Abstract: Aiming at the problem of model error and tracking dependence in the process of intelligent vehicle motion **planning**, an intelligent vehicle model transfer **trajectory** **planning** method based on deep reinforcement learning is proposed, which obtain an effective control action sequence directly. Firstly, an abstract model of the real environment is extracted. On this basis, Deep Deterministic Policy Gradient (DDPG) and vehicle dynamic model are adopted to jointly train a reinforcement learning model, and to decide the optimal intelligent driving maneuver. Secondly, the actual scene is transferred to equivalent virtual abstract scene by transfer model, furthermore, the control action and **trajectory** sequences are calculated according to trained deep reinforcement learning model. Thirdly, the optimal **trajectory** sequence is selected according to evaluation function in the real environment. Finally, the results demonstrate that the proposed method can deal with the problem of intelligent vehicle **trajectory** **planning** for continuous input and continuous output. The model transfer method improves the model generalization performance. Compared with the traditional **trajectory** **planning**, the proposed method output continuous rotation angle control sequence, meanwhile, the lateral control error is also reduced.

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In the following chapters, a **trajectory** **planning** method for FRM, based on Genetic Algorithms to minimize vibration and/or executing time while moving between the initial and final points, is presented. First, a finite element model for describing FRM dynamics is introduced (Section 2). Kinematics redundancy is integrated into the **planning** method as variables (Section 3). Quadrinomial and quintic polynomial are used to describe the paths which connect the initial, intermediate and final points in joint space (Section 4). The **trajectory** **planning** for FRM is formulated as a problem of optimization (Section 5). Suitable parameters for each polynomial between two points and suitable initial and final configurations are determined using GAs (Section 6). Finally, a planar FRM with three flexible links is used in simulations, and two case studies are conducted and discussed (Section 7).

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In motion **planning**, the robot follows a planned path from its initial point to the target. **Trajectory** **planning** deals with robot position, velocity and acceleration in time. However, when a mobile robot should traverse along a given path, there are infinite possible trajectories that the robot can run. Although, only finite numbers of them are appropriate to run in applications. Generally these suitable trajectories are generated based on optimality criteria related with time and vehicle dynamic-kinematic constraints. Namely some related works include time minimizing in the spline curve path [11], polynomial s-curve motion **planning** [12], straight-line, circular segments, and continuous-curvature path **planning** [13], optimizing **trajectory** based on dynamic potential function [14]. In [15] time-optimal trajectories for car-like robots are obtained after solving a formulated dynamic optimization problem. In [16] to steer agricultural machinery automatically, the paper applied continuous-curvature path **planning** known from mobile robotics to generate feasible headland turn manoeuvres trajectories. In [17] motion **planning** of autonomous on-road driving is considered in order to determining the most feasible **trajectory** in motion time. Among the various types of geometric curves are usually employed in mobile robots path **planning**, Bezier curves are known methods to generate trajectories for curvature path [18-21].

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trial movements and acquires satisfactory tracking accuracy. Khouki et.al[10] 2008,studied the problem of minimum-time **trajectory** **planning** for a three degrees-of-freedom planar manipulator using a hierarchical hybrid neuro-fuzzy system. A first neuro-fuzzy network named NeFIK was considered to solve the inverse kinematics problem. After a few pre-processing steps characterizing the minimum-time **trajectory** and the corresponding torques, a second neuro-fuzzy controller was built. Its purpose was to fit the robot dynamic behavior corresponding to the determined minimum-time **trajectory** with respect to actuators models, torque nominal values, as well as position, velocity, acceleration and jerk boundary conditions. Xiaoping Liao et.al[11] 2010,planned **trajectory** using an adaptive genetic algorithm while considering constraints of displacement, velocity, acceleration and jerk of each joint. According to the optimal time intervals generated, the results of simulation on robot kinematics showed that the method designed for robot **trajectory** **planning** can obtain the goal **trajectory**.

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speed limit constraints, i.e., found trajectories respecting the given model of dynamics. The experimental evaluation, where we introduced two versions of augmented A* and Theta*, namely, the lite versions (the nodes distinguished only by their positions) and the full versions (the nodes also distinguished by directions and speed intervals). The experimental results we got showed that the lite versions did not have much worse per- formance than the basic versions even though the lite versions brought additional expres- siveness. However, we did not successfully solve all the test problems by the lite versions even though the problems were solvable. Fortunately, the number of problems incorrectly marked as unsolvable were quite low (up to 2% for the lite version of Theta*). On the other hand, this percentage could increase in environments with high density of obstacles (blocked cells) and/or it is also dependent on the particular model of dynamics. Identi- fication of such problems as mentioned before remains an open problem and should be investigated in future. Despite the incompleteness the results showed the reasonability of using the lite versions (especially the Theta* one) in **trajectory** **planning**, where we have to deal with dynamics such as speed limit constraints.

