Heuristic methods employ certain assumptions to reduce the complexity of a problem. Arguably, the most commonly used heuristic method in robot motion **planning** is A* Algorithm which was introduced by [17] and used in [8], [18] and [19]. Other heuristic algorithms mimic biological ones, such Genetic Algorithms [6, 19] and Ant Colony Optimization [18, 20], then physical phenomena, such as Simulated Annealing [9] or human decision making such as Fuzzy Logic Control [21-23]. The drawback of these methods is that they use multiple variables and coefficients that must be chosen by the algorithm designer. There is no literature that defines a particular method for variable selection and thus results are not consistent for different scenarios. For instance, a genetic algorithm requires the selection of mutation and cross-over factors, encoding and decoding methods, selection criteria, fitness function design, number of generations, population size and finally number of individuals and their string length. All these variables require fine-tuning by the designer and they do not guarantee optimal solutions. As a consequence, heuristic methods do not produce general solutions. For different situation the variables of a heuristic algorithm may require adjustment.

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The TS algorithm. In the study by Chaari et al., 23 we pro- posed a TS-based **path** planner (TS **PATH**). We adapted and applied the different theoretical concepts of the TS **approach** to solve the **path** **planning** problem in grid map environments. The TS **PATH** algorithm starts with an initial **path** generated randomly using the greedy **approach**. Then, it attempts iteratively to improve the current **path** around an appropriately defined neighbourhood until a pre- defined termination criterion is satisfied. Each neighbour **path** is reached from the current **path** by applying a small transformation called move, and we consider three differ- ent moves in TS-**PATH**: insert move, remove move and swap move. Before accepting a new move, we must verify that it improves the current solution and also that the move is not tabu. To avoid being trapped at a local optimum and backtracking to already visited paths, the TS **approach** keeps track of the recent moves in a temporary buffer referred to as tabu list. Two tabu lists are considered in TS **PATH**: TabuListIn and TabuListOut. TabuListIn contains the edges that are added to a **path** after carrying out a move and TabuListOut contains the edges that are removed from the **path** after performing a move. A move that exists in a tabu list is considered a tabu move. To avoid the search stagnation during a certain number of consecu- tive iterations, we designed a new method of diversification to guide the search towards new paths that are not explored. The diversification begins with drawing a straight line between the start and the goal positions. At the radius of

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The cost function is designed to best explain previous behaviour and therefore predict future pedestrian positions. To make the cost function transferable to other environments, six parameters are used. The first is a constant feature for every grid cell of the configuration space. The second is an indicator for if an obstacle exists in a particular cell. The third to sixth are four "blurs" of obstacle occupancies that dissipate the cost in the cell into neighbouring ones (please see Fig. 4 in [189] for visual demonstration). Using a small number of parameters is shown to be more effective, as when comparing the results to a variable-length Markov model, the paper for this model concludes that "the variable-length Markov model (and similar directed graphical model approaches) are generally much more difficult to train and do not generalize well because their number of parameters is significantly larger than the number of parameters of the cost function employed in our **approach**" [189]. Predicting Pedestrian Trajectories A mixed Markov model [190] was also de- veloped to predict pedestrian trajectories, evaluated using a museum environment. A training dataset of 691 people was used, with an average participation time of 1h 31m per person. The model can predict the next discrete movement of a pedestrian from a probability-distribution obtained when training, using a maximum likeli- hood function. This can provide an informed approximation towards how individual pedestrians may move by making discrete destination predictions. However, these discrete predictions are not specific coordinates, but are topological points at exhi- bitions in a museum. Using a pedestrian-flow simulator [192] the model produced a 74.1% success-rate, as the more available history of transitions from exhibition to exhibition was available the better it faired. However, this level of accuracy may not be achievable if predicting movement trajectories of individual pedestrians. As a provided comparison the more basic Markov model and Hidden-Markov Model achieved much lower success rates of 16.9% and 4.2%, respectively. The model also achieved a 64% success rate for the prediction of real pedestrian movements in a real-life exhibition.

