Navigation of underwater robot based on dynamically adaptive harmony search algorithm

Abstract

The current research work has employed an evolutionary based novel navigational strategy to trace the collision free near optimal path for underwater robot in a three-dimensional scenario. The population based harmony search algorithm has been dynamically adapted and used to search next global best pose for underwater robot while obstacle is identified near about robot’s current pose. Each pose is evaluated based on their respective value for objective function which incorporates features of path length minimization as well as obstacle avoidance. Dynamic adaptation of control parameters and new perturbation schemes for solution vectors of harmony search has been proposed to strengthen both exploitation and randomization ability of present search process in a balanced manner. Such adaptive tuning process has found to be more effective for avoiding early convergence during underwater motion in comparison with performances of other popular variants of Harmony Search. The proposed path planning method has also shown better navigational performance in comparison with improved version of ant colony optimization and heuristic potential field method for avoiding static obstacles of different shape and sizes during underwater motion. Simulation studies and corresponding experimental verification for three-dimensional navigation are performed to check the accuracy, robustness and efficiency of proposed dynamically adaptive harmony search algorithm.

Appendix

Fig. 12

Three-dimensional simulated paths traced by using proposed DAHS algorithm for different values of $BW_{{min}}$ (cases 1–4)

Fig. 13

Three-dimensional simulated paths traced by using proposed DAHS algorithm by changing $BW_{{min}}$ from 0.15 to 0.5

In this section, a trial and error process has been performed to find out $BW_{{min}}$ which may enable proposed DAHS algorithm to achieve safe clearance from obstacles during navigation. For this purpose, a navigational scenario (Figs. 12 or 13) with three static obstacles has been considered in three-dimensional simulated scenario of MATLAB. From extensive literature review it has been found that BW values can be chosen within the range from 0.0001 to 0.1 based on the attributes of optimization problems to be solved. To improve degree of accuracy while selecting value of $BW_{{min}}$, one more range of values (0.1–0.9) is additionally considered here for three-dimensional navigation. Primarily, numerous simulations have been performed for same three-dimensional scenario by changing $BW_{min}$ of proposed DAHS algorithm within four ranges of bw values, specified as: {0.0001–0.0009} (case 1), {0.001–0.009} (case 2), {0.01–0.09} (case 3) and {0.1–0.9} (case 4). By altering $BW_{{min}}$ within each mentioned range, variation in path length and obstacle avoidance for given situation has been observed in Fig. 12 and observations have been documented in Table 8.

Table 8 List of path lengths as drawn by DAHS algorithm for different values of $BW_{{min}}$

It has been found from Table 8 that both safe collision avoidance during navigation and shorter path length can be achieved only for $BW_{{min}}$ values of 0.3 and 0.5. To find out more specific value of $BW_{\mathrm{min}}$ required for safe navigation and shorter path length, another set of simulations are performed by varying $BW_{{min}}$ between 0.15 to 0.5 in Fig. 13 where obstacle arrangement and start and goal positions are kept same as Fig. 12. Details of path length and obstacle avoidance for varying $BW_{{min}}$ values (0.15 to 0.5) are illustrated in Table 9. $BW_{{min}}$ values in the range of 0.25 to 0.5 are found to be successful for safe avoidance from collision with the obstacles. When $BW_{min}$ is 0.35, the shortest path has been found by underwater robot in given scenario as depicted in Table 9. Therefore, $BW_{{min}}$ is kept fixed at 0.35 for proposed DAHS algorithm while applying as three-dimensional navigational strategy in any other scenarios.

Table 9 Variation in path length for specific range of $BW_{{min}}$ values