Over the last decade, nature-inspired algorithms have motivated researchers to work in all fields of **optimisation**. Such algorithms can efficiently provide near optimal solution with better efficiency and least computational complexity even in large environments. Angus 6 , solved the problem of **path** **planning** using **ant** **colony** **optimisation** and tested on mound, volcano, valley terrains using both vector and multiplication combination methods. Behzadi 7 , et al., developed a genetic algorithm for solving the shortest **path** problem using the graph connectivity and implemented on road maps of Tehran, the capital city of Iran. An extensive survey on the available heuristic methods for **path** **planning** discussing the pros and cons was provided by Mac 8 , et al., A hybrid algorithm through the combination of genetic algorithm and the adaptive fuzzy logic controller was implemented by Bakdi 9 , et al., for pathfinding on a two-wheeled indoor mobile robot. The piecewise cubic hermite interpolating polynomial is then applied on it to get a An **Intelligent** **Gain**-**based** **Ant** **colony** **optimisation** **Method** for **Path** **Planning** of

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This chapter presents a mission **planning** problem for a cooperative team of **unmanned** **ground** **vehicles** (UGVs), which includes multiple rovers and a solar-powered mobile charging station. The team is required to start at an initial point and visit a series of objective points before arriving at the final point selected from the set of objective points, where the UGVs will be charged from the solar-powered mobile charging station. This mission is represented as a multi-Hamiltonian **Path** Problem (mHPP). In order to effectively coordinate the team, an understanding of the mission environment is first obtained by generating a scalar field representation of the solar insolation of the environment from a visual-spectrum image. Then, a cascaded heuristic optimization (CHO) algorithm, using modified genetic algorithm and particle swarm optimization, is used to generate a time-optimized mission plan for the team of UGVs, which guides each UGV to its assigned objective points and then rendezvous at the final charging location while guaranteeing compliance with the net energy **gain** constraint.

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This paper presents an approach for optimal **path** **planning** for a remote sens- ing autonomous robot in a cluttered and hazardous indoor environment. The operating scenario of this robot is applicable during the search and rescue mis- sions, where **unmanned** **ground** **vehicles** (UGVs) are favored, to survey and sense the environment for various detectable phenomena such as gases, fire or smoke detection and etcetera. The proposed algorithm can be generalized to any given map and as an example simulation scenario; we present an application of **path** **planning** of a mobile robot in an urban search and rescue mission to navi- gate through an indoor hazardous building for remote-sensing and assessment of the hazardous situation. The sensing of the environment would enable the first responders’ team to determine the severity of the emergency and would help them to decide on rescuing the victims with the least risk towards the team. With the proposed system, the robot will navigate autonomously by utilizing probabilistic roadmaps (PRM) to find out all the possible navigation paths for autonomous navigation of the robot, given the building map. With the various solutions of the probabilistic roadmaps, an optimal **path** that would be selected, **based** on particle swarm optimization algorithm, that covers most of the indoor area to provide the best possible assessment of the hazard situation.

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Considerable literatures have been reported on the sub- ject of **path** **planning**. The main methods currently devel- oped for **path** **planning** include graph-**based**, population- **based** evolutionary algorithms, and distributed approaches [11]. The graph-**based** algorithms include Voronoi diagram search **method**, directed graph-**based** **method**, A ∗ search algorithms, mathematical programming **method**, artificial potential field **method** (APF), and D ∗ lite algorithms. The graph-**based** algorithms, however, have shown weakness in practical situations due to its difficulty to address the motion constraints of UAV. The population-**based** algorithms contain particle swarm optimization (PSO), **ant** **colony** optimization (ACO), **intelligent** water drops optimization (IWD), grav- itational search algorithm (GSA), and artificial bee **colony** (ABC). The population-**based** evolutionary algorithms have advantages of reduced complexity and dimensions in the **planning** phase [12, 13]. Distributed **path** **planning** off loads the **path** **planning** to environment using message exchanges between **intelligent** nodes. While these methods require minimized onboard processing, they rely on the smart infrastructures to be preinstalled. All of these methods have been applied to **path** **planning** in the literature, but each of them has its own disadvantages in certain aspects. For example, the APF **method** fails to generate **path** effectively in the situation with a more dense group of obstacles. The target cannot be reached if there are obstacles near the target. Moreover, jitter may occur in the **planning** **path** when it is near to an obstacle or in a narrow passageway [14, 15]. As for the ACO algorithm, it requests large amount of computation and the efficiency very much depends on the parameter. If the parameter is set incorrectly, the solution speed is slow and the quality of the solution is poor. Although an optimal solution can be obtained through exchanging information, the efficiency will be inevitably reduced when the content of the problem is too large. Meanwhile, ACO algorithm has a slow convergence speed and can easily fall into local optimal solution due to its lack of initial information [16, 17].

