Optimizing Control for Continuum Robots: A PSO-based Breakthrough

By Samudrapom DamReviewed by Susha Cheriyedath, M.Sc.Jan 11 2024

In an article recently published in the journal Scientific Reports, researchers proposed a dynamic model and two particle swarm optimization (PSO)-based control approaches for modeling and control of continuum robots.

Background

Continuum robots consist of a flexible backbone to which several discs are attached. These robots have an exceptional degree of flexibility as they can be built using multiple sections. Continuum robot structures can curve continuously along their length due to elastic deformation.

Thus, these robots are suitable for medical uses and working in an unstructured and complex space, where they can adapt to various shapes, and effectively interact with surroundings and handle objects. Continuum robots are complex structures that require sophisticated control and modeling methods to realize accurate motion and position tracking along desired trajectories.

The derivation of mathematical models with high accuracy is crucial for the improved control, analysis, and design of continuum robots. However, the continuum robots are nonlinear, highly-coupled systems with numerous degrees of freedom that pose a major challenge for conventional approaches.

A new modeling and control approach

In this study, researchers presented a two-section continuum robot dynamic model based on the Euler–Lagrange formulation with the assumption of piecewise constant curvature (PCC) where the gravity and elasticity effects of the continuum robot were considered.

They also developed and applied a multiple iteration PSO algorithm to optimize/tune the parameters of the controllers developed in this work, including an inverse dynamic fuzzy logic controller (FLC) and an inverse dynamic proportional integral derivative (PID) controller.

These two control algorithms were developed and implemented for precise position trajectory tracking control. PSO was employed to optimize the parameter constants of the developed PID and to tune the membership function range for every output and input of the developed FLC.

The Euler–Lagrange approach based on the PCC assumption utilizes system-developed potential and kinetic energy in developing the continuum robot equation of motion. The integral time of absolute error (ITAE) was utilized as the objective function for the PSO algorithm.

Evaluation of the approach

Researchers validated the proposed model and the PSO-optimized controllers through various designed trajectories simulated using unique animated MATLAB simulation. A comparative analysis was performed to display the multiple optimization enhancements and dynamic responses for every designed controller in mapped two-dimensional (2D) trajectories.

The MATLAB Simulink was used to simulate the continuum robot arm response for the proposed PSO-FLC and PSO-PID controllers for both desired trajectories and different step inputs.

Step Response: The PSO-optimized PID controller provided a faster and more accurate response to changes in the desired degree values, which indicated that the PSO-optimized PID controller could improve the continuum robot performance by decreasing settling time and overshoot, resulting in a more accurate and stable control.

Additionally, the PSO optimization developed more suitable ranges for the outputs and inputs membership function for the FLC. This indicated effective FLC membership function optimization by PSO, leading to a more responsive and accurate robot movement control.

The response comparison between PSO-FLC and PSO-PID for every configuration space parameter showed that the dynamic response of the continuum robot improved significantly when PSO was used to optimize the FLC membership function. Specifically, the robot could realize the desired angles more quickly and accurately, which is important in applications requiring rapid and precise movement. The FLC also outperformed the PID controller based on ITAE.

Trajectory Tracking Response: Results demonstrated that PSO-FLC and PSO-PID controllers could track the infinity path with low error and high accuracy. The PSO-PID controller displayed a smaller settling time and a faster response time compared to the PSO-FLC controller, while the PSO-FLC controller showed no overshoot and a smoother response compared to the PSO-PID controller. These results indicated that the PSO-FLC controller is feasible for applications requiring precise and smooth tracking, while the PSO-PID controller is effective for applications requiring robust and fast tracking.

Additionally, the adaptability of the FLC controller to complex and non-linear behavior was higher than the adaptability of the PID controller, which indicated the FLC controllers’ effectiveness in managing systems with complex dynamics. FLC was also more advantageous compared to PID in enabling the robot to follow the rectangular path with sufficient accuracy.

Significance of this research

Both PSO-PID and PSO-FLC controllers proposed in the study showed superiority and effectiveness over the existing PID and FLC controllers based on robustness, stability, and accuracy. The results demonstrated that the PSO-PID controller improved the settling time, overshoot percentage, and rise time by 64.9%, 31.1%, and 16.3%, respectively, compared to the PID controller without PSO.

Overall, the PSO-FLC controller displayed the best performance among all controllers investigated in this study, with a 0.7 s settling time and 0.4 s rise time, resulting in the highest level of precision in trajectory tracking. Moreover, the ITAE error for the PSO-FLC controller was 29.9% and 11.4% lower than that of the FLC and PSO-PID controllers, respectively.