human partners. Originality/value The proposed method extends the dynamical system approach with an admittance control law to allow a robot motion being adjusted in real time. Besides, the authors propose a novel ADF method to model the robot’s impedance characteristics as a function of the task requirements.

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