A novel algorithm to estimate the external forces of mechatronic systems without real force sensors

The performance of engineering systems is often susceptible to the effects of disturbances. For example,  the additional force added to the nominal control inputs due to collisions or actuator faults is a common disturbance for robotic systems. These disturbances cause perturbations to the dynamics of the systems and may lead to  degradation to its desired performance. Numerous control methods, such as adaptive, fault-tolerant, and disturbance observer-based controls, are available for suppressing the detrimental effects of these disturbances. There are also some extrinsic force sensors available to directly measure the additional forces. Since these sensors are typically very expensive, it is imperative to develop accurate disturbance estimation methods to replace these sensors currently in use.

Conventional approaches to disturbance estimation rely on observers to reconstruct the unknown system states and inputs using measurable outputs like perturbation observers. Although observer-based methods can recognize the disturbance and formulate extended state observation problems, they experience several drawbacks limiting their practical applications. Lately, sliding mode observers (SMO) have emerged as a promising solution for solving the inadequacies of observer-based methods. SMO uses high-frequency switching to promote the balance between the high gains and error dynamics stability to obtain robust disturbance estimation. However, it is challenging to achieve a balance between the chattering attenuation and the robustness.

Significant research efforts have been devoted to addressing these inherent challenges hindering the development of robust and highly effective. For example, the integral sliding mode observer (ISMO) is an improved version of SMO, which has been used in various robotic systems. However, the assumption considered in its development does not hold for generic robotics. Similarly, the boundary layer method commonly used to avoid the chattering phenomenon suffers from small gains and low estimation accuracy. Thus, a detailed analysis of the effects of the boundary layer on the estimation method is needed.

Herein, Postdoctoral fellow Dr. Zengjie Zhang from The University of British Columbia, Professor Dirk Wollherr from Technical University of Munich and Professor Homayoun Najjaran from the University of Victoria developed a novel force-sensor-less method for robust disturbance estimation for robotic systems. This new method is based on ISMO, which was used as a second-order differentiator for system position measurement. The passivity property was substituted with a general assumption to address the nonlinearity and discontinuity problems and extend the ISMO to general second-order robotic systems. Furthermore, the boundary-layer method was adopted to attenuate the chattering phenomena and analyze its influence on the estimation accuracy via Lyapunov method. Their research work is currently published in the peer-reviewed, International Journal of Robust Nonlinear Control.

The research team reported the estimation of the system states and disturbances without using the velocity and force measurements explicitly. Unlike the conventional SMO methods, the boundary layer analysis of ISMO is of great significance owing to the effects of the cascaded sliding mode structure. The influence of the boundary-layer method on the system states and the disturbance estimation accuracy was established and presented in analytical forms as a reference for parameter selection.

The authors validated the feasibility of the proposed continuous ISMO through a simulation case involving a robot manipulator. It exhibited several advantages, including improved estimation accuracy and responsiveness, compared to conventional methods. Additionally, it could be extended to a wide range of robotic systems, expanding its application scope. The results indicated the potential application of continuous ISMO to specific force-perception tasks for second-order and force-sensor-less robotic systems.

In summary, the researchers reported the generalization of the ISMO method based on proposed general assumptions and its extension to more general systems to overcome the limitations of observer-based methods. The obtained results are important in determining feasible parameters for the designed parameters to meet the prerequisites of practical tasks. In a statement to Advances in Engineering, corresponding author, Professor Homayoun Najjaran said that the study provided new perspectives for accomplishing advanced robotic tasks using force-sensor-less methods.