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The global navigation problem deals with navigation on a larger scale in which the robot cannot observe the goal state from its initial position. Global approaches can be classified into three basic categories: The **roadmap** methods, the cell decomposition methods and the potential field methods [7]. **Roadmap** methods extract a network representation of the environment and then apply graph search algorithms to find a **path** [8]. Different **Roadmap** methods differ in the way they define the set of nodes, the set of pathways and the algorithm of finding feasible paths [9]. Cell decomposition **approach**, is a graph technique widely used in both static and dynamic environments as the implementation is easier, accurate and easy to be updated [10]. Potential field methods treat the robot, represented as a point in configuration space, as a particle under the influence of an artificial potential field [11]. One shortcoming of this **approach** is that a robot can get stuck in a local minimum of the potential. A variety of approaches have been proposed for a robot to find its way out of these spots, including active search, backtracking, and random walks [12].

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Abstract—We address the problem of **planning** a **path** for a ground robot through unknown terrain, using observations from a flying robot. In search and rescue missions, which are our target scenarios, the time from arrival at the disaster site to the delivery of aid is critically important. Previous works required exhaustive exploration before **path** **planning**, which is time-consuming but eventually leads to an optimal **path** for the ground robot. Instead, we propose active exploration of the environment, where the flying robot chooses regions to map in a way that optimizes the overall response time of the system, which is the combined time for the air and ground **robots** to execute their missions. In our **approach**, we estimate terrain classes throughout our terrain map, and we also add elevation information in areas where the active exploration algorithm has chosen to perform 3D reconstruction. This terrain information is used to estimate feasible and efficient paths for the ground robot. By exploring the environment actively, we achieve superior response times compared to both exhaustive and greedy exploration strategies. We demonstrate the performance and capabilities of the proposed system in simulated and real-world outdoor experiments. To the best of our knowledge, this is the first work to address ground robot **path** **planning** using active aerial exploration.

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A key part of navigation is the model used to represent the environment; how is data for it gathered, how it is interpreted, what data points are discarded or kept and when is the decision to remove them made. Many different methods of rep- resenting the terrain and storing the data were considered because “If you get the data structures right, the effort will make development of the rest of the program much easier [40].” The most simplistic ‘model’ is to only consider that which is currently being viewed and involves constantly determining if what is visible con- sists of traversable terrain or hazards/obstacles. This situation is comparable to a human with absolutely no short term memory. At the other end of the spectrum is building up a near perfect model, taking advantage of a robot’s precision and recall. Though simplistic, the first model is highly **adaptive** and can easily handle random errors in the input data as well as issues such as slipping or sudden dis- /reorientation. A detailed robotic model may be able to successfully distinguish errors in input but this will require a significant amount of processing and com- parison with input points around the error. The issues of orientation and position are extremely difficult for a precision model to overcome, requiring immense time to process or leading to substantial errors in judgement.

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Therefore, this paper presents an optimized RRT-A* **path** **planning** method based on morphological dila- tion (MD), goal-biased RRT, A* heuristic algorithm and cubic spline interpolation to compute safe and optimal **path** for **autonomous** mobile **robots** in par- tially known complex environment. A step size is usually used in goal-biased RRT for the generation of the RRT. In this paper, additional step-size is intro- duced to speed up the generation of the tree towards the goal based on the random sample value. In [24], A* heuristic function was applied at every iteration to select the nearest node during the generation of the tree which had high time cost in **path** computation. In this paper, the A* heuristic algorithm is used to optimize and obtain the shortest **path** after the **path** is generated using the modified goal-biased RRT. To provide safe and smooth **path** for feasible navigation, MD technique is used to inflate the obstacles before generating the **path**, and cubic spline interpolation (CSI) is used to smoothen the **path**. **Path** replanning is provided by generating new **path** from a current po- sition of the robot when a random obstacle obstructs its navigation **path**. ORRT-A* **approach** addresses the local minima problem reported with RRT-A* [24] and generates safe and optimal **path** with low time cost in partially known environment.

