Fig 1.
Kinematic Model of the Forklift-type AGVAt the center point of the rear axle of the forklift-type AGV, the velocity is:.
Fig 2.
Three-Degree-of-Freedom AGV Dynamic Model.
By conducting a force analysis on the longitudinal, lateral, and yaw dynamics of the forklift-type AGV, we obtain.
Fig 3.
Point set distribution of Logistic map, showing sparser distribution in the middle and denser at the edges.
Fig 4.
Point set distribution of Tent map, demonstrating a more uniform spatial distribution.The Tent map is adopted to replace random values for initializing the sparrow population. Since the Tent map sequence exhibits small-scale periodicity, a random value is introduced into its fundamental expression to prevent the sequence from falling into periodic behavior. The improved expression is given as.
Fig 5.
In summary, The uniform distribution provided by Tent chaotic initialization is particularly advantageous for MPC parameter tuning, where the optimal weight combination may lie anywhere within a bounded search space. A well-distributed initial population increases the probability of covering the feasible region from the outset, reducing the risk of the algorithm converging to suboptimal parameters due to poor initialization. This directly addresses the limitation of the standard SSA, which often suffers from uneven population distribution and insufficient global exploration when optimizing MPC weight parameters.
Fig 6.
AT-ISSA-MPC tracks the reference trajectory more closely than FT-MPC, achieving higher overall accuracy.
Fig 7.
AT-ISSA-MPC has smaller lateral error fluctuations, with a maximum error of 0.07183 m.
Fig 8.
AT-ISSA-MPC has smaller heading angle deviations (especially around curves), achieving higher overall heading tracking accuracy than FT-MPC.
Fig 9.
Heading angle error comparison.
AT-ISSA-MPC has smaller heading angle error fluctuations, with a maximum error of 0.75766°.
Table 1.
Analysis of lateral displacement error.
Table 2.
Analysis of heading angle error.
Fig 10.
AT-ISSA-MPC has smaller overshoot, faster convergence, and completes tracking earlier.To validate the performance of the proposed improved ISSA-MPC algorithm, a comparative experiment on straight-line path tracking was designed. Starting from the same initial positional deviation, both the improved ISSA-MPC algorithm and a classical MPC algorithm were tasked with tracking the same reference straight-line path.
Fig 11.
Figs 12 and 13 present a comparative analysis of the motion trajectories between the improved ISSA-MPC controller and the classical MPC controller on the experimental platform. Based on the data in Table 3, the following results are obtained: the maximum lateral displacement error of the classical MPC is 0.68502 m, while that of the improved ISSA-MPC is 0.34762 m, representing a reduction of 49.25% compared to the classical MPC. The mean square error of lateral displacement for the classical MPC is 0.069578 m, whereas that of the improved ISSA-MPC is 0.017335 m, a reduction of 75.09%. Based on the above analysis, under these test conditions, the improved algorithm proposed in this paper demonstrates satisfactory overall control performance in trajectory tracking, indicating good practical applicability.
Fig 12.
AT-ISSA-MPC tracks the reference trajectory more closely with smaller overall fluctuations.
Fig 13.
AT-ISSA-MPC has smaller error fluctuations, higher accuracy, and better stability.
Table 3.
Analysis of lateral displacement error.