Comparative Analysis of Computed Torque Control and Adaptive Computed Torque Control for a 2 Planar Manipulator under Sudden Payload Variation

Abstract

This paper explores the performance of Computed Torque Control (CTC) and Adaptive Computed Torque Control (ACTC) for a 2R planar robotic manipulator performing precise joint movements. While CTC relies on a fixed model of the manipulator, ACTC adapts in real time to handle unexpected changes in the system’s dynamics. The manipulator follows a smooth sinusoidal trajectory, and during the operation, a sudden external load is applied to test the robustness of the controllers. Simulation results, including joint positions, tracking errors, control torques, and end-effector motion, indicate that ACTC successfully maintains accurate tracking and stability, whereas CTC experiences noticeable deviations when the load is introduced. A corresponding animation visually highlights the manipulator’s motion, clearly showing the moment when the load affects the system. The study demonstrates that ACTC provides a robust and adaptive solution, making it better suited for real-world scenarios where manipulator parameters can change unexpectedly.

Introduction

Robotic manipulators are widely used in industries, healthcare, and research where precise motion tracking is essential. Traditional control techniques such as Computed Torque Control (CTC) provide accurate trajectory tracking when the system parameters (like link mass and length) are known exactly. However, in real-world conditions where unexpected changes such as payload variations occur, CTC performance may degrade, leading to tracking errors or instability.

To address this limitation, Adaptive Computed Torque Control (ACTC) is introduced. ACTC improves the classical CTC method by estimating system parameters in real time, allowing the manipulator to adapt to uncertain or changing dynamics. This research compares the performance of CTC and ACTC using a 2R planar manipulator that follows a sinusoidal trajectory. During the motion, a sudden payload of 5 kg is applied at 5 seconds, simulating a realistic disturbance.

The manipulator dynamics are modeled using nonlinear equations involving inertia, Coriolis/centripetal forces, and gravity. While CTC cancels nonlinear dynamics using a known model to achieve stable error convergence, ACTC includes an adaptive mechanism that continuously updates parameter estimates using a regressor matrix and adaptive laws.

Simulation results evaluate joint tracking accuracy, tracking errors, control torques, and end-effector motion. The findings show that while CTC struggles to maintain accuracy when the payload changes, ACTC successfully adapts to the disturbance and maintains stable trajectory tracking. Therefore, ACTC is more robust and suitable for real-world robotic applications where system parameters may vary unexpectedly.

Conclusion

The outcome of our comparative study is a conclusive instruction for real-world robotics: Computed-Torque Control (CTC) and its adaptive version Adaptive Computed-Torque Control (ACTC) both yield good performance in ideal and predictable scenarios for a basic 2R arm, but ACTC is the outright winner for the unexpected changes of the real world.The pivotal event leading to this conclusion was the experiment with a sudden unknown change of the weight being lifted. The CTC control (inert, non-adaptive), which was based on a fixed model of the system, broke down instantly and clearly and continually made errors in tracking the desired motion which exposed its basic dependence on the correctness of its internal dynamic model and its fragility when that was not the case. At the other end of the spectrum, the ACTC control exhibited the intelligence of a real system. It very quickly employed its internal estimation mechanism to figure out the new dynamics, applied the necessary compensatory torques, and performed a spectacular recovery in real time. This excellent peddling of error and real-time recovery resulted in a non-negotiable quality of robots working in dynamic environments that is very much today expected of robots; hence it is ACTC that becomes the closer, better option for high precision and at the same time adaptable systems. The straggling simulation results must be moved to the forefront and turned into field performance through experimental verification and advanced enhancements. The very next step is to put the controllers into practice on hardware capable of supporting the testing and enduring the complexities of the real world such as sensor noise, joint friction, and unmodeled dynamics. Moreover, the analysis should be extended to cover more complicated industrial systems such as 3R or 6R arms which will confirm not only the ability of ACTC to cope with the challenges posed by the high number of degrees of freedom (DOF) and tightly coupled systems but also its computational feasibility. Lastly, for the sake of industry uptake, future developments need to include stronger and wiser control strategies (e.g., adaptive sliding mode or projection operators) alongside systematic assessments of the robustness of non-ideal conditions on control performance.

References

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Copyright

Copyright © 2026 Hariharan S, Manoranjan R, Anbarasi M. P.. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.