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proportional controller (plus feedforward). This simple **approach** works reasonably well. However, if one tries to improve tracking accuracy by reducing b (so as to bring B close to the ground contact point), the control effort quickly increases. Trajectory tracking with b (i.e., for the actual contact point on the ground) can be achieved using dynamic feedback linearizion. In particular, this method provides a one-dimensional dynamic compensator that transforms the unicycle into a parallel of two double integrators, which is then glob- ally stabilized with a proportional-derivative controller (plus feedforward). In contrast to static feedback linearizion, no residual zero dynamics is present in the transformed system. However, the dynamic compensator has a singularity when the unicycle driving velocity is zero. This is expected, because otherwise the tracking controller would represent a univer- sal controller. Note that dynamic feedback realizability using the x, y outputs is related to them being flat, the two properties are equivalent.

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(Parhi,2018) performed a review analysis on navigational methodologies of **robots** through different artificial intelligence techniques including Neural Network, Particle Swarm Optimisation (PSO),Fuzzy Logic, Genetic Algorithm and additional Artificial Intelligence techniques. During the survey analysis the review was carried out systematically and the role of several artificial intelligence techniques were utilized to control and navigate different kinds of **robots** facing different environmental conditions.(Song et al., 2017) uses η3 -splines along with a modified particle swarm optimization (MPSO) to propose a new **approach**. At first, the η3 - splines are utilized for including an arbitrary arrangement of points where the kinematic parameters are chosen to relate with the movement and the control of mobile **robots**. The MPSO algorithm comprises of **adaptive** random fluctuations (ARFs) and is for the most part created to control the frequently oversaw local convergence. The issue is the system of arranging the smooth worldwide way. The MPSO algorithm has shown the evolutionary state incorporating classification averagely at each iteration as provided by the evaluated evolutionary factor. There exists a switch in the velocity improving dynamics for the varying modes as per the evolutionary state along with the ARFs .Theses are imposed on the global/local best particles in a way suggested by the existing iteration.

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In the PSO algorithm, first the system is initialized with a population of random solutions for particles, and each particle is also assigned with a random velocity. PSO relies on the exchange of information between particles of the population in the swarm. In the iterative process, each particle adjusts its trajectory towards its best solution (fitness) that is its trajectory towards the best previous position attained by any member of its group. This value is called ‘gbest’. Each particle moves in the search space with an **adaptive** velocity. The fitness function is used to evaluate the performance of particles to determine whether the best fitting solution is achieved. During the iteration process the fitness of the best individual improves over time and typically tends to stagnate.The process terminates when it coincides with successful discovery of the global optimum.

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This paper has presented our current research efforts towards an **Autonomous** Compliant Motion system. The focus points are on: (i) more advanced estima- tion (where “advanced” means that non-linearities and “global” optimization are taken into account), (ii) a next generation of task specification (based on task- directed models instead of servo-level setpoints), and (iii) the development of the software support (an ACM cannot perform its task in the quite hierarchical control frameworks of past and current robot controllers).

Mobile **robots** have the capability to move around in their environment, they are not supposed to be fixed to one physical location [15]. By contrast, industrial **robots** are usually more- or-less stationary, consisting of a jointed arm (multi-linked manipulator) and gripper assembly (or end effector) attached to a fixed surface [15]. Mobile **robots** come in many shapes and sizes, but they all contain three main components. First, there is some combination of sensors that are used for understanding the environment. Then, there is the onboard computer for **planning** and decision making. Finally, a form of locomotion allowing the robot to act in its environment [18].

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Robot navigational **path** **planning** has been cited as a vital research in the field of robotics. **Path** **planning** is pertaining to active navigation that guides a robot to locations within the built map to improve localization. It is a task of determining the optimal **path** by minimizing a cost function such as the distance travelled. A **path** is optimal if the sum of its transition costs is minimal across all possible paths leading from the initial position to goal position. Several approaches have been proposed over the last decades to deal with **path** **planning** problem such as A* algorithm [14], Bug algorithm [15], and Potential functions (PF) [16]. This research doesn't need to use any of these algorithms to solve this problem. As soon as a robot gets map of its surrounding area by the proposed method in this work, it can easily reach to its target by the most direct **path** as explained in Pseudo Code:

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International Regulations for Preventing Collisions at Sea (COLREGs) are marine traffic rules for all vessels working in water environment. It is not only essential for human navigated ships but also for **Autonomous** Surface Vessel, since it should behave same way to other ships when encounters other ships for collision avoidance. This paper presents an artificial potential field method to guide the ASV cruise in the river and be able to avoid obstacles. The repulsive potential is modified to ensure that the evasive manoeuvre complies with COLREGs. The recover manoeuvre is also achieved to make the ASV fast return back to its original **path**. The simulation results illustrate that the proposed **approach** is effective for obstacles avoidance and **path** **planning** for ASV navigation in riverine environment.

