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Neuromorphic Control of a Pendulum

Raphael Schmetterling, Fulvio Forni, Alessio Franci, Rodolphe Sepulchre

TL;DR

This paper investigates neuromorphic, event-based control of a pendulum by treating both plant and controller as rhythmic systems and coupling them through timed actuator events. The approach combines a rhythmic automaton (implemented via half-centre oscillator motifs) with an output-feedback regulator and adaptive mechanisms to achieve entrainment and energy regulation. Key contributions include a two-state pendulum automaton, a neuromorphic HCO-based actuator architecture in IN-PHASE and ANTI-PHASE configurations, a mixed neuromorphic implementation, and phase- and adaptive-control strategies that broaden stability in both overdamped and underdamped regimes. The results suggest energy-efficient, sparse-event control with potential benefits for distributed actuation in neuromorphic robotics.

Abstract

We illustrate the potential of neuromorphic control on the simple mechanical model of a pendulum, with both event-based actuation and sensing. The controller and the pendulum are regarded as event-based systems that occasionally interact to coordinate their respective rhythms. Control occurs through a proper timing of the interacting events. We illustrate the mixed nature of the control design: the design of a rhythmic automaton, able to generate the right sequence of events, and the design of a feedback regulator, able to tune the timing of events.

Neuromorphic Control of a Pendulum

TL;DR

This paper investigates neuromorphic, event-based control of a pendulum by treating both plant and controller as rhythmic systems and coupling them through timed actuator events. The approach combines a rhythmic automaton (implemented via half-centre oscillator motifs) with an output-feedback regulator and adaptive mechanisms to achieve entrainment and energy regulation. Key contributions include a two-state pendulum automaton, a neuromorphic HCO-based actuator architecture in IN-PHASE and ANTI-PHASE configurations, a mixed neuromorphic implementation, and phase- and adaptive-control strategies that broaden stability in both overdamped and underdamped regimes. The results suggest energy-efficient, sparse-event control with potential benefits for distributed actuation in neuromorphic robotics.

Abstract

We illustrate the potential of neuromorphic control on the simple mechanical model of a pendulum, with both event-based actuation and sensing. The controller and the pendulum are regarded as event-based systems that occasionally interact to coordinate their respective rhythms. Control occurs through a proper timing of the interacting events. We illustrate the mixed nature of the control design: the design of a rhythmic automaton, able to generate the right sequence of events, and the design of a feedback regulator, able to tune the timing of events.
Paper Structure (8 sections, 3 equations, 10 figures)

This paper contains 8 sections, 3 equations, 10 figures.

Table of Contents

  1. Introduction
  2. The automaton of a pendulum
  3. Event-based Control Architecture
  4. Neuromorphic implementation
  5. Control by entrainment
  6. Phase Control
  7. Neuromorphic Adaptive Control
  8. Discussion

Figures (10)

  • Figure 1: The two distinct configurations of event actuation. Left: in-phase identical actuating events (IN-PHASE). Right: anti-phase actuating events of opposite sign (ANTI-PHASE). Sketch courtesy of @artjoy2015.
  • Figure 2: The anti-phase rhythm of a Half-Centre Oscillator (HCO) circuit. The size of the bursts is modulated midway. Top: the voltages of the two neurons. The dashed horizontal line denotes the voltage threshold, above which the motor is active. Bottom: the corresponding actuating events.
  • Figure 3: Simulation of the HCOs and actuator events. Top: the total torque $I$. Middle: the voltages of HCO 1. Bottom: the voltages of HCO 2. At $t = 8$ s (indicated by the dashed black line), the system's configuration is switched from ANTI-PHASE and, after a transient period, it settles on IN-PHASE.
  • Figure 4: Block diagram of the complete architecture, including the event-based feedback loops introduced in Sections \ref{['phase']} and \ref{['adaptive']}. Small arrows over signal transmission lines indicate event-based communication as described in Section \ref{['architecture']}. The HCO block architecture is described in Sections \ref{['architecture']} and \ref{['implementation']}.
  • Figure 5: Small oscillations in the overdamped regime (damping $\alpha = 1.4$). As the burst size of the neural oscillation increases (from top row to bottom row), so does the amplitude of the pendulum's oscillation.
  • ...and 5 more figures