Showing papers on "Motion planning published in 2010"

A Tutorial on Graph-Based SLAM

Abstract: Being able to build a map of the environment and to simultaneously localize within this map is an essential skill for mobile robots navigating in unknown environments in absence of external referencing systems such as GPS. This so-called simultaneous localization and mapping (SLAM) problem has been one of the most popular research topics in mobile robotics for the last two decades and efficient approaches for solving this task have been proposed. One intuitive way of formulating SLAM is to use a graph whose nodes correspond to the poses of the robot at different points in time and whose edges represent constraints between the poses. The latter are obtained from observations of the environment or from movement actions carried out by the robot. Once such a graph is constructed, the map can be computed by finding the spatial configuration of the nodes that is mostly consistent with the measurements modeled by the edges. In this paper, we provide an introductory description to the graph-based SLAM problem. Furthermore, we discuss a state-of-the-art solution that is based on least-squares error minimization and exploits the structure of the SLAM problems during optimization. The goal of this tutorial is to enable the reader to implement the proposed methods from scratch.

A Survey of Motion Planning Algorithms from the Perspective of Autonomous UAV Guidance

Abstract: A fundamental aspect of autonomous vehicle guidance is planning trajectories. Historically, two fields have contributed to trajectory or motion planning methods: robotics and dynamics and control. The former typically have a stronger focus on computational issues and real-time robot control, while the latter emphasize the dynamic behavior and more specific aspects of trajectory performance. Guidance for Unmanned Aerial Vehicles (UAVs), including fixed- and rotary-wing aircraft, involves significant differences from most traditionally defined mobile and manipulator robots. Qualities characteristic to UAVs include non-trivial dynamics, three-dimensional environments, disturbed operating conditions, and high levels of uncertainty in state knowledge. Otherwise, UAV guidance shares qualities with typical robotic motion planning problems, including partial knowledge of the environment and tasks that can range from basic goal interception, which can be precisely specified, to more general tasks like surveillance and reconnaissance, which are harder to specify. These basic planning problems involve continual interaction with the environment. The purpose of this paper is to provide an overview of existing motion planning algorithms while adding perspectives and practical examples from UAV guidance approaches.

Path Planning for Autonomous Vehicles in Unknown Semi-structured Environments

Abstract: We describe a practical path-planning algorithm for an autonomous vehicle operating in an unknown semi-structured (or unstructured) environment, where obstacles are detected online by the robot’s sensors. This work was motivated by and experimentally validated in the 2007 DARPA Urban Challenge, where robotic vehicles had to autonomously navigate parking lots. The core of our approach to path planning consists of two phases. The first phase uses a variant of A* search (applied to the 3D kinematic state space of the vehicle) to obtain a kinematically feasible trajectory. The second phase then improves the quality of the solution via numeric non-linear optimization, leading to a local (and frequently global) optimum. Further, we extend our algorithm to use prior topological knowledge of the environment to guide path planning, leading to faster search and final trajectories better suited to the structure of the environment. We present experimental results from the DARPA Urban Challenge, where our robot demonstrated near-flawless performance in complex general path-planning tasks such as navigating parking lots and executing U-turns on blocked roads. We also present results on autonomous navigation of real parking lots. In those latter tasks, which are significantly more complex than the ones in the DARPA Urban Challenge, the time of a full replanning cycle of our planner is in the range of 50—300 ms.

Incremental Sampling-based Algorithms for Optimal Motion Planning

Abstract: During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs) have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the solution obtained by these algorithms have been established so far. The first contribution of this paper is a negative result: it is proven that, under mild technical conditions, the cost of the best path in the RRT converges almost surely to a non-optimal value. Second, a new algorithm is considered, called the Rapidly-exploring Random Graph (RRG), and it is shown that the cost of the best path in the RRG converges to the optimum almost surely. Third, a tree version of RRG is introduced, called the RRT$^*$ algorithm, which preserves the asymptotic optimality of RRG while maintaining a tree structure like RRT. The analysis of the new algorithms hinges on novel connections between sampling-based motion planning algorithms and the theory of random geometric graphs. In terms of computational complexity, it is shown that the number of simple operations required by both the RRG and RRT$^*$ algorithms is asymptotically within a constant factor of that required by RRT.

