Mobile Robots Perception & Navigation Part 7 docx

Comparative Analysis of Mobile Robot Localization Methods Based On Proprioceptive and Exteroceptive Sensors 231 The room has been modelled very carefully, permitting a precise evaluation of the distance and angle errors between the final position and the corresponding configuration estimated by the Algorithm 4; Table 5 resumes these results. final position error 0.0061 Alg 4 θ Δ 0.27 Table 5. Estimation distance errors (in meters) and corresponding angular errors (in degrees). In order to investigate further the efficiency of the developed Algorithm 4 and to evaluate its correction performances, it has been imposed a wrong initial position (see Table 6 and Fig. 8). error of initial position error of final position error 0.2236 0.0152 θ Δ 1.5 0.73 Table 6. Distance (in meters) and angle (in degrees) errors introduced on the initial position and corresponding errors on the final position. Fig. 8. Estimated trajectory with a wrong initial positioning. As a result, it has been seen that the Algorithm 4 is able to correct possible errors on the initial positioning, as confirmed by the results reported in Table 6. 4.4 Comments As shown by the developed experimental tests (see Table 4), Algorithm 4 permits to obtain a much more reliable and accurate positioning than that one obtained by Algorithm 3. Note that estimation errors on the final position of the Algorithm 3 are due to the angle drift introduced by the gyroscope. Additionally, Algorithm 4 improves the positioning accuracy in spite of a wrong initial positioning. Table 6 shows as the possible errors introduced by a wrong initial pose, have been efficiently corrected by the Extended Kalman Filter. 232 Mobile Robots, Perception & Navigation 5. Concluding remarks This chapter has presented a concise look at the problems and methods relative to the mobile robot localization. Both the relative and absolute approaches have been discussed. Relative localization has the main advantage of using a sensor equipment which is totally self-contained in the robot. It is relatively simple to be used and guarantees a high data rate. The main drawback is that the localization errors may considerably grow over time. The three corresponding algorithms which have been proposed only use odometric and gyroscopic measures. The experimental tests relative to Algorithm 1 show that the incremental errors of the encoder readings heavily affect the orientation estimate, thus reducing the applicability of the algorithm to short trajectories. A significant improvement is introduced by Algorithm 2 where the odometric measures are integrated with the angular measures provided by a gyroscope. Algorithm 3 uses the same measures of Algorithm 2 but operates in a stochastic framework. The localization problem is formulated as a state estimation problem and a very accurate estimate of the robot localization is obtained through a suitably defined EKF. A further notable improvement is provided by the fusion of the internal measures with absolute laser measures. This is clearly evidenced by Algorithm 4 where an EKF is again used. A novelty of the EKF algorithms used here is that the relative state-space forms include all the available information, namely both the information carried by the vehicle dynamics and by the sensor readings. The appealing features of this approach are: • The possibility of collecting all the available information and uncertainties of a different kind in the compact form of a meaningful state-space representation, • The recursive structure of the solution, • The modest computational effort. Other previous, significant experimental tests have been performed at our Department using sonar measures instead of laser readings (Bonci et al., 2004; Ippoliti et al., 2004). Table 7 reports a comparison of the results obtained with Algorithm 3, Algorithm 4, and the algorithm (Algorithm 4(S)) based on an EKF fusing together odometric, gyroscopic and sonar measures. The comparative evaluation refers to the same relatively long trajectory used for Algorithm 4. Alg 3 Alg 4 Alg 4(S) error 0.8079 0.0971 0.1408 θ Δ 2. 4637 0.7449 1. 