Improved rapidly exploring random tree using salp swarm algorithm

3.1 Key steps of the RRT algorithm

• The robot’s basic setup is the only node in the tree initially.

• Iteration is carried out through the robot’s configuration space, and a new, random configuration is generated each time.

• The current tree structure closest to the randomly selected one is identified.

• We can generate a new configuration by guiding the robot from its closest neighbor to the randomly sampled configuration.

• Whether the updated setup does not conflict with the current tree is verified. The setup is disregarded and another trial is performed if a collision happens.

• The new configuration is connected to its nearest neighbor and added to the tree if collision will not occur.

• The process keeps going until something triggers it to end, such as when we attain a certain configuration objective or when the number of iterations is reached.

3.2 Limitations of the RRT algorithm

• The sampling approach greatly affects the efficiency of RRTs, and they may provide pathways that are not optimal.

• Two factors that can impact the algorithm’s efficiency are how complex is the robot’s geometry and how many dimensions there are in the configuration space.

• The performance of RRTs can change depending on the starting configuration and the objective’s location, and they do not ensure that the optimal path will be found.

• Adapting RRTs to contexts where barriers are constantly shifting might be challenging.

5.1 Algorithmic steps

• The algorithm starts with the robotic system’s initial configuration by initializing the RRT tree.

• An assortment of SSA parameters are defined, including the salp count, convergence criterion, and exploration–exploitation balance. IRRT-SSA employs an iterative expansion technique. On the basis of the conventional RRT procedure, the RRT tree is expanded in each iteration by connecting nodes and randomly sampling them.

• SSA guides the exploration procedure. The salps’ actions collectively drive the tree’s growth toward more favorable areas in the configuration space.

• IRRT-SSA incorporates a step to enhance the path in each iteration, unlike the typical RRT. SSA is used for refinement to improve the quality and flexibility of the generated pathways for dynamic situations.

• Convergence is evaluated using established criteria to guarantee that the algorithm exits after a good solution is achieved. This step entails checking whether the RRT tree has converged and whether the optimization is successful with SSA.

We explain the important parameters of IRRT-SSA to help with thorough understanding and reproducibility.

• The number of salps (N) controls the swarm’s size and impacts its exploration ability.

• A convergence threshold (CT) specifies the minimum value at which the RRT and SSA parts must converge.

A steady equilibrium is maintained in the iterative expansion’s exploration vs exploitation debate.

Two goals are achieved by including SSA in the RRT architecture. Exploration is improved by SSA’s adaptations, modeled after the group behavior of salps. In line with the ever-changing nature of real-world robotic applications, RRT’s iterative structure permits path improvement with each iteration.

IRRT-SSA deftly blends the benefits of SSA with those of the traditional RRT algorithm. With its iterative nature and SSA-guided path refinement, IRRT-SSA shows promise as a solution to the problems of robotic path planning in dynamic and complicated situations.

The RRT limitations include a lack of assurances about optimality, potentially inefficient path length and computing resources, and inadequate path quality. Improving these areas and streamlining the path planning process are IRRT-SSA’s primary goals.

5.2 Utilization of SSA for improvement

SSA is a metaheuristic that IRRT-SSA introduces to improve the optimization and exploration capabilities of the classic RRT. It is an optimization technique that takes its cues from the way salps, a type of marine invertebrates, work together. The system simulates the behavior of ocean salps, which change their locations depending on local and global data.

Several improvements are realized by integrating SSA into IRRT.

• SSA uses the swarm’s collective intelligence to facilitate a more effective exploration of the configuration space. Two possible outcomes are a more complete picture and a more rapid convergence toward ideal solutions.

• SSA balances discovery and exploitation by integrating global and local search tactics, finding good pathways in complicated and multimodal situations.

• A swarm-based approach such as SSA makes it easy to adjust to changing conditions. This algorithm outperforms the conventional RRTs in terms of versatility given its ability to react to changes in the configuration space.

• IRRT-SSA aims to solve the suboptimality problems with conventional RRTs by including SSA to enhance the quality of generated pathways.