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Our work expands on the algorithms of [1], [2]. The proposed software architecture takes advantage of distributed computing resources and multi-core CPUs to provide glob- ally dense workspaces (robot task space) within minutes. By creating memory-optimal data structures to represent CTRs and the inverse kinematics problems, the developed infras- tructure can, in real-time, leverage the dense workspaces for on-demand **path**-**planning** with on-line local inverse kinemat- ics to guide the user along safe trajectories. Further, our research contributes to Implicit Active Constraints (IAC) for CTRs by proposing constraint generation based on the generated **path**-plans. Contrary to ACs, which are manually defined, IACs are algorithmically generated and tailored to the respective task based on limited user input [20]. As such, IACs are both more complex to define and to estimate intraoperatively, further increasing the benefit of a software architecture that enables real-time safe and effective robot guidance. Further expanding upon the work in the literature, the developed software requires minimal pre-computation, and is quick and reliable for incorporation in telemanipula- tion control schemes of CTRs. The computational benefits are supported by extensive quantitative evaluation. User- based evaluation of the guidance scheme is carried out

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Abstract—This paper presents a multiobjective optimisation **approach** for **path** **planning** of **autonomous** surface vehicles (ASVs). A unique feature of the technique is the unification of the Convention on the International Regulations for Preventing Collisions at Sea (COLREGs) with good seamanship’s practice alongwith hierarchical (rather than simultaneous) inclusion of objectives. The requirements of collision avoidance are for- mulated as mathematical inequalities and constraints in the optimisation framework and thus collision-free manoeuvres and COLREGs-compliant behaviours are provided in a seafarer- like way. Specific expert knowledge is also taken into account when designing the multiobjective optimisation algorithm. For example, good seamanship reveals that if allowed, an evasive manoeuvre with course changes is always preferred over one with speed changes in practical maritime navigation. As a result, a hierarchical sorting rule is designed to prioritize the objective of course/speed change preference over other objectives such as **path** length and **path** smoothness, and then incorporated into a specific evolutionary algorithm called hierarchical multiobjective particle swarm optimisation (H-MOPSO) algorithm. The H- MOPSO algorithm solves the real-time **path** **planning** problem through finding solutions of the formulated optimisation prob- lem. The effectiveness of the proposed H-MOPSO algorithm is demonstrated through both desktop and high-fidelity networked bridge simulations.

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There has been a great number of studies coping with controlling flexible-arm **robots**, many of which investigate both theoretical and experimental aspects in this field [4] [5]. On grounds of the flexibility of the arms, along with a trajecto- ry-tracking control problem, vibration control should be also considered for such systems to improve the control system performance [6]. As a result of the vibrations caused by the flexibility of the arms, designing controllers for such systems becomes a challenging task. There exist several research works in the li- terature addressing the flexibility of the arm. Passive control methods are one way to deal with the vibrations of elastic arms which require modification in physical parameters of the system structure [7]. Due to these structural modifi- cations, absorption properties of the structure can be employed to increase damping properties of the arms. Active control approaches have also been wide- ly used to control flexible systems, in which actuation moments and forces are applied to address the vibrations [8] [9]. However, the mere use of passive con- trol methods to reduce vibrations does not seem to suffice. Merely using active control approaches is not sufficient as well. It is because vibration modes with frequencies near actuators frequencies can lead to instability. Hence, a combina- tion of passive and active controllers can be employed as a suitable solution to vibrations reduction [10] [11]. The boundary feedback scheme is another way to dampen the vibrations of flexible manipulators [12]. Luo et al. [13] controlled the vibrations of a class of flexible **robots** using a shear feedback control method. Lyapunov-based control has also been vastly utilized to cope with the challenges associated with controlling flexible structures [14]. As another example of Lya- punov-based methods, Dadfarnia et al. [15] used the Lyapunov stability theory to develop a piezoelectric controller for flexible **robots**.

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