4324 Table 7. Estimation errors (in meters) in correspondence of the final vehicle configuration (distance between the actual and the corresponding estimated configuration) and corresponding angular errors (in degrees). Table 7 evidences that in spite of a higher cost with respect to the sonar system, the localization procedure based on odometric, inertial and laser measures does really seem to be an effective tool to deal with the mobile robot localization problem. A very interesting and still open research field is the Simultaneous Localization and Map Building (SLAM) problem. It consists in defining a map of the unknown environment and simultaneously using this map to estimate the absolute location of the vehicle. An efficient solution of this problem appears to be of a dominant importance because it would definitely confer autonomy to the vehicle. The SLAM problem has been deeply investigated in (Leonard et al., 1990; Levitt & Lawton, 1990; Cox, 1991; Barshan & Durrant-Whyte, 1995; Kobayashi et al., 1995; Thrun et al., 1998; Sukkarieh et al., 1999; Roumeliotis & Bekey, 2000; Comparative Analysis of Mobile Robot Localization Methods Based On Proprioceptive and Exteroceptive Sensors 233 Antoniali & Orialo, 2001; Castellanos et al., 2001; Dissanayake et al., 2001a; Dissanayake et al., 2001b; Zunino & Christensen, 2001; Guivant et al., 2002; Williams et al., 2002; Zalama et al., 2002; Rekleitis et al., 2003)). The algorithms described in this chapter, represent a solid basis of theoretical background and practical experience from which the numerous questions raised by SLAM problem can be solved, as confirmed by the preliminary results in (Ippoliti et al., 2004; Ippoliti et al., 2005). 6. References Anderson, B.D.O. & Moore, J.B. (1979). Optimal Filtering. Prentice-Hall, Inc, Englewood Cliffs Antoniali, F.M. & Oriolo, G. (2001). Robot localization in nonsmooth environments: experiments with a new filtering technique, Proceedings of the IEEE International Conference on Robotics and Automation (2001 ICRA), Vol. 2, pp. 1591–1596 Arras, K.O.; Tomatis, N. & Siegwart, R. (2000). Multisensor on-the-fly localization using laser and vision, Proceedings of the 2000 IEEE/RSJ International Conference onIntelligent Robots and Systems, (IROS 2000), Vol. 1, pp. 462–467 Barshan, B. & Durrant-Whyte, H.F. (1995). Inertial navigation systems for mobile robots. 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IEEE Transactions on Robotics and Automation, Vol. 17, No. 3, pp. 229–241 234 Mobile Robots, Perception & Navigation Dissanayake, G.; Sukkarieh, S.; Nebot, E. & Durrant-Whyte, H.F. (2001b). The aiding of a low-cost strapdown inertial measurement unit using vehicle model constraints for land vehicle applications. IEEE Transactions on Robotics and Automation, Vol. 17, pp. 731–747 Durrant-Whyte, H.F. (1988). Sensor models and multisensor integration. International Journal of Robotics Research, Vol. 7, No. 9, pp. 97–113 Fioretti, S.; Leo, T. & Longhi, S. (2000). A navigation system for increasing the autonomy and the security of powered wheelchairs. IEEE Transactions on Rehabilitation Engineering, Vol. 8, No. 4, pp. 490–498 Garcia, G.; Bonnifait, Ph. & Le Corre, J F. (1995). A multisensor fusion localization algorithm with self-calibration of error-corrupted mobile robot parameters, Proceedings of the International Conference in Advanced Robotics, ICAR’95, pp. 391–397, Barcelona, Spain Gu, J.; Meng, M.; Cook, A. & Liu, P.X. (2002). Sensor fusion in mobile robot: some perspectives, Proceedings of the 4th World Congress on Intelligent Control and Automation, Vol. 2, pp. 1194–1199 Guivant, J.E.; Masson, F.R. & Nebot, E.M. (2002). Simultaneous localization and map building using natural features and absolute information. In: Robotics and Autonomous Systems, pp. 79–90 Ippoliti, G.; Jetto, L.; La Manna, A. & Longhi, S. (2004). Consistent on line estimation of environment features aimed at enhancing the efficiency of the localization procedure for a powered wheelchair, Proceedings of the Tenth International Symposium on Robotics with Applications - World Automation Congress (ISORA-WAC 2004), Seville, Spain Ippoliti, G.; Jetto, L.; La Manna, A. & Longhi, S. (2005). Improving the robustness properties of robot localization procedures with respect to environment features uncertainties, Proceedings of the IEEE International Conference on Robotics and Automation (ICRA 2005), Barcelona, Spain Jarvis, R.A. (1992). Autonomous robot localisation by sensor fusion, Proceedings of the IEEE International Workshop on Emerging Technologies and Factory Automation, pp. 446–450 Jetto, L.; Longhi, S. & Venturini, G. (1999). Development and experimental validation of an adaptive extended Kalman filter for the localization of mobile robots. IEEE Transactions on Robotics and Automation, Vol. 15, pp. 219–229 Killian, K. (1994). Pointing grade fiber optic gyroscope, Proceedings of the IEEE Symposium on Position Location and Navigation, pp. 165–169, Las Vegas, NV,USA Kobayashi, K.; Cheok, K.C.; Watanabe, K. & Munekata, F. (1995). Accurate