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Fig. 1 | Journal of NeuroEngineering and Rehabilitation

Fig. 1

From: Supplemental vibrotactile feedback control of stabilization and reaching actions of the arm using limb state and position error encodings

Fig. 1

Simplified model of closed-loop feedback control for goal-directed reaching. a Simplified model demonstrating how feedback delay (∆) and information content (Sensor Function) impacts performance of a proportional controller regulating the position θa of a damped inertial “limb” modeled as a second order differential equation relating changes in limb kinematics (position, velocity and acceleration) to changes in the control input u. Controller gain φ was varied to test the capabilities of the model system. b Simulation results of limb displacement (vertical axis) plotted as a function of time (horizontal axis) when the feedback path emulates proprioception (i.e., Delay ∆ = 0.06 s and Sensor Function θf = θa + 0.15 dθa/dt). Arrow indicates the time of change in desired position (depicted in arbitrary units of displacement). Dotted line: t = 1 s. Grey band: goal target zone. The limb obtains the goal within the time constraint over a broad range of controller gains with position + velocity feedback (Thick blue trace: φ = 20; Thin trace: φ = 130). c Simulated reaching under visual guidance (Red: Delay ∆ = 0.12 s and Sensor Function θf = θa; Thick red trace: φ = 5; Thin trace: φ = 10; dashed trace: φ = 20). With position feedback, no value of φ enables success when ∆ = 0.12 s. Also shown (Purple; φ = 20) is an acceptable solution obtained when simulated visual feedback also includes velocity information: θa + 0.15 dθa/dt. For panels b and c, the horizontal scale bar depicts 1 s whereas the vertical scale bar represents 5 cm displacement

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