This paper proposed a cubic spline interpolation-based path planning method to maintain the smoothness of moving the robot’s path. Several path nodes were selected as control points for cubic spline interpolation. A full path was formed by interpolating on the path of the starting point, control points, and target point. In this paper, a novel chaotic adaptive particle swarm optimization (CAPSO) algorithm has been proposed to optimize the control points in cubic spline interpolation. In order to improve the global search ability of the algorithm, the position updating equation of the particle swarm optimization (PSO) is modified by the beetle foraging strategy. Then, the trigonometric function is adopted for the adaptive adjustment of the control parameters for CAPSO to weigh global and local search capabilities. At the beginning of the algorithm, particles can explore better regions in the global scope with a larger speed step to improve the searchability of the algorithm. At the later stage of the search, particles do fine search around the extremum points to accelerate the convergence speed of the algorithm. The chaotic map is also used to replace the random parameter of the PSO to improve the diversity of particle swarm and maintain the original random characteristics. Since all chaotic maps are different, the performance of six benchmark functions was tested to choose the most suitable one. The CAPSO algorithm was tested for different number of control points and various obstacles. The simulation results verified the effectiveness of the proposed algorithm compared with other algorithms. And experiments proved the feasibility of the proposed model in different dynamic environments.

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Summary This article deals with state estimation of complex nonlinear discrete fractional‐order systems with unknown noise statistics by means of an adaptive fractional‐order Unscented Kalman filter (AFUKF). Firstly, in order to alleviate the communication burden of fractional‐order Unscented Kalman filter, short‐term memory effect is utilized to decide an appropriate memory length. Then aiming at the problem of filtering divergence and accuracy degradation caused by unknown statistical characteristics of noise, based on the maximum a posterior (MAP) principle, a noise statistical estimator is introduced to estimate and correct the statistical characteristics of noise in real‐time. Finally, the unbiasedness of the proposed algorithm is analyzed to verify that the estimated mean and covariance of noise are unbiased. The effectiveness and accuracy of AFUKF are demonstrated via simulation experiments.

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