global positioning via fuzzy logic Kalman filter-based sensor fusion technique, Proceedings of the 1995 IEEE IECON 21st International Conference on Industrial Electronics, Control, and Instrumentation, Vol. 2, pp. 1136–1141, Orlando, FL ,USA Komoriya, K. & Oyama, E. (1994). Position estimation of a mobile robot using optical fiber gyroscope (ofg), Proceedings of the 1994 International Conference on Intelligent Robots and Systems (IROS’94), pp. 143–149, Munich, Germany Leonard, J.; Durrant-Whyte, H.F. & Cox, I. (1990). Dynamic map building for autonomous mobile robot, Proceedings of the IEEE International Workshop on Intelligent Robots and Systems (IROS ’90), Vol. 1, pp. 89–96, Ibaraki, Japan Comparative Analysis of Mobile Robot Localization Methods Based On Proprioceptive and Exteroceptive Sensors 235 Levitt, T.S. & Lawton, D.T. (1990). Qualitative navigation for mobile robots. Artificial Intelligence Journal, Vol. 44, No. 3, pp. 305–360 Mar, J. & Leu, J H. (1996). Simulations of the positioning accuracy of integrated vehicular navigation systems. IEE Proceedings - Radar, Sonar and Navigation, Vol. 2, No. 143, pp. 121–128 Martinelli, A. (2002). The odometry error of a mobile robot with a synchronous drive system. IEEE Transactions on Robotics and Automation, Vol. 18, No. 3, pp. 399–405 Ojeda, L.; Chung, H. & Borenstein, J. (2000). Precision-calibration of fiber-optics gyroscopes for mobile robot navigation, Proceedings of the 2000 IEEE International Conference on Robotics and Automation, pp. 2064–2069, San Francisco, CA, USA Panzieri, S.; Pascucci, F. & Ulivi, G. (2002). An outdoor navigation system using GPS and inertial platform. IEEE/ASME Transactions on Mechatronics, Vol. 7, No. 2, pp. 134–142 Rekleitis, I.; Dudek, G. & Milios, E. (2003). Probabilistic cooperative localization and mapping in practice, Proceedings of the IEEE International Conference on Robotics and Automation (ICRA ’03), Vol. 2, pp. 1907 – 1912 Roumeliotis, S.I. & Bekey, G.A. (2000). Bayesian estimation and Kalman filtering: a unified framework for mobile robot localization, Proceedings of the IEEE International Conference on Robotics and Automation (ICRA ’00), Vol. 3, pp. 2985–2992, San Francisco, CA, USA Sukkarieh, S.; Nebot, E.M. & Durrant-Whyte, H.F. (1999). A high integrity IMU GPS navigation loop for autonomous land vehicle applications. IEEE Transactions on Robotics and Automation, Vol. 15, pp. 572–578 Talluri, R. & Aggarwal, J.K. (1992). Position estimation for an autonomous mobile robot in an outdoor environment. IEEE Transactions on Robotics and Automation, Vol. 8, No. 5, pp. 573–584 TGR Bologna (2000). TGR Explorer. Italy [Online]. Available on-line: http://www.tgr.it. Thrun, S.; Fox, D. & Burgard, W. (1998). A probabilistic approach to concurrent mapping and localization for mobile robots. Machine Learning Autonom. Robots, Vol. 31, pp. 29–53. Kluwer Academic Publisher, Boston Wang, C.M. (1988). Localization estimation and uncertainty analysis for mobile robots, Proceedings of the Int. Conf. on Robotics and Automation, pp. 1230–1235 Williams, S.B.; Dissanayake, G. & Durrant-Whyte, H.F. (2002). An efficient approach to the simultaneous localization and mapping problem, Proceedings of the 2002 IEEE International Conference on Robotics and Automation, pp. 406–411, Washington DC, USA Ye, C. & Borenstein, J. (2002). Characterization of a 2d laser scanner for mobile robot obstacle negotiation, Proceedings of the IEEE International Conference on Robotics and Automation (ICRA ’02), Vol. 3, pp. 2512 – 2518, Washington DC, USA Yi, Z.; Khing, H. Y.; Seng, C.C. & Wei, Z.X. (2000). Multi-ultrasonic sensor fusion for mobile robots, Proceedings of the IEEE Intelligent Vehicles Symposium, Vol. 1, pp. 387–391, Dearborn, MI, USA Zalama, E.; Candela, G.; Gómez, J. & Thrun, S. (2002). Concurrent mapping and localization for mobile robots with segmented local maps, Proceedings of the 2002 IEEE/RSJ Conference on Intelligent Robots and Systems, pp. 546–551, Lausanne, Switzerland 236 Mobile Robots, Perception & Navigation Zhu, R.; Zhang, Y. & Bao, Q. (2000). A novel intelligent strategy for improving measurement precision of FOG. IEEE Transactions on Instrumentation and Measurement, Vol. 49, No. 6, pp. 1183–1188 Zhuang, W. & Tranquilla, J. (1995). Modeling and analysis for the GPS pseudo-range observable. IEEE Transactions on Aerospace and Electronic Systems, Vol. 31, No. 2, pp. 739–751 Zunino, G. & Christensen, H.I. (2001). Simultaneous localization and mapping in domestic environments, Proceedings of the International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2001), pp. 