6.1 Improvement in average path length

Significant implications exist for real-world robotic applications of IRRT-SSA with 49% improvement in average path length. The practical value of this enhancement in improving the overall efficiency and performance of robotic systems in varied settings is substantial, going beyond its status as a purely statistical parameter. To further explain the relevance, we consider the following points:

• A robotic system can navigate from the starting point to the destination with a significantly lower trip distance, as shown by the 49% reduction in average path length. Robotic systems that are short on resources, such as energy, or functioning in a time-sensitive environment must prioritize this optimization.

• Robotic mobility uses less energy when pathways are shorter. The capacity to accomplish the same task with less energy increases operational endurance. It aligns with sustainable and cost-effective practices, especially in energy-intensive applications such as mobile robots or autonomous drones.

• Faster traversal times are achieved with shorter average path lengths. Reaching destinations faster improves a robot’s responsiveness and overall work efficiency in time-critical scenarios such as emergency response or manufacturing processes.

• In confined areas, robots can move more efficiently along shorter routes. This characteristic is especially helpful in settings where the robot must be accurate in its movements, such as hospitals, warehouses, or locations hit by natural disasters, where it must navigate narrow passages to reach the objective.

• A robot’s capacity to detect and avoid risks and barriers is enhanced when it can identify shorter paths. Autonomous vehicles and robotic systems operating in unpredictable and dynamic surroundings are two examples of applications where this capacity is crucial for safety reasons.

• An indication of IRRT-SSA’s adaptation across varied contexts is the improvement in average path length. The algorithm’s capacity to locate shorter paths efficiently increases its versatility and practicality in various real-world circumstances, whether navigating through crowded locations or open areas.

The overall improvement in average path length of 49% is a real step forward that will have far-reaching effects on robotic systems rather than only a numerical one. A significant advancement in robotics and autonomous systems, IRRT-SSA enables robots to function more economically, efficiently, and safely in real-world environments.

6.2 Impact of 54% reduction in the number of nodes

IRRT-SSA cuts the number of nodes by 54% compared with the original RRT, which has various important consequences on the algorithm’s performance and efficiency. The number of nodes is the sum of all the points along the built tree. This reduction indicates a search space that is more streamlined and efficient with resources. As the number of nodes drops, the computational load also decreases. The algorithm’s memory and processing requirements are reduced, improving the computational efficiency given the fewer nodes to assess. For applications requiring instantaneous decisions, this improvement is of utmost importance. A reduced number of nodes allows for a more targeted search of the configuration space, which speeds up the discovery of good pathways. Faster path planning is the outcome of the algorithm’s improved navigation of the search space. Situations requiring quick responses and decisions benefit from this acceleration.

One way to improve memory utilization is by reducing the number of nodes. This aspect is crucial for robots that must function in settings with limited resources or applications where memory is an issue. Because it can accomplish its goals with fewer nodes, the algorithm is more flexible and can be used in different computational environments. The scalability of IRRT-SSA is improved by reducing the number of nodes. Without experiencing an exponential rise in computing needs, it can efficiently handle search areas that are larger and more complicated. Applications that require the algorithm to adapt to different robotic platforms and environmental situations must have this scalability.

Reducing the number of nodes also allows the algorithm to zero down on areas of the configuration space where optimum pathways are more probable. The algorithm’s ability to locate high-quality pathways effectively, even in situations with limited computational resources, is enhanced by this targeted investigation. The needs of real-time systems are met by reducing the number of nodes. The capacity to design pathways with fewer nodes improves the system’s overall stability and guarantees quick responses in applications such as autonomous vehicles or robotics in dynamic environments. IRRT- SSA’s 54% reduced node count demonstrates computational efficiency and offers practical advantages, such as optimized memory utilization, faster path planning, enhanced scalability, and compatibility with real-time applications. Because of these benefits, IRRT-SSA is an attractive algorithm for many robotic applications prioritizing efficiency and resource utilization.