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The Dubins optimal path **planning** technique has been successfully used in solving **trajectory**- **planning** problems for both unmanned ground and aerial vehicles. Recent work [20], [17] and [18] are some of the examples for the applications of this technique in the UAVs and UGVs domain. The later used the Dubins Sets to develop a control technique for the autonomous navigation and landing of UAVs and implemented their model on the Lockheed-Martin F-16 and the AAI Corporation / Israel aircraft Industries RQ-2 Pioneer [18]. They also compared Dubins Set control technique with the Rhumb – Line control technique. After thorough calculation and considerations, the Dubins Set optimal **trajectory** was found to be time saving. Their approach using Dubins Set is adopted for use in this thesis.

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Abstract. We consider a new problem of robust **trajectory** **planning** for robots that have a physical destination and a communication con- straint. Specifically, the robot or automatic vehicle must move from a given starting point to a target point while uploading/downloading a given amount of data within a given time, while accounting for the en- ergy cost and the time taken to download. However, this **trajectory** is assumed to be planned in advance (e.g., because online computation can- not be performed). Due to wireless channel fluctuations, it is essential for the planned **trajectory** to be robust to packet losses and meet the com- munication target with a sufficiently high probability. This optimization problem contrasts with the classical mobile communications paradigm in which communication aspects are assumed to be independent from the motion aspects. This setup is formalized here and leads us to determin- ing non-trivial trajectories for the mobile, which are highlighted in the numerical result.

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ABSTRACT : In this paper, we present an experimental approach to compare various **trajectory** **planning** methods for practical application of wheeled mobile robots. The first method generates a **trajectory** according to the acceleration limits of the mobile robot and its relationship with the curvature of the planned path. The second method is an improvement of the conventional convolution-based **trajectory** generation method, on which the heading angles of a curved path is being considered. Due to the limited scope of the considered constraints of the previous approaches, A third approach that conserves the merits of the convolution operator is proposed to consider the high curvature turning points of a sophisticated curve such as a Lemniscate of Gerono,which causes geometrical limitations during robot navigation. All methods are compared experimentally on a two-wheeled mobile robot. The goal of the experiment is to determine which approach meets the criteria of time optimality and sampling time uniformity while considering the physical limits of the mobile robot and the geometrical constraints of the planned path.

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Abstract **Trajectory** **planning** is an essential part of systems controlling autonomous en- tities such as vehicles or robots. It requires not only finding spatial curves but also that dynamic properties of the vehicles (such as speed limits for certain maneuvers) must be fol- lowed. In this paper, we present an approach for augmenting existing path **planning** methods to support basic dynamic constraints, concretely speed limit constraints. We apply this ap- proach to the well known A* and state-of-the-art Theta* and Lazy Theta* path **planning** al- gorithms. We use a concept of **trajectory** **planning** based on a modular architecture in which spatial and dynamic parts can be easily implemented. This concept allows dynamic aspects to be processed during **planning**. Existing systems based on a similar concept usually add dy- namics (velocity) into spatial curves in a post-processing step which might be inappropriate when the curves do not follow the dynamics. Many existing **trajectory** **planning** approaches, especially in mobile robotics, encode dynamic aspects directly in the representation (e.g. in the form of regular lattices) which requires a precise knowledge of the environmental and dynamic properties of particular autonomous entities making designing and implementing such **trajectory** **planning** approaches quite difficult. The concept of **trajectory** **planning** we implemented might not be as precise but the modular architecture makes the design and implementation easier because we can use (modified) well known path **planning** methods and define models of dynamics of autonomous entities separately. This seems to be appro- priate for simulations used in feasibility studies for some complex autonomous systems or in computer games etc. Our basic implementation of the augmented A*, Theta* and Lazy Theta* algorithms is also experimentally evaluated. We compare i) the augmented and basic A*, Theta* and Lazy Theta* algorithms and ii) optimizing of augmented Theta* and Lazy Theta* for distance (the **trajectory** length) and duration (time needed to move through the **trajectory**).