Incremental Sampling-based Algorithms for Optimal Motion Planning.

Abstract: During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs), have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the solution obtained by these algorithms, e.g., in terms of a given cost function, have been established so far. The purpose of this paper is to fill this gap, by designing efficient incremental samplingbased algorithms with provable optimality properties. The first contribution of this paper is a negative result: it is proven that, under mild technical conditions, the cost of the best path returned by RRT converges almost surely to a non-optimal value, as the number of samples increases. Second, a new algorithm is considered, called the Rapidly-exploring Random Graph (RRG), and it is shown that the cost of the best path returned by RRG converges to the optimum almost surely. Third, a tree version of RRG is introduced, called RRT∗, which preserves the asymptotic optimality of RRG while maintaining a tree structure like RRT. The analysis of the new algorithms hinges on novel connections between sampling-based motion planning algorithms and the theory of random geometric graphs. In terms of computational complexity, it is shown that the number of simple operations required by both the RRG and RRT∗ algorithms is asymptotically within a constant factor of that required by RRT.

LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification

Abstract: Advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of attraction for smooth non-linear systems. Here we present a feedback motion-planning algorithm which uses rigorously computed stability regions to build a sparse tree of LQR-stabilized trajectories. The region of attraction of this non-linear feedback policy “probabilistically covers” the entire controllable subset of state space, verifying that all initial conditions that are capable of reaching the goal will reach the goal. We numerically investigate the properties of this systematic non-linear feedback design algorithm on simple non-linear systems, prove the property of probabilistic coverage, and discuss extensions and implementation details of the basic algorithm.

Sampling-Based Path Planning on Configuration-Space Costmaps

Abstract: This paper addresses path planning to consider a cost function defined over the configuration space. The proposed planner computes low-cost paths that follow valleys and saddle points of the configuration-space costmap. It combines the exploratory strength of the Rapidly exploring Random Tree (RRT) algorithm with transition tests used in stochastic optimization methods to accept or to reject new potential states. The planner is analyzed and shown to compute low-cost solutions with respect to a path-quality criterion based on the notion of mechanical work. A large set of experimental results is provided to demonstrate the effectiveness of the method. Current limitations and possible extensions are also discussed.

Maneuver-Based Trajectory Planning for Highly Autonomous Vehicles on Real Road With Traffic and Driver Interaction

Abstract: This paper presents the design and first test on a simulator of a vehicle trajectory-planning algorithm that adapts to traffic on a lane-structured infrastructure such as highways. The proposed algorithm is designed to run on a fail-safe embedded environment with low computational power, such as an engine control unit, to be implementable in commercial vehicles of the near future. The target platform has a clock frequency of less than 150 MHz, 150 kB RAM of memory, and a 3-MB program memory. The trajectory planning is performed by a two-step algorithm. The first step defines the feasible maneuvers with respect to the environment, aiming at minimizing the risk of a collision. The output of this step is a target group of maneuvers in the longitudinal direction (accelerating or decelerating), in the lateral direction (changing lanes), and in the combination of both directions. The second step is a more detailed evaluation of several possible trajectories within these maneuvers. The trajectories are optimized to additional performance indicators such as travel time, traffic rules, consumption, and comfort. The output of this module is a trajectory in the vehicle frame that represents the recommended vehicle state (position, heading, speed, and acceleration) for the following seconds.