6.3 Implications of 54% decrease in iterations

The time and computational resources needed for path planning are significantly affected by the remarkable 54% reduction in iterations achieved by IRRT-SSA compared with the fundamental RRT. A decrease in iterations indicates an improvement in efficiency and resource utilization. The following are important points about its consequences:

• Convergence toward optimal pathways is accelerated with fewer iterations. The time it takes for the algorithm to search for possible configurations and find ones that work is reduced. When making decisions and responding quickly are of the utmost importance, time-sensitive applications greatly benefit from this acceleration in path planning.

• The computational workload decreases directly proportional to the decrease in iterations. The algorithm’s processing power and computational resource requirements are reduced with the decreased number of iterations. This reduction is important in situations in which computing resources are limited or making the most of what is available is of the utmost importance.

• Reduced iterations meet the needs of real-time systems. The algorithm’s capacity to accomplish its goals with fewer iterations guarantees more responsive and prompt decision-making in applications such as autonomous vehicles and robotics that operate in dynamic situations, which contributes to the system’s overall reliability.

• The scalability of IRRT-SSA is improved by reducing iterations. Without a corresponding rise in computing needs, it can efficiently manage search areas that are larger and more complicated. Applications requiring the algorithm to adapt to different environmental conditions and robotic platforms rely on scalability.

• Fewer iterations indicate a more targeted and resource-efficient planning approach. By focusing its computing power on the most promising regions of the configuration space, the program can efficiently explore and identify the best paths. In situations in which the processing capacity is limited, this optimization of resources is highly valuable.

• Fewer iterations mean less power usage, particularly for robotic systems that run on batteries. By reducing the number of computation cycles needed to accomplish its path planning goals, the algorithm helps preserve energy and prolongs the operating life of the robotic platform.

The time savings achieved by IRRT-SSA – a 54% reduction in iterations – are accompanied by practical benefits, such as greater scalability, lower processing needs, improved real-time capabilities, effective resource utilization, and energy conservation. For tasks in which optimizing path planning within a limited time and computational resources is critical, IRRT-SSA stands out as an attractive approach given its many benefits.

6.4 Enhancements in path quality by IRRT-SSA

Compared with the original RRT, IRRT-SSA significantly improves path quality, promoting the construction of efficient and optimal paths. Several important factors contribute to path quality enhancement.

The generated pathways are fine-tuned using IRRT-SSA, allowing the robotic system to move continuously and smoothly. By directing the search toward more gradual configurations and less abrupt directional shifts, SSA aids in path optimization. This optimization is crucial for robotic platforms for tasks requiring reliable and controlled navigation. The trajectory will be more linear and uninterrupted because the algorithm can smooth out bumps in the road. This characteristic becomes especially useful when dealing with robotic systems navigating varied terrains or environments. Navigational stability and dependability are enhanced as a result of reduced path disturbances.

By improving the exploration process, IRRT-SSA successfully reduces the travel distance. Finding shorter routes that minimize unwanted deviations is the main emphasis of the algorithm. When saving energy or resources is paramount, this enhancement is important. By prioritizing safety, the system finds routes with fewer obstructions. With the help of SSA, IRRT-SSA can intelligently move around the configuration space, staying away from obstacles and avoiding collisions. This feature is crucial for uses in settings where hazards are constantly changing or the weather is erratic. IRRT-SSA can produce routes that are more resistant to environmental changes and disturbances. The algorithm’s improved exploration approach ensures consistent performance in real-world circumstances, which SSA drives. This strategy helps create pathways that adapt effectively to fluctuations.

By skillfully negotiating the trade space between finding new configurations and exploiting promising paths, IRRT-SSA achieves a balanced exploration–exploitation trade-off. The technique is designed to converge toward optimal solutions without getting stuck in local minima, which improves the overall quality of the pathways generated. This balance is maintained throughout the process. As a result of these improvements, we can realize the shortest pathways for less cost than those with the original RRT. The paths produced by IRRT-SSA are of high quality due to a combination of factors, including the optimized trajectory smoothness, minimized path discontinuities, reduced travel distance, improved obstacle clearance, consistent path robustness, and balanced exploration–exploitation trade-off. This optimization guarantees a higher degree of dependability, safety, and adaptability in real-world applications and produces shorter pathways. Finding the optimal shortest pathways is of the utmost importance. IRRT-SSA is a great option because of the lowered cost, which includes energy usage, computational resources, and overall system performance.