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Abstract: Frequent start-stops of automatic seedling transplanters would lengthen the seedling picking time due to alternating movement of the motor, and cause positioning errors and frequent motor vibrations when starting the machine. To solve these problems and ensure the pick-up continuity of automatic transplanters, in this study the smooth circular arc interpolation algorithm and the least square method for multinomial curve fitting were used to conduct the **trajectory** **planning** of automatic transplanter based on the movement of the pick-up arm of the transplanter. Velocity and time curves were fitted in segments to acquire motion control parameters and further tracking control was conducted. The mathematical model of the control system was established using Simulink, and simulation analysis and system debugging test were performed. Experiments show that the **trajectory** curves obtained by MATLAB’s data processing can realize the continual and smooth motion **trajectory** of the pick-up arm; stepper motor velocity control can effectively track the **planning** curve and improve the seedling pick-up efficiency. The pick-up and pushing time of each motion of the planned plug seedling transplanter reduced by 1.0678 s and the start-stop times reduced from 6 to 1, which solved the frequent motor vibrations when starting the machine and improved the stability of the system. In addition, overstep and out-of-step of the motor at the start-stop moment were avoided and displacement error was reduced.

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6. **Trajectory** **planning** . The inverse kinematics of industrial robots usually yields multiple solutions in Cartesian space. Here, the control points together with derived approach, retreat and orientation information from step 2 are used to generate a unique solution. This step can easily be achieved by standard OLP software from the robot manufacturers. In the MARWIN project, this is achieved using the ABB RobotStudio which can deal with issues such as reachability, transitions, collision avoidance, and so on. Steps 1 and 6 are outside the scope of this paper; in what follows we describe and demonstrate steps 2–5.

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T his work presents a method for optimal **trajectory** **planning** with applications to cinematography with multiple drones. Aerial cinematography with drones is growing fast due to their maneuverability and ability to create unique visual effects. However, **planning** optimal drone trajectories and camera movements is still a major challenge to autonomous aerial filming. The trajectories should meet the objectives on aesthetic quality of the videos while satisfying several constraints imposed by drone dynamics, gimbal mechanical limits and surrounding obstacles. In this work, a novel formulation of the problem is proposed by decoupling the gimbal and the drone control systems for a team of drones in a decentralized way. The problem is formulated as an optimization problem taking into account the gimbal rotation limits and collision avoidance constraints, as well as camera angle driven objective functions, to ensure feasible and smooth drone trajectories that generate visually pleasing videos. We evaluate the efficacy of our method through simulations and real-world experiments in outdoor media production.

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tracking control. **Trajectory** **planning** of the goal is to satisfy the path constraints, obstacles and kinematic constraints, the robot capable of moving fast, accurate and stable and there are no dead angle of spraying the workpiece and uniform in spraying thickness. This paper aimed at free surface and uniform spraying problems, utilization of NC machining process and spraying process similarity is proposed using NC tool path generate spray path method for the **trajectory** **planning**. Establishment of the growth of spraying coating thickness mathematical model, to improve the coating thickness uniformity as the goal, research on the impact of spraying uniformity factor .And through the experimental result to prove the spray path **planning** of rationality and speed optimization of coating thickness uniform validity.

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the method of simulated annealing [5]. One typical spatial cable robot was investigated and one direct method was used for stiness optimization and optimal **trajectory** **planning** [6]. Recently, Korayem et al. have introduced a procedure for nding the optimal path of maximum load for a cable suspended robot and a cable planar robot [7,8]. They used an indirect method and, as mentioned before, the optimization problem is converted to a two-point boundary value problem as by solving that, we can have a precise solution of the problem. This method could be used for any kind of system wherein the state space form of equations is achievable. This method is used as a competent tool for analyzing nonlinear systems and the path **planning** of dierent types of system.

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Abstract—Minimally Invasive Surgical Procedures (MISP) are an exciting choice of option for patients where surgery is performed with localized anesthesia and small incisions to the skin. Surgeons still have to decide if this option is applicable to patients based on each prognosis. If applicable, patients would greatly benefit from the procedures can be carried out in a day care setting with faster recovery time and reduced risk from the use of general anesthesia. Ultrasound is one medical imaging modality which can be used to visualize the underlying tissue during MISP. This gives the surgeon a real-time view of the anatomy without ionizing radiation. Various surgical devices and tools are utilized in MISP. This paper presents a **trajectory** **planning** for surgeons using rotational and translation orientation of three-dimensional Cartesian coordinates. The artificial Intelligence software precision guidance system then provides surgeons the ability to pre-plan in realtime the execution of the procedure and improve the procedure's efficacy. Increased development of such software and hardware solution could lead to further adoption of MISP and after that increase the wellbeing of patients.