Planning under Uncertainty for Robotic Tasks with Mixed Observability

Abstract: Partially observable Markov decision processes (POMDPs) provide a principled, general framework for robot motion planning in uncertain and dynamic environments. They have been applied to various robotic tasks. However, solving POMDPs exactly is computationally intractable. A major challenge is to scale up POMDP algorithms for complex robotic tasks. Robotic systems often have mixed observability : even when a robotâ??s state is not fully observable, some components of the state may still be so. We use a factored model to represent separately the fully and partially observable components of a robotâ??s state and derive a compact lower-dimensional representation of its belief space. This factored representation can be combined with any point-based algorithm to compute approximate POMDP solutions. Experimental results show that on standard test problems, our approach improves the performance of a leading point-based POMDP algorithm by many times.

Sampling-based motion planning with temporal goals

Abstract: This paper presents a geometry-based, multi-layered synergistic approach to solve motion planning problems for mobile robots involving temporal goals. The temporal goals are described over subsets of the workspace (called propositions) using temporal logic. A multi-layered synergistic framework has been proposed recently for solving planning problems involving significant discrete structure. In this framework, a high-level planner uses a discrete abstraction of the system and the exploration information to suggest feasible high-level plans. A low-level sampling-based planner uses the physical model of the system, and the suggested high-level plans, to explore the state-space for feasible solutions. In this paper, we advocate the use of geometry within the above framework to solve motion planning problems involving temporal goals. We present a technique to construct the discrete abstraction using the geometry of the obstacles and the propositions defined over the workspace. Furthermore, we show through experiments that the use of geometry results in significant computational speedups compared to previous work. Traces corresponding to trajectories of the system are defined employing the sampling interval used by the low-level algorithm. The applicability of the approach is shown for second-order nonlinear robot models in challenging workspace environments with obstacles, and for a variety of temporal logic specifications.

Cooperative Path Planning of Unmanned Aerial Vehicles

Abstract: About the Authors. Series Preface. Preface. Acknowledgements. List of Figures. List of Tables. Nomenclature. 1. Introduction. 1.1 Path Planning Formulation. 1.2 Path Planning Constraints. 1.3 Cooperative Path Planning and Mission Planning. 1.4 Path Planning - An Overview. 1.5 The Road Map Method. 1.6 Probabilistic Methods. 1.7 Potential Field. 1.8 Cell Decomposition. 1.9 Optimal Control. 1.10 Optimization Techniques. 1.11 Trajectories for Path Planning. 1.12 Outline of the Book. References. 2. Path Planning in Two Dimensions. 2.1 Dubins Paths. 2.2 Designing Dubins Path using Analytical Geometry. 2.3 Existence of Dubins Paths. 2.4 Length of Dubins Paths. 2.5 Design of Dubins Paths using Principles of Differential Geometry. 2.6 Path of Continuous Curvature. 2.7 Producing Flyable Clothoid Paths. 28 Producing Flyable Pythagorean Hodograph Paths (2D). References. 3. Path Planning in Three Dimensions. 3.1 Dubins Paths in Three Dimensions Using Differential Geometry. 3.2 Path Length - Dubins 3D. 3.3 Pythagorean Hodograph Paths - 3D. 3.4 Design of Flyable Paths Using PH Curves. References. 4. Collision Avoidance. 4.1 Research into Obstacle Avoidance. 4.2 Obstacle Avoidance for Mapped Obstacles. 4.3 Obstacle Avoidance of Unmapped Static Obstacles. 4.4 Algorithmic Implementation. References. 5. Path-Following Guidance. 5.1 Path Following the Dubins Path. 5.2 Linear Guidance Algorithm. 5.3 Nonlinear Dynamic Inversion Guidance. 5.4 Dynamic Obstacle Avoidance Guidance. References. 6. Path Planning for Multiple UAVs. 6.1 Problem Formulation. 6.2 Simultaneous Arrival. 6.3 Phase I: Producing Flyable Paths. 6.4 Phase II: Producing Feasible Paths. 6.5 Phase III: Equalizing Path Length. 6.6 Multiple Path Algorithm. 6.7 Algorithm Application for Multiple UAVs. 6.8 2D Pythagorean Hodograph Paths. 6.9 3D Dubins Paths. 6.10 3D Pythagorean Hodograph Paths. References. Appendix A Differential Geometry. Appendix B. Pythagorean Hodograph. Index.

