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.
Accurate prediction of electrical power consumption is essential for energy-aware motion planning, battery management, and thermal monitoring in battery-powered humanoid robots. This letter presents a physics-based, linear-in-parameters model for the electrical power consumption of the seven-degree-of-freedom left arm of the UnitreeG1 humanoid robot. The proposed formulation combines actuator loss terms with a baseline-torque correction that captures changes in gravity-compensation load and enables accurate prediction of negative net power trajectories. Pairwise interaction terms are introduced to model power coupling during simultaneous multi-joint motion. Model parameters are identified from experimental data collected on a physical UnitreeG1 using onboard power measurements as the regression target. Across 897 trajectories covering single-joint and coordinated arm motions at multiple speed levels, the identified model achieves R2=0.933 with an RMSE of 1.07 (W). Validation on 46 trajectories executed at previously unseen speeds yields R2=0.965, demonstrating strong generalisation beyond the identification dataset. Analysis of the identified parameters reveals distinct power-consumption characteristics across the arm, with viscous friction dominating most joints (shoulder pitch and all three wrist joints), copper losses dominating shoulder yaw and the elbow, and shoulder roll uniquely dominated by Coulomb friction.
Nestor N. Deniz, Sebastian Vega, Simon Parsons +1
Engineering Department at Harper Adams University, Newport, Shropshire TF10 8NB, UK · Lincoln Institute for Agri-Food Technology and Lincoln Centre for Autonomous Systems
Accurate dynamics modeling of Brushless DC (BLDC) motors is fundamental to high-performance robotic joint control. This paper presents a Physics-Informed Neural Network (PINN) with a deep residual (ResNet) backbone that learns a continuous-time surrogate of the full six-state BLDC motor dynamics. Given simulation time, applied three-phase voltages, and excitation parameters as inputs, the network directly predicts all motor state variables -- rotor angle, angular velocity, three-phase currents, and winding temperature -- while simultaneously satisfying the governing electromechanical and thermal ODEs through a composite physics-data loss. A curriculum scheduling strategy gradually activates the physics penalty to prevent premature convergence. Training runs are completed in under two minutes on a standard CPU. Crucially, once trained, PINN inference achieves latencies of 0.1--22, mu s per query, up to 118x faster than conventional ODE solvers, making it suitable for real-time observer and control applications.
Haitham El-Hussieny
Department of Mechatronics and Robotics Engineering, Egypt-Japan University of Science and Technology (E-JUST), New Burg El-Arab City, Alexandria, Egypt
Accurate dynamics models are critical for the design of predictive controllers for autonomous mobile robots. Physics-based models are often too simple to capture relevant real-world effects, while data-driven models are data-intensive and slow to train. We introduce an approach for fast adaptation of neural robot dynamic models that combines offline training with efficient online updates. Our approach learns an incremental neural dynamics model offline and performs low-rank second-order parameter adaptation online, enabling rapid updates without full retraining. We demonstrate the approach on a real quadrotor robot, achieving robust predictive tracking control in novel operational conditions.
Abdullah Altawaitan, Nikolay Atanasov
Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA 92093, USA · Kuwait University