6.5 Comparison between RRT and IRRT-SSA within a highly complex environment

RRT and IRRT-SSA were implemented using a different known environment, which is highly complex, including many obstacles and narrow passages. The algorithms were run for many iterations, and the performance was evaluated on the basis of the number of nodes generated and the path length. In accordance with the randomness of the RRT algorithm, 20 repeated tests were achieved. The first test was done by setting the starting point at (1, 1) and the target point at (7, 5.5), as shown in Figure 9; the second test was done by setting the starting point at (2, 8) and the target point at (7, 5.5), as presented in Figure 10. The results showed that IRRT-SSA generated fewer nodes than the original RRT. Specifically, RRT generated 1,578 and 1,027 nodes on average, whereas IRRT-SSA generated only 608 and 511 nodes in the first and second tests, respectively. This finding indicates that IRRT-SSA has a more efficient search strategy and explores the space more effectively.

Figure 9

Average path planning with starting point (1, 1) and target point (7, 5.5). (a) RRT and (b) IRRT-SSA.

Figure 10

Average path planning with starting point (2, 8) and target point (7, 5.5). (a) RRT and (b) IRRT-SSA.

Furthermore, the path length generated by IRRT-SSA was significantly shorter than that by RRT. Particularly, the average path length generated by RRT was 148.65 and 93.25 units, whereas that by IRRT-SSA was 57.6 and 47.25 units in the first and second tests, respectively. Therefore, IRRT-SSA is better at finding optimal smoothing paths and has a more global search ability. Both tests are demonstrated in Table 3.

Several significant changes between RRT and its improved version, IRRT-SSA, are noted. As shown by the outcomes, the variations in efficiency, path length, number of nodes, and iterations are apparent.

When exploring the configuration space, RRT-SSA outperforms the core RRT. With SSA, the exploration method becomes smarter and more flexible, which speeds up the convergence to optimal solutions. The results show that IRRT-SSA significantly optimizes path length. Paths produced by the method are, on average, shorter than those produced by the fundamental RRT because it uses SSA’s global and local optimization capabilities. A smaller number of nodes is needed to build the exploration tree using IRRT-SSA. Compared with the fundamental RRT, the simplified and less complicated tree structure is a product of SSA’s swarm intelligence, which aids in the efficient selection of nodes. In IRRT-SSA, as opposed to the fundamental RRT, the number of iterations required for path design is significantly reduced. A faster identification of optimal paths with fewer repetitions is made possible by SSA’s better exploration capabilities, which is responsible for this reduction.

Compared with the essential RRT, IRRT-SSA is more adaptable to changing conditions. In situations in which the environment changes, SSA’s swarm-based approach makes it more robust by allowing the algorithm to alter its exploration technique constantly. SSA’s capacity to integrate global and local optimization techniques allows IRRT-SSA to accomplish a more optimal exploration–exploitation balance. This equilibrium leads to superior path planning with regard to robustness and quality in comparison with the fundamental RRT.

These distinctions demonstrate how IRRT-SSA outperforms the core RRT algorithm and offers a better alternative for robotic path planning by overcoming its inherent limits.

6.6 Comparison of IRRT-SSA with other current sample-based algorithms

A comparative analysis of IRRT-SSA with other sample-based techniques may provide insights into its potential applications and enhanced performance in robotic path planning. The comparisons in Table 4 cover the capabilities of IRRT-SSA in various configurations due to the use of numerous scenarios with diverse beginnings and ends. The mean path length is a fundamental algorithmic metric for path planning. This value denotes the target-chasing distance of the automaton. The IRRT-SSA method reduces path length more effectively than alternative high-tech approaches in all cases. Real-world applications place significant emphasis on energy and resource efficiency, which makes reducing path length indispensable.

