Industrial Robot Power Model Boosts Energy Efficiency Predictions
In an era where energy efficiency is paramount, a team of researchers from Chongqing University has developed a groundbreaking method to predict the real-time power consumption of industrial robots with remarkable accuracy. The study, led by Wu Yongqiang, a master’s student, and his advisor Tang Xianzhi, an associate professor in the School of Mechanical Engineering, introduces a novel power equivalent model that could revolutionize how manufacturers optimize robotic systems for lower energy use. Published in the Journal of Chongqing University, the research offers a practical solution to one of the most persistent challenges in modern manufacturing: accurately forecasting the energy demands of highly dynamic robotic operations without relying on proprietary or inaccessible motor parameters.
The significance of this development cannot be overstated. Industrial robots are the backbone of smart manufacturing and digital workshops, driving automation across industries from automotive to electronics. However, despite their widespread adoption, these machines often operate with suboptimal energy efficiency. Their payloads are typically much lighter than their own mass, and frequent acceleration and deceleration cycles during operation lead to substantial energy waste. As global energy costs continue to rise, the pressure on manufacturers to reduce operational expenses has intensified. This has placed energy optimization at the forefront of industrial innovation, prompting researchers worldwide to explore new ways to make robotic systems more sustainable.
Existing approaches to improving robot energy efficiency have largely focused on trajectory optimization—adjusting the path and speed of robotic arms to minimize energy use. Some methods scale motion time using proportional factors, while others insert virtual control points between key trajectory nodes and apply cubic or quintic splines to generate smoother paths. More advanced techniques use B-spline curves in joint space, optimizing control points via algorithms like particle swarm optimization to achieve minimal energy consumption. While these strategies have demonstrated promising results in experimental settings, they share a critical limitation: they depend heavily on accurate power models, which are often too complex or rely on motor parameters that are either unknown or difficult to measure with precision.
This is where the work of Wu, Tang, and their colleagues stands out. Rather than attempting to refine trajectory planning directly, they took a step back to address the foundational issue—the lack of a reliable, accessible power prediction model. Traditional models incorporate detailed electrical and mechanical characteristics of motors, including resistance, inductance, and magnetic flux linkage. These parameters are not only difficult to obtain but also vary between individual units and degrade over time, making long-term predictions unreliable. In response, the team proposed a simplified yet powerful alternative: a high-order polynomial model that maps the robot’s power loss to two readily measurable variables—motor torque and angular velocity.
The core idea behind the model is elegant in its simplicity. Instead of delving into the intricate physics of permanent magnet synchronous motors (PMSMs), which power most industrial robots, the researchers treated the entire system as a “black box” whose energy losses could be empirically characterized. They recognized that while the internal workings of motors and servo drives are complex, the relationship between input (torque and speed) and output (power loss) could be approximated using mathematical functions derived from real-world data. By collecting measurements of joint torque, angular velocity, and total power consumption during robot operation, they were able to fit a polynomial equation that captures the dominant sources of energy dissipation, including copper losses in motor windings, iron losses due to magnetic hysteresis and eddy currents, and switching and conduction losses in inverters.
What sets this model apart is its reliance on the least squares method for parameter identification. This statistical technique allows the researchers to determine the coefficients of the polynomial by minimizing the difference between predicted and actual power values across a large dataset. The result is a highly adaptable framework that does not require prior knowledge of the robot’s internal motor specifications. This makes it particularly valuable for industrial users who may not have access to detailed technical documentation or who operate mixed fleets of robots from different manufacturers.
To validate their approach, the team conducted experiments on a KUKA KR60-3, a six-degree-of-freedom industrial robot capable of handling 60-kilogram loads. They designed a specialized excitation trajectory using a finite-term Fourier series function with a base frequency of 0.0417 Hz and a period of 24 seconds. This type of trajectory was chosen for several reasons. First, it produces a closed-loop motion, enabling repeated testing under consistent conditions. Second, because the path is mathematically defined, joint velocities and accelerations can be calculated analytically, reducing noise and errors associated with numerical differentiation. Third, the rich frequency content of the Fourier-based motion ensures that the robot operates across a wide range of speeds and torques, providing comprehensive data for model training.