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We tested the ACO-RRT* algorithm performance with a holonomic robot in three simulated scenarios (see Figure 5). We chose a holonomic robot, since it enables us to abstract the algorithm capabilities from the robot’s kinodynamic constraints. We assume that the robot corresponds to a single point. However, more complex robot shapes could easily be introduced within this framework. The three sce- narios correspond to realistic scenarios that could be encountered while navigating an indoor facility. Moreover, similar scenarios have been considered to evaluate some of the most recent state-of-the art methods. 7,24 Analysis in more complex scenarios and the consideration of kinody- namic constraints is left for future research. All scenarios measure 100 m 100 m and the goal is to find the optimal **path** that goes from x A to x B . Since Scenario 3 is more structured, the placement of the initial position plays a crucial role. Therefore, in Scenario 3 we consider different possible starting positions x A , which are randomly selected in each simulation run. For the evaluation we consider a goal region centred around the goal position, not just a single state. Scenario 1 is composed of 10 rectangles of different sizes and the optimal **path** measures 88 m. Sce- nario 2 contains a narrow passage, which is often consid- ered one of the most challenging **path**-**planning** problems.

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This work presents a new proposal to solve the problem of **path** **planning** for mobile robots; it is **based** on TWPSS-ACOA to find the best route according to certain cost function. There are two core steps about **path** **planning** methods: environment modeling and **planning** algorithm. So we firstly build the environment model of robot by EVB-CT--GM [32] , since this **method** was certified to be an effective **method** to overcome environment traps problem, and then TWPSS-ACOA proposed in [33] is used to adequately develop mutual cooperation ability between ants. But in view of that the TWPSS-ACOA has the defects of losing some feasible paths and even optimal paths, a new ants meeting judgment **method** that can judge if ants meet according to the kind of pheromones is proposed. And then a new **method**, which rationally distributes initial pheromone of ants, is given to speed up the convergence velocity of initial stages of ACO algorithm, since equivalent Manuscript received October 14, 2011.

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In the development of collision avoidance algorithms, only a simple kinematic model of the vehicle is used normally. This greatly simplifies the analysis and design of collision avoidance algorithms. However, the model in the verification stage must be as close to the real world as possible, which demands a much more complicated model. A simplified model of a vehicle and its operational environment is used in the algorithm development process while the real vehicle and its operational environment are much more complicated, with possibly a much high order of dynamics, nonlinearity, and much more complicated operation scenarios. This causes structural uncertainties in the verification of collision avoidance algorithms. The parameter uncertainties represent the variations of parameters that capture the changes of vehicle dynamics and its operational environment. The variations of the autonomous vehicle dynamics in operation may arise due to the changes in the vehicle itself (e.g. the change of mass or the centre of gravity) or the change of the operation environment (e.g. tyre friction for different road surfaces). In the online motion **planning**, **unmanned** **vehicles** must be able to sense obstacles, determine the obstacles positions and velocities, and reach the target position. However, there is inevitably uncertainty in the sensor data due to the limited accuracy of the robot’s sensors and environmental noises. Therefore, it is necessary to verify whether or not an OAS under question is able to avoid obstacles with uncertain sensor data.

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Abstract. In order to improve the efficiency in **path** **planning** of security robot, this paper addresses to construct three kinds of grid obstacle models from simple to complicated, and use the integrated **ant** **colony**-particle algorithm to make global **path** **planning**. For further explaining the effectiveness of the combined algorithm implementation, this paper compares the different effects in **path** **planning** of the traditional **ant** **colony** algorithm and the combined **ant** **colony**-particle swarm optimization from three aspects, which are the iteration number of searching the optimal solution, the shortest **path** length and the running time. It is found that the integrated **ant** **colony**-particle algorithm enhances the search efficiency of the optimal solution and reduces the number of iterations of the search, so as to complete the optimal **path** of the security robot from the start point to the end point.

