The paper introduces an action recognition framework that uses concepts from the theory of chaotic systems to model and analyze nonlinear dynamics of human actions. Trajectories of reference joints are used as the representation of the non-linear dynamical system that is generating the action. Each trajectory is then used to reconstruct a phase space of appropriate dimension by employing a delay-embedding scheme. The properties of the reconstructed phase space are captured in terms of dynamical and metric invariants that include Lyapunov exponent, correlation integral and correlation dimension. Finally, the action is represented by a feature vector which is a combination of these invariants over all the reference trajectories. Our contributions in this paper include :1) investigation of the appropriateness of theory of chaotic systems for human action modelling and recognition, 2) a new set of features to characterize nonlinear dynamics of human actions, 3) experimental validation of the feasibility and potential merits of carrying out action recognition using methods from theory of chaotic systems.

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The equation of large deflection of functionally graded beam subjected to arbitrary loading condition is derived. In this work assumed that the elastic modulus varies by exponential and power function in longitudinal direction. The nonlinear derived equation has not exact solution so shooting method has been proposed to solve the nonlinear equation of large deflection. Results are validated with finite element solutions. The method will be useful toward the design of compliant mechanisms driven by smart actuators. Finally the effect of different elastic modulus functions and loading conditions are investigated and discussed.