Design and Experimental Validation of Closed-Form CBF-Based Safe Control for Stewart Platform Under Multiple Constraints

Anonymous Authors for Double-Blind Review
Paper Video Code

Overview Video

Abstract

This paper presents a closed-form Control Barrier Function (CBF)–based control framework for ensuring safe operation of a Stewart platform prototype. The proposed formulation simultaneously enforces multiple position and velocity safety constraints. An explicit closed-form solution is derived for the associated safety condition, thereby eliminating the need to solve a Quadratic Program (QP) at each control step and enabling efficient real-time implementation. Furthermore, necessary and sufficient conditions to avoid singularity in the closed-form calculation is also presented. The approach is validated through both simulation and experimental studies on a physical Stewart platform, demonstrating that the closed-form controller achieves safety performance equivalent to the QP-based method while significantly reducing computational overhead. The results confirm the feasibility and robustness of the proposed framework for real-time deployment in safety-critical parallel robotic systems.

Architecture of the proposed safe Stewart platform controller

Architecture of the proposed safe Stewart platform controller. The user inputs the desired trajectories of the platform, which will be used to calculate the nominal controller. The nominal controller and the current platform states are used in the CBF-based safety filter. The output of this safety filter produced the safe control inputs, which are then used for the Stewart platform system.

Simulation Results

Simulation results comparing QP and closed-form CBF controllers for Stewart platform safety.

The simulation results evaluate the effectiveness of the proposed closed-form controller with the QP-CBF method. This plot shows the enforcement of velocity safety constraints. Black indicates the uncontrolled system, magenta corresponds to QP-CBF, and blue denotes the proposed closed-form approach.

Simulation video visualizing the Stewart platform behavior under the proposed closed-form controller and its QP counterpart. It also shows the 3D view of the platform's movement.

Experimental Results

Experimental results comparing QP and closed-form CBF controllers enforcing Stewart platform position constraints.
Experimental results comparing QP and closed-form CBF controllers enforcing Stewart platform velocity constraints.

The proposed controller is deployed to the Stewart platform prototype. The experiment results evaluate the performance of the QP-CBF and the proposed closed-form solution. It also compares the compuation time required to synthesize the safe controllers. The result shows that in the real-time deployment, the closed-form solution offers a lower average computational time, compared to its QP counterpart which increased whenever the platform reaches the unsafe regions.

Experimental results illustrating the trade-off between performance and safety for different values of the CBF parameters. Larger parameter values relax safety enforcement, leading to less conservative but potentially riskier behavior.