LQG-MP: Optimized Path Planning for Robots with Motion Uncertainty and Imperfect State Information

Abstract: In this paper we present LQG-MP (linear-quadratic Gaussian motion planning), a new approach to robot motion planning that takes into account the sensors and the controller that will be used during the execution of the robot’s path. LQG-MP is based on the linear-quadratic controller with Gaussian models of uncertainty, and explicitly characterizes in advance (i.e. before execution) the a priori probability distributions of the state of the robot along its path. These distributions can be used to assess the quality of the path, for instance by computing the probability of avoiding collisions. Many methods can be used to generate the required ensemble of candidate paths from which the best path is selected; in this paper we report results using rapidly exploring random trees (RRT). We study the performance of LQG-MP with simulation experiments in three scenarios: (A) a kinodynamic car-like robot, (B) multi-robot planning with differential-drive robots, and (C) a 6-DOF serial manipulator. We also present a method that applies Kalman smoothing to make paths Ck-continuous and apply LQG-MP to precomputed roadmaps using a variant of Dijkstra’s algorithm to efficiently find high-quality paths.

A Simple Adaptive Control Approach for Trajectory Tracking of Electrically Driven Nonholonomic Mobile Robots

Abstract: Almost all existing controllers for nonholonomic mobile robots are designed without considering the actuator dynamics. This is because the presence of the actuator dynamics increases the complexity of the system dynamics, and makes difficult the design of the controller. In this paper, we propose a simple adaptive control approach for path tracking of uncertain nonholonomic mobile robots incorporating actuator dynamics. All parameters of robot kinematics, robot dynamics, and actuator dynamics are assumed to be uncertain. For the simple controller design, the dynamic surface control methodology is applied and extended to mobile robots that the number of inputs and outputs is different. We also adopt the adaptive control technique to treat all uncertainties and derive adaptation laws from the Lyapunov stability theory. Finally, simulation results demonstrate the effectiveness of the proposed controller.

A probabilistic model for estimating driver behaviors and vehicle trajectories in traffic environments

Abstract: This paper presents a filter that is able to simultaneously estimate the behaviors of traffic participants and anticipate their future trajectories. This is achieved by recognizing the type of situation derived from the local situational context, which subsumes all information relevant for the drivers decision making. By explicitly taking into account the interactions between vehicles, it achieves a comprehensive situational understanding, inevitable for autonomous vehicles and driver assistance systems. This provides the necessary information for safe behavior decision making or motion planning. The filter is modeled as a Dynamic Bayesian Network. The factored state space, modeling the causal dependencies, allows to describe the models in a compact fashion and reduces the computational complexity of the inference process. The filter is evaluated in the context of a highway scenario, showing a good performance even with very noisy measurements. The presented framework is intended to be used in traffic environments but can be easily transferred to other robotic domains.

Combined task and motion planning for mobile manipulation

Abstract: We present a hierarchical planning system and its application to robotic manipulation. The novel features of the system are: 1) it finds high-quality kinematic solutions to task-level problems; 2) it takes advantage of subtask-specific irrelevance information, reusing optimal solutions to state-abstracted sub-problems across the search space. We briefly describe how the system handles uncertainty during plan execution, and present results on discrete problems as well as pick-and-place tasks for a mobile robot.

