Fractional-order kinematic analysis of biomechanical inspired manipulators

Abstract

Present-day mechanical manipulators reveal limited performances when compared with the human arm. Joint-driven manipulators are sub-optimal due to the high actuator requirements imposed by the transients of the operational space tasks. Muscle-actuated arms are superior because the anatomic structures adapt the task requirements to the driving linear actuators. However, the advantages of muscle actuation are difficult to unravel using the standard integer-order kinematics based on the integer derivatives, namely the positions, velocities and accelerations. This paper investigates the human arm and evaluates the influence of biomechanics upon the driving actuators by means of a new method of kinematic analysis and visualisation. The proposed method uses the tools of fractional calculus for computing the continuous propagation of the signals between positions and accelerations. The behaviour of the variables is compared in the joint and muscle spaces, using both the kinematics in the time domain and the describing function method. In this line of thought, the classical integer-order kinematics, with three discrete levels of visualisation, is generalised to a continuous description represented by the fractional-order kinematics.

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“…where 𝑥𝑥 𝑖𝑖 (𝑡𝑡) is the state of agent i at time t, N(i) denotes the set of neighbors of i, and α is a weighting factor that influences the rate of convergence [31]. Figure 1 illustrates the communication protocol model within a swarm robotics system.…”

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