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After analysis, we can know that when the number of ants’ increases, the number of collections and the number of elements contained in the collection is large, the algorithm complexity becomes high, and the search for a long time problem is particularly prominent. These wireless sensor network nodes will cause heavy computational burden, resulting in network bottlenecks [12-13]. Is mainly due to defects caused by : basic **ant** **colony** algorithm would choose over all subsets are updated at each cycle, which can only be fixed to select a subset of , and with the increase of the solution space , different sub- set close to each other the possibility of transition probabilities greater , which reduces the efficiency of the search results optimization , making the search behavior of ants can quickly focus on the optimal solution of the field , the corresponding increase of search time . To this end, we have made improvements on the **ant** **colony** algorithm: The initial time in a limited subset of randomly selected place ants, after each cycle, the optimal solution is only a subset of the selected **ant** pheromone increases, so the ants tend to choose to constitute a minimal set covering subset, thus improving the ants search capabilities. Repeated cycle of implementation what is the above process, when the number of cycles to meet the conditions, then the output of the minimum number of collections.

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In order to analyze the adaptability of the algorithm to deal with dynamic environments, after the best solution is found, we have applied the algorithm to a changing environment. This is an extension of the previous investigation presented in [16]. **Based** on the literature, we have applied two kinds of changes: removing an edge (equivalent to adding an obstacle) and moving the goal position. Before recalling the runMMAS procedure to search for the new solution, we have called the applySmoothing procedure (line 5). This is a procedure suggested by the MMAS algorithm to smooth the pheromone amount when the algorithm has converged [4]. This mechanism increases the pheromone trails proportionally to their difference to the maximum pheromone trail limit:

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Some of the best known classification techniques, such as support vector machine (SVM) and perceptron-**based** classifiers, rely upon constructing mathematical functions having weights that efficiently separate two or more classes of data in the feature space. In two- dimensional spaces, the separation boundary might be nonlinear and thus the decision boundaries might be complex. SVM deals with this situation by either projecting the data on a higher-dimensional space or using a “kernel trick”, which provides a separator not limited to a linear or polynomial function. The adoption of a kernel is equivalent to transposing the data to many dimensions, but the accuracy depends on the right choice of the kernel functions as well as on several other parameters. The latter choice is usually performed through manual trial and error.

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request. The above mentioned process is not suitable for the OBS scenario as each incoming burst request will be delayed by the set-up procedure. This is too costly as the set-up procedure must wait for all the ants to return. However, **ant** **based** algorithms have been proposed for OBS (Ngo et al., 2006). This algorithm reduces the set-up delay for each incoming burst request by means of using a routing table to immediately determine a **path**. The ants in this approach are continuously launched throughout the network. This is done in order to update the routing tables, monitor the current network state, share gathered information as well as scoring paths **based** on the **path** length and number of available wavelengths. **Ant**-**based** algorithms have been further developed for OBS, specifically for a network with no buffers under the WCC (Pedro et al., 2009; Donato et al., 2012). A **path** for the incoming connection request is immediately determined from the routing table. The dominant **path** is selected for the specific source and destination node pair within the routing table and given a randomly selected wavelength at the source node (Pedro et al., 2009). However, in (Donato et al., 2012), the **path** is selected probabilistically at the source node with a wavelength assigned by First Fit at the source node and is thereafter selected **based** on the highest pheromone levels. **Ant** **Colony** Routing and Wavelength Assignment (ACRWA) is of particular interest as it utilises a globally distributed approach in which the **ant** colonies share information with one another as a solution to the RWA problem for dynamic WDM OBS networks with the WCC (Triay and Cervello-Pastor, 2010).

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Generally, **path** **planning** problem can be classified into two categories: local **path** **planning** (LPP) and global **path** **planning** (GPP) [11,12]. LPP mainly relies on the un- known or partially known environmental information that is obtained from the acoustic sensors, such as forward-looking sonar. In dealing with the LPP problem, some ap- proaches have been applied, such as artificial potential field **method** [13], fuzzy logic algorithm [14], and the rolling windows **method** [15]. However, those methods always exists some significant problems such as high computational cost, ineffective in **path** **planning** when the underwater space is large, and even deadlock phenomenon.

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Instant Scene Modeler (iSM) is a vision system for generating calibrated photo-realistic 3D models of unknown environments quickly using stereo image sequences. Equipped with iSM, **Unmanned** **Ground** **Vehicles** (UGVs) can capture stereo images and create 3D models to be sent back to the base station, while they explore unknown environments. Rapid access to 3D models will increase the operator situational awareness and allow better mission **planning** and execution, as the models can be visualized from different views and used for relative measurements. Current military operations of UGVs in urban warfare threats involve the operator hand-sketching the environment from live video feed. iSM eliminates the need for an additional operator as the 3D model is generated automatically. The photo-realism of the models enhances the situational awareness of the mission and the models can also be used for change detection. iSM has been tested on our autonomous vehicle to create photo-realistic 3D models while the rover traverses in unknown environments.