Push-grasping with dexterous hands: Mechanics and a method

Abstract: We add to a manipulator's capabilities a new primitive motion which we term a push-grasp. While significant progress has been made in robotic grasping of objects and geometric path planning for manipulation, such work treats the world and the object being grasped as immovable, often declaring failure when simple motions of the object could produce success. We analyze the mechanics of push-grasping and present a quasi-static tool that can be used both for analysis and simulation. We utilize this analysis to derive a fast, feasible motion planning algorithm that produces stable pushgrasp plans for dexterous hands in the presence of object pose uncertainty and high clutter. We demonstrate our algorithm extensively in simulation and on HERB, a personal robotics platform developed at Intel Labs Pittsburgh.

Global Manipulation Planning in Robot Joint Space With Task Constraints

Abstract: We explore global randomized joint-space path planning for articulated robots that are subjected to task-space constraints. This paper describes a representation of constrained motion for joint-space planners and develops two simple and efficient methods for constrained sampling of joint configurations: tangent-space sampling (TS) and first-order retraction (FR). FR is formally proven to provide global sampling for linear task-space transformations. Constrained joint-space planning is important for many real-world problems, which involves redundant manipulators. On the one hand, tasks are designated in workspace coordinates: to rotate doors about fixed axes, to slide drawers along fixed trajectories, or to hold objects level during transport. On the other hand, joint-space planning gives alternative paths that use redundant degrees of freedom (DOFs) to avoid obstacles or satisfy additional goals while performing a task. We demonstrate that our methods are faster and more invariant to parameter choices than the techniques that exist.

Object Detection and Tracking for Autonomous Navigation in Dynamic Environments

Abstract: We address the problem of vision-based navigation in busy inner-city locations, using a stereo rig mounted on a mobile platform. In this scenario semantic information becomes important: rather than modeling moving objects as arbitrary obstacles, they should be categorized and tracked in order to predict their future behavior. To this end, we combine classical geometric world mapping with object category detection and tracking. Object-category-specific detectors serve to find instances of the most important object classes (in our case pedestrians and cars). Based on these detections, multi-object tracking recovers the objects’ trajectories, thereby making it possible to predict their future locations, and to employ dynamic path planning. The approach is evaluated on challenging, realistic video sequences recorded at busy inner-city locations.

Goal Babbling Permits Direct Learning of Inverse Kinematics

Abstract: We present an approach to learn inverse kinematics of redundant systems without prior- or expert-knowledge. The method allows for an iterative bootstrapping and refinement of the inverse kinematics estimate. The essential novelty lies in a path-based sampling approach: we generate training data along paths, which result from execution of the currently learned estimate along a desired path towards a goal. The information structure thereby induced enables an efficient detection and resolution of inconsistent samples solely from directly observable data. We derive and illustrate the exploration and learning process with a low-dimensional kinematic example that provides direct insight into the bootstrapping process. We further show that the method scales for high dimensional problems, such as the Honda humanoid robot or hyperredundant planar arms with up to 50 degrees of freedom.

Planning and Implementing Trajectories for Autonomous Underwater Vehicles to Track Evolving Ocean Processes Based on Predictions from a Regional Ocean Model

Abstract: Path planning and trajectory design for autonomous underwater vehicles (AUVs) is of great importance to the oceanographic research community because automated data collection is becoming more prevalent. Intelligent planning is required to maneuver a vehicle to high-valued locations to perform data collection. In this paper, we present algorithms that determine paths for AUVs to track evolving features of interest in the ocean by considering the output of predictive ocean models. While traversing the computed path, the vehicle provides near-real-time, in situ measurements back to the model, with the intent to increase the skill of future predictions in the local region. The results presented here extend preliminary developments of the path planning portion of an end-to-end autonomous prediction and tasking system for aquatic, mobile sensor networks. This extension is the incorporation of multiple vehicles to track the centroid and the boundary of the extent of a feature of interest. Similar algorithms to those presented here are under development to consider additional locations for multiple types of features. The primary focus here is on algorithm development utilizing model predictions to assist in solving the motion planning problem of steering an AUV to high-valued locations, with respect to the data desired. We discuss the design technique to generate the paths, present simulation results and provide experimental data from field deployments for tracking dynamic features by use of an AUV in the Southern California coastal ocean.