Data was collected at a sampling rate of 12 milliseconds, capturing joint positions and torques directly from the robot controller. Total power consumption was measured externally using precision instrumentation. Using this dataset, the researchers applied the least squares algorithm to identify the coefficients of the power loss model. The identified parameters included not only the variable losses tied to torque and speed but also constant power components from auxiliary systems such as teach pendants and cooling fans, which were determined through standby testing.
The results were striking. When comparing the model’s predictions against actual measurements, the root mean square (RMS) relative error for instantaneous power was just 8.11%. For total energy consumption over a complete cycle, the relative error dropped to approximately 1.04%, indicating that positive and negative deviations in power prediction tended to cancel out over time. To further test the robustness of the model, the team conducted a separate validation experiment using a different trajectory—one not used during the parameter identification phase. Even under these conditions, the RMS relative error remained below 8%, and the total energy prediction error was only 1.13%.
These figures represent a significant improvement over existing methods that rely on simplified or proxy metrics for energy estimation. Previous studies have used approximations such as the square of joint torque, pseudo-power, or mechanical energy to represent robot power consumption. However, as the authors point out, these metrics fail to capture the full picture of system-level losses, particularly those occurring in power electronics and transmission components. By contrast, the new model accounts for both mechanical and electrical inefficiencies, offering a more holistic view of energy use.
The implications of this research extend beyond academic interest. For factory managers and automation engineers, the ability to accurately predict power consumption opens up new possibilities for real-time energy monitoring, predictive maintenance, and cost forecasting. It enables more informed decisions about production scheduling—such as running energy-intensive tasks during off-peak hours—or evaluating the return on investment for upgrading to more efficient robotic systems. Moreover, because the model can be calibrated using standard sensor data available on most modern robots, it can be deployed without requiring expensive hardware modifications.
Another advantage is scalability. The model structure is general enough to be applied to robots with different configurations and payloads. While the current study focused on a six-axis articulated robot, the underlying principles could be extended to SCARA, delta, or collaborative robots with minimal adjustments. The modular nature of the loss function—where each joint contributes independently to the total power—also makes it easier to isolate and diagnose inefficiencies in specific axes, aiding in targeted maintenance and performance tuning.
From a broader technological perspective, this work aligns with the growing trend toward digital twins and smart manufacturing. A digital twin is a virtual replica of a physical system that mirrors its behavior in real time. Accurate power modeling is a crucial component of such systems, enabling simulations that reflect not just kinematics and dynamics but also energy flow and thermal performance. By providing a reliable way to estimate power without deep system knowledge, the Chongqing University team has taken a meaningful step toward making digital twins more accessible and practical for industrial applications.
The success of this project also highlights the importance of interdisciplinary collaboration in robotics research. The team combined expertise in mechanical engineering, control systems, and data analysis to tackle a problem that sits at the intersection of hardware and software. Their approach reflects a shift in how engineers think about complex systems—not as collections of isolated components, but as integrated networks where energy, motion, and information are deeply interconnected.
Looking ahead, the researchers suggest several directions for future work. One is to incorporate temperature effects into the model, as motor resistance and magnetic properties can change with heat, affecting efficiency. Another is to explore online adaptation, where the model continuously updates its parameters based on real-time feedback, allowing it to track performance degradation over time. Additionally, integrating the power model into trajectory optimization algorithms could lead to truly energy-optimal motion planning, closing the loop between prediction and control.
The study also underscores the role of open science in advancing engineering knowledge. By publishing their methodology and results in a peer-reviewed journal, the team has made their work available for scrutiny, replication, and extension by others. This transparency fosters trust and accelerates innovation, as other researchers can build upon proven techniques rather than starting from scratch.
In conclusion, the power equivalent model developed by Wu Yongqiang, Tang Xianzhi, Song Wei, Jiang Pei, Zhou Jin, and Chen Yuanjie at Chongqing University represents a significant leap forward in the field of industrial robotics. It addresses a long-standing challenge with a practical, data-driven solution that balances accuracy with usability. By enabling precise power prediction without requiring detailed motor specifications, it lowers the barrier to energy optimization for manufacturers around the world. As industries continue to seek ways to reduce their environmental footprint and operating costs, this research offers a powerful tool for building smarter, greener, and more sustainable production systems.
Wu Yongqiang, Tang Xianzhi, Song Wei, Jiang Pei, Zhou Jin, Chen Yuanjie, School of Mechanical Engineering, Chongqing University; Journal of Chongqing University, DOI: 10.11835/j.issn.1000-582X.2020.015