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A method to consider noise in a multi-train optimisation procedure has been described which seeks to find robust solutions to the multi-train trajec- tory **planning** problem. For a small demonstration network it is shown to be effective in finding robust control strategies in the presence of two different types of uncertainty: the accuracy of the CPs (i.e. differences in applica- tion point for traction, coasting or braking relative to a planned **trajectory**), and variation in station DTs. These uncertainties were first considered sep- arately, before it was shown that they could be considered simultaneously in the optimisation, in which case it is predicted that the system will still achieve good levels of robustness. For both types of uncertainty a trade-off was observed between the robustness and the average cost function score at utilisation, which represents a combination of delay and energy costs for the train **trajectory** solution. The aim here was to explore the concept of including uncertainties in train **trajectory** **planning** using a simple network (technology readiness level, TRL, 2-3, proof of concept) in preparation for fu- ture application at TRL 7-9 (operational demonstration). The procedure for including training noise in the optimisation process is generalisable to include the many different uncertainties that can affect railway system operation.

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The entire tree is a complete set of trajectories from P 0 to P n P and represents a solution of the MGA **trajectory** **planning** problem. Thus, a plan is fully defined by assigning a value to the parameters in Table 1 for all legs i 0,..., n P 1 . Algorithm 1 keeps track of all the trajectories in the tree, and yields a list L containing all the possible conditions of arrival at the last reachable planet. If no **trajectory** in the set associated to leg i satisfies the phasing problem, then planet i 1 cannot be reached and the algorithm terminates. A partial or incomplete solution is the set of parameters sufficient to describe a solution up to leg i. Furthermore, if no solution to the phasing problem exists at leg i, the plan is broken and the solution is said to be infeasible at leg i. Furthermore, an upper bound on the time of flight of the entire **trajectory**, or of some legs, is introduced. Trajectories that exceed the total or partial time of flight constraint are discarded from the list. The information of infeasibility at a given transfer will be used to fill in a taboo list of broken or incomplete solutions. For each of the trajectories found, the model computes: the sum of all the deep space manoeuvres, or total v and the launch excess velocity, v 0 ; the relative velocity at the last planet, v ; the total time of flight of the **trajectory**, T. The

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Abstract—In this paper, a special class of **trajectory** optimization problems is formulized and solved. It involves the optimization of different Unmanned Vehicle (UMV) trajectories, which are coupled through reciprocal constraints. It is shown in the paper that searching for a solution to the problem at hand may stipulate not just **planning** a longer than the shortest possible path for each UMV, but also choosing slower travel speeds in order to coordinate between the UMVs. Although it seems that solving the problem possesses merits, it has been only partially treated before. Here we suggest solving it by utilizing an evolutionary approach which involves a new algorithmic feature that allows striving towards the desired optimality. The approach is demonstrated and studied through solving and simulating several **trajectory** **planning** problems. It is shown that a wide range of problems might be related to that class of problems.

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Given a set of celestial bodies, the problem of finding an optimal sequence of gravity assist manoeuvres, deep space manoeuvres (DSM) and transfer arcs connecting two or more bodies in the set is combinatorial in nature. The number of possible paths grows exponentially with the number of celestial bodies. Therefore, the design of an optimal multiple gravity assist (MGA) **trajectory** is a NP-hard mixed combinatorial-continuous problem, and its automated solution would greatly improve the assessment of multiple alternative mission options in a shorter time. This work proposes to formulate the complete automated design of a multiple gravity assist **trajectory** as an autonomous **planning** and scheduling problem. The resulting scheduled plan will provide the planetary sequence for a multiple gravity assist **trajectory** and a good estimation of the optimality of the associated trajectories. We propose the use of a two-dimensional **trajectory** model in which pairs of celestial bodies are connected by transfer arcs containing one DSM. The problem of matching the position of the planet at the time of arrival is solved by varying the pericentre of the preceding swing-by, or the magnitude of the launch excess velocity, for the first arc. By using this model, for each departure date we can generate a full tree of possible transfers from departure to destination. Each leaf of the tree represents a planetary encounter and a possible way to reach that planet. An algorithm inspired by Ant Colony Optimization (ACO) is devised to explore the space of possible plans. The ants explore the tree from departure to destination adding one node at the time: every time an ant is at a node, a probability function is used to select one of the remaining feasible directions. This approach to automatic **trajectory** **planning** is applied to the design of optimal transfers to Saturn and among the Galilean moons of Jupiter, and solutions are compared to those found through traditional genetic-algorithm-based techniques.

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