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tion strategies are discussed in the context of **ground** **vehicles** but are applicable to aerial applications when constraints are not a factor. Ahmadzedah et al applied receding horizon optimization techniques to minimize the time required to persistently cover a designated area [8]. Strictly satisfying image refresh requirements over a long period was found to be uncertain. Gorecki et al [42] apply model predictive control optimal costs to balance explo- ration, safety, and mission termination specifications. Persistence is not directly considered but could be accommodated with an iterative execution of their algorithm. Performance guarantees for coverage would also require additional development. Nigam and Kroo [43] develop persistent surveillance policies for single and multiple agent applications. Their results show the merits of basing plans on feasible **path** lengths rather than Euclidean dis- tances, especially when turn rate capability is relatively low. Their approach to multiple UAS persistent surveillance, which is **based** on an optimum policy for a single-UAS case, validates the idea of basing team performance on the analysis of a single agent. Acevedo et al present an area partitioning strategy to solve the problem for irregular areas and het- erogeneous UAS [44]. Caraballo et al [45] generalize the concept using a strategy defined as the block-sharing technique to accelerate convergence to an optimal partition. Vehicle capability in their model is specified by speed and sensor/camera field-of-view; fixed-wing maneuver constraints are not included. Mixed Integer Linear Programming solutions have been developed by How et al [46] for maximizing coverage but not for persistent applica- tions. Wallar et al [47] directly address persistence in the context of a reactive planner tailored for agile quad-rotor platforms, so further work would be required to accommodate fixed-wing levels of maneuverability. Finally, in this survey, Cowlagi presents the case for a hierarchical approach to optimal **planning** between points [48].

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Overarching Concept. Small mechanized infantry and ar- mor combat units normally operate and fight as teams. In mounted operations the smallest team consists of two ve- hicles in which a section leader (with crew) in one combat vehicle is accompanied by a subordinate wingman (with crew) in another vehicle. The section leader, following broad guidance from his superiors, usually determines routes to be followed, positions to be occupied, formations to be used during movement, and actions to be taken during various situations. In combat, when two or more enemy targets are encountered, the section leader will give fire commands to determine which enemy targets he will attack and which will be attacked by the Wingman. The Wingman is constantly observing his designated sector and reports any changes or dangers to the leader. The Wingman’s observations and communications often result in the section leader changing his initial plans **based** on more complete information. A Wingman could perform section missions normally assigned to a manned Wingman vehicle. The **unmanned** Wingman would be capable of functioning at the highest states of alert indefinitely. It would be able to routinely conduct missions that would normally be considered extremely risky for a manned system. The Wingman would be able to automati- cally move about the battlefield—remaining within assigned areas or on designated routes—as directed by the section leader. Through its sophisticated sensor package the Wingman would provide eyes and ears to the section leader who could give early warning of danger and increase the survival rate for the manned vehicle. The Wingman could provide 360-degree observation or focus solely on a specific sector as directed by the section leader. It would provide an RSTA capability that would allow it to recognize natural and manmade features as well as nearby people, **vehicles**, ob- stacles, and other information. The Wingman would trans- mit observed information to the section leader. This intelli- gence would allow the section leader to continue with the current plan, adjust movement, maneuver to a more advanta- geous position, directly attack an enemy target, request other assistance to accomplish the task, or take any number of ac- tions as necessary. The Wingman would be able to perform continuous local security while soldiers slept or were other- wise occupied.

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and m is the number of enemy radars located at the navigational space. The h(n) plays a significant role in the search process when w value is smaller; the number of vertices to be explored would be decreased. The choice of w between 0 and 1 gives the flexibility to place weight on exposure to threats or fuel expenditure de- pending on the particular mission scenario. For example when w = 0, the search process would proceed from the starting location to the target location by exploring the least number of vertices. However the generated **path** is not stealthy and may cause UAV to enter high radar risk region. A w value closer to 0 would result in the shortest paths, with little regard for the exposure to enemy radar, while a value closer to 1 would result in paths that avoid threat exposure at the expense of longer **path** length. For this case, the cost weighting parameter w was chosen to give a reasonable tradeoff between proximity of the **path** to threats and the **path** length. The evaluation function, (10) is tested empirically and compared in terms of the number of nodes visited. During the test, the cost weighting parameter w is varied from 0.0 to 1.0 and the test result is demonstrated in Table 1. The experimen- tally defined value for the w ranges from [0.1, 0.3] in which the generated **path** is optimal and computationally inexpensive, which is in line with our algorithm objec- tives. The generated **path** is neither the safest possible **path** nor the shortest possible **path**, but represents a com- promise between the two objectives.

