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Modeling PWM-Time-SOC Interaction in a Simulated Robot

Vidyut Pradeep, Shirantha Welikala

TL;DR

This work develops a physics and data-informed model from a simulation that predicts SOC depletion as a function of time and PWM duty cycle for a simulated 4-wheel Arduino robot to construct a unified nonlinear model that captures SOC(t, p).

Abstract

Accurate prediction of battery state of charge is needed for autonomous robots to plan movements without using up all available power. This work develops a physics and data-informed model from a simulation that predicts SOC depletion as a function of time and PWM duty cycle for a simulated 4-wheel Arduino robot. A forward-motion simulation incorporating motor electrical characteristics (resistance, inductance, back-EMF, torque constant) and mechanical dynamics (mass, drag, rolling resistance, wheel radius) was used to generate SOC time-series data across PWM values from 1-100%. Sparse Identification of Nonlinear Dynamics (SINDy), combined with least-squares regression, was applied to construct a unified nonlinear model that captures SOC(t, p). The framework allows for energy-aware planning for similar robots and can be extended to incorporate arbitrary initial SOC levels and environment-dependent parameters for real-world deployment.

Modeling PWM-Time-SOC Interaction in a Simulated Robot

TL;DR

This work develops a physics and data-informed model from a simulation that predicts SOC depletion as a function of time and PWM duty cycle for a simulated 4-wheel Arduino robot to construct a unified nonlinear model that captures SOC(t, p).

Abstract

Accurate prediction of battery state of charge is needed for autonomous robots to plan movements without using up all available power. This work develops a physics and data-informed model from a simulation that predicts SOC depletion as a function of time and PWM duty cycle for a simulated 4-wheel Arduino robot. A forward-motion simulation incorporating motor electrical characteristics (resistance, inductance, back-EMF, torque constant) and mechanical dynamics (mass, drag, rolling resistance, wheel radius) was used to generate SOC time-series data across PWM values from 1-100%. Sparse Identification of Nonlinear Dynamics (SINDy), combined with least-squares regression, was applied to construct a unified nonlinear model that captures SOC(t, p). The framework allows for energy-aware planning for similar robots and can be extended to incorporate arbitrary initial SOC levels and environment-dependent parameters for real-world deployment.
Paper Structure (39 sections, 34 equations, 5 figures, 6 tables)

This paper contains 39 sections, 34 equations, 5 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Literature Review
  4. Preliminaries: Sparse Identification of Nonlinear Dynamics (SINDy)
  5. The SINDy Framework
  6. Sparse Regression
  7. Battery State of Charge for Mobile Robots
  8. Mobile Robot Energy Consumption
  9. Fundamental Governing Equations for SOC
  10. Theoretical SOC Model Derivation
  11. Transient Regime
  12. Steady-State Regime
  13. Bridging the Two Regimes
  14. Why a Coupled $(t,p)$ Model Is Necessary
  15. Simulation Framework
  16. ...and 24 more sections

Figures (5)

  • Figure 1: Simulation workflow showing the progression of the data collection from the MATLAB simulated robot. Illustrates the pathways the code goes to before giving an output.
  • Figure 2: Expanded block of the Mechanical Drive and Dynamics block
  • Figure 3: Methodology workflow showing the progression from parameter definition through simulation, data collection, model identification using SINDy, and validation.
  • Figure 4: Battery SOC at 90% PWM. (a) Complete time series showing close agreement between recorded (blue) and predicted (red) values. (b) Magnified view of initial transient region where logarithmic terms capture the steep early discharge.
  • Figure 5: Battery SOC at 40% PWM. (a) Complete time series showing very close agreement between recorded (blue) and predicted (red) values. (b) Magnified initial region showing smaller but still present transient "hook" accurately captured by the model.