Modeling PWM-Time-SOC Interaction in a Simulated Robot
Authors: Vidyut Pradeep, Shirantha Welikala
Organizations: South Brunswick High School, Monmouth Junction, New Jersey, United States · Stevens Institute of Technology, Hoboken, New Jersey, United States
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.
Figures & tables
Fig. 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.
Fig. 2 : Expanded block of the Mechanical Drive and Dynamics block
Fig. 3 : Methodology workflow showing the progression from parameter definition through simulation, data collection, model identification using SINDy, and validation.
Time (s)
Battery SOC (%)
0
100.00
10
99.63
20
99.41
30
99.20
40
98.99
50
98.77
TABLE I : Example Dataset for 40% PWM
Parameter
Numerical Value
a1
100.1
b1
0.00131
c1
0.000114
d1
9.93×10−6
e1
3.17×10−7
f1
0.00107
TABLE II : Coefficients for Model 1: SOC (t,p)
Parameter
Numerical Value
a2
0.0021
b2
1.1496
c2
101.011
TABLE III : Coefficients for Model 2: SOC (p) at t=300 s
Parameter
Numerical Value
a3
0.00131
b3
9.93×10−6
c3
3.17×10−7
d3
0.00107
e3
0.014
f3
0.106
TABLE IV : Coefficients for Model 3: ∂t∂SOC
Time (s)
Recorded SOC (%)
Predicted SOC (%)
0
100.00
99.18
20
96.88
96.80
40
94.63
94.63
60
92.41
92.49
80
90.22
90.36
100
88.05
88.23
TABLE V : Validation at 90% PWM: Recorded vs. Predicted SOC
Fig. 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.
Time (s)
Recorded SOC (%)
Predicted SOC (%)
0
100.00
99.92
20
99.42
99.42
40
98.99
98.99
60
98.56
98.58
80
98.14
98.17
100
97.72
97.77
TABLE VI : Validation at 40% PWM: Recorded vs. Predicted SOC
Fig. 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.
Engineering Department at Harper Adams University, Newport, Shropshire TF10 8NB, UK · Lincoln Institute for Agri-Food Technology and Lincoln Centre for Autonomous Systems
Department of Mechatronics and Robotics Engineering, Egypt-Japan University of Science and Technology (E-JUST), New Burg El-Arab City, Alexandria, Egypt