Research on the Forward Kinematics of Stewart Platforms Based on a Multi-Strategy Improved Dung Beetle Optimization Algorithm

Abstract The forward kinematics of the six-degree-of-freedom Stewart parallel mechanism constitutes a typical problem involving the solution of multivariate, strongly coupled, and nonlinear systems of equations. To address the high sensitivity of traditional numerical iterative methods to initial values, as well as the limitations of standard swarm intelligence algorithms-namely, their tendency to entrapment in local optima and insufficient convergence accuracy when solving high-dimensional complex problems-this paper proposes an Improved Dung Beetle Optimizer (IDBO). This algorithm integrates Tent chaotic mapping, a nonlinear adaptive weight strategy, and a Cauchy mutation mechanism. The IDBO functions through three specific enhancements: First, Tent chaotic sequences are employed to initialize the population, thereby enhancing the ergodicity of the solution space. Second, an adaptive weight factor is introduced during the ball-rolling phase to balance the algorithm's global exploration and local exploitation capabilities. Finally, a Cauchy mutation operator is applied to perturb stagnant individuals, enabling the algorithm to escape local extrema. Experimental results indicate that, compared with the standard DBO algorithm and Particle Swarm Optimization (PSO), the IDBO algorithm exhibits superior convergence performance. It effectively breaks through local extrema and converges the fitness to the magnitude of 1e-12. Specifically, the static solution accuracy is improved by 5 to 7 orders of magnitude. In dynamic trajectory tracking, the algorithm displays exceptional tracking capability and stability; the comprehensive tracking error is reduced by 3 to 4 orders of magnitude, effectively mitigating phase lag and control signal chattering. In conclusion, the proposed IDBO provides an effective numerical computational scheme for the forward kinematics and real-time high-precision control of Stewart platforms.