Kinodynamic Motion Planning

Abstract: This article extends the capabilities of the harmonic potential field (HPF) approach to planning to cover both the kinematic and dynamic aspects of a robot's motion. The suggested approach converts the gradient guidance field from a harmonic potential to a control signal by augmenting it with a novel type of damping forces called nonlinear, anisotropic, damping forces (NADF). The HPF (harmonic potential field) approach to planning is emerging as a powerful paradigm for the guidance of autonomous agents.

LTLMoP: Experimenting with language, Temporal Logic and robot control

Abstract: The Linear Temporal Logic MissiOn Planning (LTLMoP) toolkit is a software package designed to assist in the rapid development, implementation, and testing of high-level robot controllers. In this toolkit, structured English and Linear Temporal Logic are used to write high-level reactive task specifications, which are then automatically transformed into correct robot controllers that can be used to drive either a simulated or a real robot. LTLMoP's modular design makes it ideal for research in areas such as controller synthesis, semantic parsing, motion planning, and human-robot interaction.

Motion Planning With Dynamics by a Synergistic Combination of Layers of Planning

Abstract: To efficiently solve challenges related to motion-planning problems with dynamics, this paper proposes treating motion planning not just as a search problem in a continuous space but as a search problem in a hybrid space consisting of discrete and continuous components. A multilayered framework is presented which combines discrete search and sampling-based motion planning. This framework is called synergistic combination of layers of planning ( SyCLoP) hereafter. Discrete search uses a workspace decomposition to compute leads, i.e., sequences of regions in the neighborhood that guide sampling-based motion planning during the state-space exploration. In return, information gathered by motion planning, such as progress made, is fed back to the discrete search. This combination allows SyCLoP to identify new directions to lead the exploration toward the goal, making it possible to efficiently find solutions, even when other planners get stuck. Simulation experiments with dynamical models of ground and flying vehicles demonstrate that the combination of discrete search and motion planning in SyCLoP offers significant advantages. In fact, speedups of up to two orders of magnitude were obtained for all the sampling-based motion planners used as the continuous layer of SyCLoP.

Path Planning for Virtual Human Motion Using Improved A* Star Algorithm

Abstract: Calculating and generating optimal motion path automatically is one of the key issues in virtual human motion path planning. To solve the point, the improved A* algorithm has been analyzed and realized in this paper, we modified the traditional A* algorithm by weighted processing of evaluation function, which made the searching steps reduced from 200 to 80 and searching time reduced from 4.359s to 2.823s in the feasible path planning. The artificial searching marker, which can escape from the barrier trap effectively and quickly, is also introduced to avoid searching the invalid region repeatedly, making the algorithm more effective and accurate in finding the feasible path in unknown environments. We solve the issue of virtual human's obstacle avoidance and navigation through optimizing the feasible path to get the shortest path.

Sampling-Based Motion and Symbolic Action Planning with geometric and differential constraints

Abstract: To compute collision-free and dynamically-feasibile trajectories that satisfy high-level specifications given in a planning-domain definition language, this paper proposes to combine sampling-based motion planning with symbolic action planning. The proposed approach, Sampling-based Motion and Symbolic Action Planner (SMAP), leverages from sampling-based motion planning the underlying idea of searching for a solution trajectory by selectively sampling and exploring the continuous space of collision-free and dynamically-feasible motions. Drawing from AI, SMAP uses symbolic action planning to identify actions and regions of the continuous space that sampling-based motion planning can further explore to significantly advance the search. The planning layers interact with each-other through estimates on the utility of each action, which are computed based on information gathered during the search. Simulation experiments with dynamical models of vehicles carrying out tasks given by high-level STRIPS specifications provide promising initial validation, showing that SMAP efficiently solves challenging problems.