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The contributions of this paper are as follows. First, we propose an optimization-**based** strategy for the generation of optimal UAV rendezvous trajectory onto a moving UGV. In order to generate realistic rendezvous trajectories, the strategy has to explicitly take into account the dynamics and kinematics of the UAV and UGV. The coupled UAV-UGV dynamics and the constraints arising from the rendezvous maneuver make the design of the strategy complex. We set up the rendezvous optimal control problem in terms of a suitable error dynamics which describe the coupled dynamics. The error dynamics make the analysis and design of the rendezvous strategy simpler, because the key for achieving successful rendezvous is that the error coordinates are zero at the rendezvous point. Second, we identify an aggressiveness index in our rendezvous optimal control problem which allows us to control the UAV rendezvous behavior. The aggressiveness index is **based** on the performance limitations of the UAV (i.e., the constraint limits on the state, input variables), thus allowing us to compute aggressive trajectories (several dynamic constraints are active while the UAV is approaching the UGV) or very smooth ones. The proposed optimal solution framework for the UAV-UGV rendezvous can be seen as a framework which allows one to select (in form of tuning knob) the type of UAV trajectory. Finally, through numerical computations, we show the effectiveness of our approach and discuss a set of interesting features of the rendezvous trajectories. We provide an application scenario in which we validate the proposed strategy. Given the (local) optimal trajectory, the flight **path** angle, the course angle, the **ground** speed, and the desired altitude are set as reference signals to the autopilot of a com- plete six-degree-of-freedom, twelve-state equations of motion, UAV model, [24]. We show that the aggressive trajectory of the 3D point mass model is “close” to the trajectory of the complex UAV model. A preliminary work on the UAV-UGV rendezvous problem was proposed by the authors in [25]. In this paper, we have extended the framework to address wind disturbances in the UAV-UGV coupled error dynamics, and have reformulated the optimal control problem by introducing an aggressiveness index term through which the complete UAV rendezvous behavior can be controlled compared with the 13 terms used in [25], and we have carried out numerical computations analyzing the effect of the aggressiveness index. The rest of the paper is organized as follows. In Section II, we propose the optimal control formulation for the UAV- UGV rendezvous. In Section III, we describe the optimal control **based** strategy for effectively solving the rendezvous optimal control problem. This technique is evaluated through numerical computations and illustrated in Section IV. The conclusions are given in Section V.

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As discussed, the neighboring nodes are included in the priority queue. Consequently, the search algorithm resumes its search until it reaches a node with the lowest value in the queue less than f. The value of the shortest **path** is the value of f considering h at a zero value for the building entrance within an acceptable empirical test. Furthermore, ACO optimizes the resulting **path** to generate the ideal **path** from the gate as a starting point to the entrance as a final destination. At the early time, ants randomly search for food to return with them to their **colony**. Using pheromone, ants mark their **path** to food leading other ants to follow this **path**. The **path** that has the highest value of pheromone is the one leads to food. Thus, the value is determined by the pheromone-**based** on the usage of such by ants. In this proposed model, food is given the value of (0, 1). In the case of an empty parking bay, the status of the parking is zero (0) which refers to food for ants. In the case of a full parking bays, the status of the parking is one (1) which refers to no food for ants. On another perspective, ants use pheromone for the **path** they followed for food. However, this pheromone fades over time when the **path** is not used. This case suggests that ants follow another **path** of food. This process updates ants with the latest ideal **path** for food. Therefore, in this model, ants are referred to as a number and pheromone are referred to as a value that changes **based** on ants’ usage of paths. Finally, when ants find an empty parking bay within the parking suggested by A* algorithm, it begins its **path** optimization according to certain measures. In the beginning, the ACO will initialize its parameters which are the nodes and ants’ number, the initial **path** is generated by A* algorithm and the pheromone. Then ACO will set the distances of the nods and the matrices. Once all the parameters are ready, the ACO will start by the first **ant** which is K assigned as 1 and locate it on the initial node which is the gate used by the car. Then the **ant** will start from the first node and will define a random number from zero to one. The random number is defined as 0.5. If this random number is smaller than the initial **path** which is q0, that means there is a **path** and **ANT** should follow this **path** which means perform (1). Otherwise **ANT** will explore new paths then perform (2).

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