The average number of nodes indicates the exploratory efficacy of an algorithm. IRRT-SSA expedites research in comparison with alternative methodologies through the progressive reduction of nodes. IRRT-SSA could transverse the search space and identify the optimal paths. Node exploration reduction improves computational efficiency in real-time applications, where making fast decisions requires less data.

The computation efficacy of an algorithm can be indicative of the average number of iterations performed. Its low number of iterations indicates that IRRT-SSA can converge to optimal solutions while conserving computational resources. The IRRT-SSA method successfully identifies feasible solutions. The significance of robot computer efficiency in real-time applications lies in the correlation between the pace at which decisions are made and the robot’s ability to react and navigate.

The previously mentioned results illuminate the algorithm’s prospective practical implementations and validate its efficacy compared with previous methodologies. The effective trajectory determination facilitated by IRRT-SSA is critical for autonomous robotics and other utilizations [34,35].

7.1 Influence on the practical deployment of robotics

In situations that need fast path planning and navigation, the improvements achieved by IRRT-SSA have far-reaching consequences on the real-world application of robotics. The following examples show how these enhancements can benefit practical uses:

• Real-time navigation is made more efficient with IRRT-SSA because of its optimized path creation. This algorithm is perfect for situations that require quick decisions and responses because it can efficiently explore and modify courses in dynamic settings, allowing robotic devices to travel efficiently.

• Robots’ ability to navigate complicated situations is strengthened by the enhanced path quality, defined by less abrupt trajectories and fewer interruptions. IRRT-SSA is well suited for deployment in settings with varied terrain, barriers, or uncertain conditions due to its ability to evaluate safety margins and adjust to perturbations, guaranteeing reliable performance.

• Resource-efficient path design is aided by RRT-SSA’s emphasis on minimizing path length and computational overhead. For real-world applications, this aspect means less strain on robotic systems, better use of computing resources, and optimized energy use. Applications dealing with limited resources must prioritize these variables.

• Path length, number of nodes, and iterations are just a few of the metrics this algorithm can handle, making it suitable for various robotics tasks. The advancements made to IRRT-SSA apply to a wide range of deployment scenarios, whether the objective is to optimize pathways for efficiency, preserve energy, or navigate through crowded settings safely.

• The capacity of IRRT-SSA to create pathways with shorter travel distances and enhanced energy efficiency results in lower operational and maintenance costs. By reducing mechanical stress and optimizing wear and tear on robotic components, the optimized pathways save energy and contribute to a lengthened lifespan of the system.

• The algorithm uses SSA to improve the precision and accuracy of navigation. With the help of SSA’s intelligent exploration method, IRRT-SSA can move and position robotic devices precisely by navigating complicated configuration spaces.

• The breakthroughs made by IRRT-SSA greatly aids autonomous robotic systems. Robots can now navigate and plan their paths efficiently with this algorithm, allowing them to work autonomously in various settings with minimal human oversight. This feature is of paramount importance for uses such as driverless cars, drone surveillance, and robotic exploration.

Overall, the advancements made possible by IRRT-SSA should have a major impact on the actual implementation of robots. The algorithm’s versatility, efficiency, resilience, optimization of resources, and capacity to handle complicated real-world scenarios make it a great tool for improving intelligent robotic systems and autonomous navigation.

7.2 Limitations of the study

• IRRT-SSA would not construct pathways efficiently if the hyperparameters are not ideal. Finding the optimal hyperparameters for diverse situations remains difficult.

• The proposed study may struggle with changing environmental dynamics. The algorithm’s versatility might be tested in changing environments or dynamically imposed hurdles during path planning.

• The performance of IRRT-SSA, which assumes homogeneous terrain, may be affected by environments with severely nonuniform surfaces, different friction characteristics, or intricate terrains.

• Initial configuration space data precision affects algorithm performance. Suboptimal route planning can occur from erroneous or missing environmental data, highlighting the importance of high-quality input data.