Table S1. Ranks achieved by the Friedman test in the main study case. The computed statistics and the related p-value are also shown. AlgorithmsRanks

Mobile robots are currently exploited in various applications to enhance efficiency and reduce risks in hard activities for humans. The high autonomy in those systems is strongly related to the path-planning task. The path-planning problem is complex and requires in its formulation the adjustment of path elements that take the mobile robot from a start point to a target one at the lowest cost. Nevertheless, the identity or the number of the path elements to be adjusted is unknown; therefore, the human decision is necessary to determine this information reducing autonomy. Due to the above, this work conceives the path-planning as a Variable-Length-Vector optimization problem (VLV-OP) where both the number of variables (path elements) and their values must be determined. For this, a novel variant of Differential Evolution for Variable-Length-Vector optimization named VLV-DE is proposed to handle the path-planning VLV-OP for mobile robots. VLV-DE uses a population with solution vectors of different sizes adapted through a normalization procedure to allow interactions and determine the alternatives that better fit the problem. The effectiveness of this proposal is shown through the solution of the path-planning problem in complex scenarios. The results are contrasted with the well-known A* and the RRT*-Smart path-planning methods.

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The fusion of bio-inspired algorithms into online controller tuning (adaptive controller tuning) is one of the main topics in Intelligent Control. One crucial issue is to reduce the times that the tuning process performs over time. In this work, a novel Asynchronous Adaptive Controller Tuning (AACT) approach is proposed to reduce the number of tuning process activations, and hence, this promotes resource savings in the overall computational cost for the tuning process. In this approach, an event function is designed to determine the control parameter update where the use of identification and predictive stages set the current control parameters. Furthermore, an elitist initialization in the differential evolution algorithm is also incorporated for solving the optimization problems at each stage. The speed regulation of the DC motor under disturbances is the study case in the ACCT approach. Comparative results with state-of-theart bio-inspired algorithms in control tuning reveal in the AACT approach that the elitist initialization in differential evolution notably benefits the controller performance. Moreover, the comparative results with the Synchronous Adaptive Controller Tuning (SACT) approach show that the proposal reduces 61% the tuning process computation frequency with a similar speed regulation performance when disturbances appear.INDEX TERMS Optimal controller tuning, DC motor, Event based tuning, Bio-inspired algorithm.

The efficiency in the controller performance of a BLDC motor in an uncertain environment highly depends on the adaptability of the controller gains. In this paper, the chaotic adaptive tuning strategy for controller gains (CATSCG) is proposed for the speed regulation of BLDC motors. The CATSCG includes two sequential dynamic optimization stages based on identification and predictive processes, and also the use of a novel chaotic online differential evolution (CODE) for providing controller gains at each predefined time interval. Statistical comparative results with other tuning approaches evidence that the use of the chaotic initialization based on the Lozi map included in CODE for the CATSCG can efficiently handle the disturbances in the closed-loop system of the dynamic environment.