The Vehicle Routing Problem with Time Windows (VRPTW) has drawn considerable attention in the last decades. The objective of VRPTW is to find the optimal set of routes for a fleet of vehicles in order to serve a given set of customers within capacity and time window constraints. As a combinatorial optimization problem, VRPTW is proved NP-hard and is best solved by heuristics. In this paper, a hybrid swarm intelligence algorithm by hybridizing Ant Colony System (ACS) and Brain Storm Optimization (BSO) algorithm is proposed, to solve VRPTW with the objective of minimizing the total distance. In the BSO procedure, both inter-route and intra-route improvement heuristics are introduced. Experiments are conducted on Solomon’s 56 instances with 100 customers benchmark, the results show that 42 out of 56 optimal solutions (18 best and 24 competitive solutions) are obtained, which illustrates the effectiveness of the proposed algorithm.

Applying swarm intelligence to actual swarm robotic systems is a challenging task especially with adequately consideration of corresponding practical constraints. Under the restrictions of the field-of-view limited relative positioning, local sensing and communication, kinematic limitations as well as anti-collision issues, this paper presents a constrained Particle Swarm Optimization (PSO) based collaborative searching method for robotic swarms. Besides, the proposed method follows the concept of evolution speed and a modified aggregation degree to determine the adaptive weights in the robotic PSO model. The modified aggregation degree is associated with the number of members in one’s field-of-view. Unlike the traditional position update method, the proposed method updates the forward speed and angular velocity of the robot using the non-holonomic model to realize the motion control of each robot. The simulation results show that the proposed method has the potential for the practical implementation of collaborative searching tasks for robotic swarms in different types of environments.

By forming a specific formation during motion, the robotic swarm is a good candidate for unknown region exploration applications. The members of this kind of system are generally low complexity, which limits the communication and perception capacities of the agents. How to merge to the desired formation under those constraints is essential for performing relevant tasks. In this paper, a limited visual field constrained formation control strategy inspired by flying geese coordinated motion is introduced. Usually, they flock together in a V-shape formations, which is a well-studied phenomenon in biology and bionics. This paper illustrates the proposed methods by taking the research results from the above subjects and mapping them from the swarm engineering point of view. The formation control is achieved by applying a behavior-based formation forming method with the finite state machine while considering anti-collision and obstacle avoidance. Furthermore, a cascade leader–follower structure is adopted to achieve the large-scale formations. The simulation results from several scenarios indicate the presented method is robust with high scalability and flexibility.

Particle Swarm Optimization (PSO) is an excellent population-based optimization algorithm. Meanwhile, because of its inspiration source and the velocity update feature, it is also widely used in the collaborative searching tasks for swarm robotics. One of the PSO-based models for robotic swarm searching tasks is Robotic PSO (RPSO). It adds additional items for obstacle avoidance into standard PSO and has been applied to many single-target search tasks. However, due to PSO’s global optimization characteristics, it is easy to converge to a specific position in the search space and lose the ability to explore further. When faced with the problem of multitarget searching, it may become inefficient or even invalid. This paper proposes an Exploration Enhanced Robotic PSO (E2RPSO) method for multitarget searching problems for robotic swarms. The proposed method modifies the third item in the RPSO as an additional attraction term. This item not only enables the robot to avoid collisions but also guides the swarm to search unexplored regions as much as possible. This operation increases the swarm’s task-specific (top-down) diversity, making the system cover a broader search area and avoid falling into local optimums. Besides, the aggregation degree and evolution speed factors are also included in determining the inertia weight of the proposed method, which adjusts the swarm’s internal (bottom-up) diversity dynamically. The comparison results show that this method can balance the relationship between exploration and exploitation well, which has the potential to be applied to multitarget searching scenarios.

Efficient distributed processing is vital for collaborative searching tasks of robotic swarm systems. Typically, those systems are decentralized, and the members have only limited communication and processing capacities. What is illustrated in this paper is a distributed processing paradigm for robotic swarms moving in a line or v-shape formation. The introduced concept is capable of exploits the line and v-shape formations for 2-D filtering and processing algorithms based on a modified multi-dimensional Roesser model. The communication is only between nearest adjacent members with a simple state variable. As an example, we applied a salient region detection algorithm to the proposed framework. The simulation results indicate the designed paradigm can detect salient regions by using a moving line or v-shape formation in a scanning way. The requirement of communication and processing capability in this framework is minimal, making it a good candidate for collaborative exploration of formatted robotic swarms.

Purpose: This paper aims to propose a dynamic trajectory-tracking control method for robotic transcranial magnetic stimulation (TMS), based on force sensors, which follows the dynamic movement of the patient’s head during treatment. Design/methodology/approach: First, end-effector gravity compensation methods based on kinematics and back-propagation (BP) neural networks are presented and compared. Second, a dynamic trajectory-tracking method is tested using force/position hybrid control. Finally, an adaptive proportional-derivative (PD) controller is adopted to make pose corrections. All the methods are designed for robotic TMS systems. Findings: The gravity compensation method, based on BP neural networks for end-effectors, is proposed due to the different zero drifts in different sensors’ postures, modeling errors in the kinematics and the effects of other uncertain factors on the accuracy of gravity compensation. Results indicate that accuracy is improved using this method and the computing load is significantly reduced. The pose correction of the robotic manipulator can be achieved using an adaptive PD hybrid force/position controller. Originality/value: A BP neural network-based gravity compensation method is developed and compared with traditional kinematic methods. The adaptive PD control strategy is designed to make the necessary pose corrections more effectively. The proposed methods are verified on a robotic TMS system. Experimental results indicate that the system is effective and flexible for the dynamic trajectory-tracking control of manipulator applications.