Topic
Autonomous system (mathematics)
About: Autonomous system (mathematics) is a research topic. Over the lifetime, 1648 publications have been published within this topic receiving 38373 citations.
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01 Apr 1990
TL;DR: An optimization approach that provides for the acceleration or deceleration of the vehicle is developed, as is the duration of the time for which this control must be applied to avoid a collision with moving objects.
Abstract: The problem of collision-free navigation and guidance for mobile robots is essential to the survival of unmanned terrain vehicles. This communication adds complexity to the guidance problem by introducing moving objects that may cross the desired navigational path of an autonomous vehicle. The vehicle is equipped with sensors that report locations of the moving objects. Speed and direction of each moving object are modeled as random walk processes. An optimization approach that provides for the acceleration or deceleration of the vehicle is developed, as is the duration of the time for which this control must be applied to avoid a collision with moving objects. The constraints on the objective function are given in terms of collision probabilities, and simulation results are presented for a collision-free environment. Implications of this approach for autonomous vehicles are given in terms of the flexibility of path planning. >
70 citations
TL;DR: The results of this work represent the first report on the phenomenon of extreme multistability in a jerk system and thus deserve dissemination.
Abstract: This paper studies the dynamics of a novel memristive 4D autonomous system obtained by replacing the memristive diode bridge in the original circuit of [Chaos, Solitons and Fractals 91 180–197 (2016)] with a flux control memristor. The new memristor oscillator is described by a continuous time four-dimensional autonomous system with a line of equilibria. The analysis is carried out in terms of its parameters by using bifurcation diagrams, phase space trajectory plots, Poincare sections, bifurcation like sequences, and graphs of Lyapunov exponents. The system is shown to experience the unusual phenomenon of extreme multistability characterized by the possibility of an infinite number of attractors for the same parameters setting. Period doubling and symmetry restoring crisis scenarios are reported. To the best of the authors’ knowledge, the results of this work represent the first report on the phenomenon of extreme multistability in a jerk system and thus deserve dissemination.
69 citations
TL;DR: In this paper, an algorithm for constructing meromorphic solutions of autonomous nonlinear ODEs in explicit form is presented, including rational, periodic, elliptic, and rational ODE solutions.
69 citations
TL;DR: It is concluded that the four-scroll chaotic attractor of this system, which is observed on both computer and oscilloscope, cannot actually exist in theory.
Abstract: Recently, we have investigated a new chaotic system of three-dimensional autonomous quadratic ordinary differential equations, and found that the system visually displays a four-scroll chaotic attractor confirmed by both numerical simulations and circuit implementation. In this paper, we further study the following question: Is it really true that this system can generate a four-scroll chaotic attractor, or is it only a numerical artifact? By a more careful theoretical analysis along with some further numerical simulations, we conclude that the four-scroll chaotic attractor of this system, which we observed on both computer and oscilloscope, cannot actually exist in theory. The fact is that this system has two co-existing two-scroll chaotic attractors that are arbitrarily close in the phase space for some system parameters, therefore extremely tiny numerical round-off errors or signal fluctuations will nudge the system orbit to switch from one attractor to another, thereby forming the seemingly single four-scroll chaotic attractor on screen display.
68 citations
TL;DR: Using the framework, autonomous functions were constructed for maintaining postural stability constraint while satisfying the desired trajectory of operation points, including the feet, while interacting with the environment.
Abstract: This paper introduces a framework for whole-body motion generation integrating operator's control and robot's autonomous functions during online control of humanoid robots. Humanoid robots are biped machines that usually possess multiple degrees of freedom (DOF). The complexity of their structure and the difficulty in maintaining postural stability make the whole-body control of humanoid robots fundamentally different from fixed-base manipulators. Getting hints from human conscious and subconscious motion generations, the authors propose a method of generating whole-body motions that integrates the operator's command input and the robot's autonomous functions. Instead of giving commands to all the joints all the time, the operator selects only the necessary points of the humanoid robot's body for manipulation. This paper first explains the concept of the system and the framework for integrating operator's command and autonomous functions in whole-body motion generation. Using the framework, autonomous functions were constructed for maintaining postural stability constraint while satisfying the desired trajectory of operation points, including the feet, while interacting with the environment. Finally, this paper reports on the implementation of the proposed method to teleoperate two 30-DOF humanoid robots, HRP-1S and HRP-2, by using only two 3-DOF joysticks. Experiments teleoperating the two robots are reported to verify the effectiveness of the proposed method.
67 citations