SLAM-based robotic wheelchair navigation system designed for confined spaces

Abstract: In the present work, a robotic wheelchair navigation system which is specially designed for confined spaces is proposed. In confined spaces, the movements of wheelchairs are restricted by the environment more than other unicycle type vehicles. For example, if the wheelchair is too close to a wall, it can not rotate freely because the front or back may collide with the wall. The navigation system is composed by a path planning module and a control module; both use the environment and robot information provided by a SLAM algorithm to attain their objectives. The planning strategy uses the Monte Carlo technique to find a minimum path within the confined environment and takes into account the variance propagation in the predicted path for ensuring the safe driving of the robot. The objective of the navigation system is to drive the robotic wheelchair within the confined environment in order to reach a desired orientation or posture.

Planning short paths with clearance using explicit corridors

Abstract: A central problem of applications dealing with virtual environments is planning a collision-free path for a character. Since environments and their characters are growing more realistic, a character's path needs to be visually convincing, meaning that the path is smooth, short, has some clearance to the obstacles in the environment, and avoids other characters. Up to now, it has proved difficult to meet these criteria simultaneously and in real-time. We introduce a new data structure, i.e. the Explicit Corridor Map, which allows creating the shortest path, the path that has the largest amount of clearance, or any path in between. Besides being efficient, the corresponding algorithms are surprisingly simple. By integrating the data structure and algorithms into the Indicative Route Method, we show that visually convincing short paths can be obtained in real-time.

The study of ship collision avoidance route planning by ant colony algorithm

Abstract: Maritime traffic is becoming more complex every day. At present, due to technological advances and to new maritime regulations, there is increasing demand for new nautical marine instruments to be installed into the bridge, and the breadth of navigational information complicates on-duty officers' decisions. Therefore, if decision support tools can be used to help deal with navigational decision-making, human errors arising from subjective judgments can be reduced, and sea transport safety improved. This research uses the concept of e-navigation as a framework, positioning collision avoidance path planning as the main theme, and applies an Ant Colony Algorithm (ACA) in the field of artificial intelligence to construct a collision avoidance model that imitates optimization behaviors in real-life applications. This model combines navigational practices, a maritime laws/regulations knowledge base and real-time navigation information from the AIS to plan a safe and economical collision avoidance path. Through using such planning, recommendations can be made for collision avoidance and return to course. Lastly, a Geographic Information System (GIS) was used as the platform for a navigation decision support system, combining related navigation information, collision avoidance models and electronic charts. This is a source of reference for VTS (Vessel Traffic Service) operators and on-duty officers to assess collisions in territorial waters, achieving objectives such as warning and pre-collision preparations.

An optimization variant of multi-robot path planning is intractable

Abstract: An optimization variant of a problem of path planning for multiple robots is addressed in this work. The task is to find spatial-temporal path for each robot of a group of robots such that each robot can reach its destination by navigating through these paths. In the optimization variant of the problem, there is an additional requirement that the makespan of the solution must be as small as possible. A proof of the claim that optimal path planning for multiple robots is NP-complete is sketched in this short paper.

Search-based planning for manipulation with motion primitives

Abstract: Heuristic searches such as A* search are highly popular means of finding least-cost plans due to their generality, strong theoretical guarantees on completeness and optimality and simplicity in the implementation. In planning for robotic manipulation however, these techniques are commonly thought of as impractical due to the high-dimensionality of the planning problem. In this paper, we present a heuristic search-based manipulation planner that does deal effectively with the high-dimensionality of the problem. The planner achieves the required efficiency due to the following three factors: (a) its use of informative yet fast-to-compute heuristics; (b) its use of basic (small) motion primitives as atomic actions; and (c) its use of ARA* search which is an anytime heuristic search with provable bounds on solution suboptimality. Our experimental analysis on a real mobile manipulation platform with a 7-DOF robotic manipulator shows the ability of the planner to solve manipulation in cluttered spaces by generating consistent, low-cost motion trajectories while providing guarantees on completeness and bounds on suboptimality.