67–72 12 Composite Models for Mobile Robot Offline Path Planning Ellips Masehian, M. R. Amin-Naseri Tarbiat Modares University Iran 1. Introduction As new technological achievements take place in the robotic hardware field, an increased level of intelligence is required as well. The most fundamental intelligent task for a mobile robot is the ability to plan a valid path from its initial to terminal configurations while avoiding all obstacles located on its way. The robot motion planning problem came into existence in early 70’s and evolved to a vast and active research discipline as it is today. Numerous solution methods have been developed for robot motion planning since then, many of them being variations of a few general approaches: Roadmap, Cell Decomposition, Potential Fields, mathematical programming, and heuristic methods. Most classes of motion planning problems can be solved using these approaches, which are broadly surveyed in (Latombe, 1991), (Hwang & Ahuja, 1992), and (Choset et al., 2005). This chapter introduces two new offline path planning models which are founded on the Roadmap and Potential Fields classic motion planning approaches. These approaches have their unique characteristics and strategies for solving motion planning problems. In fact, each one has its own advantage that excels others in certain aspects. For instance, the Visibility Graph yields the shortest path; but its computational time exceeds other methods. Or, while the Voronoi Diagram plans the safest path and is easy to calculate in 2D, it often produces overly lengthy paths, and yields poor results in higher space dimensions. On the other hand, Potential Fields are easy to compute and are suitable for high dimensional problems, but they suffer from the local minima problem, and the oscillating paths generated near narrow passages of configuration space reduce their efficiency. A brief review on these underlying methods is given in this section. In order to benefit from the strong aspects of these classic path planning methods and compensate their drawbacks, a policy of combining these basic approaches into single architectures is adopted. In devising the new planners it is intended to aggregate the superiorities of these methods and work out efficient and reliable composite algorithms for robot motion planning. 1.1 Roadmap Methods The Roadmap approach involves retracting or reducing the robot’s free Configuration space (C free ) onto a network of one-dimensional lines (i.e. a graph). Motion planning is then reduced to a graph-searching problem. At first, two paths are constructed from the start and 238 Mobile Robots, Perception & Navigation goal positions to the roadmap, one for each. Then a path is planned between these points on the roadmap. The correctness of the solution strongly depends on the connectivity of the roadmap representing the entire C-space. If the roadmap does not represent the entire C- space, a solution path may be missed. The Visibility Graph is the collection of lines in the free space that connects a feature of an object to that of another. In its principal form, these features are vertices of polygonal obstacles, and there are O(n 2 ) edges in the visibility graph, which can be constructed in O(n 2 ) time and space in 2D, where n is the number of features (Hwang & Ahuja, 1992). The Reduced Generalized Visibility Graph can be constructed in O(n 3 ) time and its search performed in O(n 2 ) time. The shortest path can be found in O(n 2 logn) time using the A* algorithm with the Euclidean distance to the goal as the heuristic function (Latombe, 1991). Works such as (Oommen et al., 1987) and (Yeung & Bekey, 1987) have employed this approach for path planning. The Voronoi Diagram is defined as the set of points that are equidistant from two or more object features. Let the set of input features be denoted as s 1 , s 2 , …, s n . For each feature s i , a distance function D i (x) = Dist(s i , x) is defined. Then the Voronoi region of s i is the set V i = {x| D i (x)  D j (x) ∀ j ≠ i }. The Voronoi diagram partitions the space into such regions. When the edges of convex obstacles are taken as features and the C-space is in ℜ 2 , The Voronoi diagram of the C free consists of a finite collection of straight line segments and parabolic curve segments, referred to as Medial Axis, or more often, Generalized Voronoi Diagram (GVD). In an ℜ k space, the k-equidistant face is the set of points equidistant to objects C 1 , , C k such that each point is closer to objects C 1 , , C k than any other object. The Generalized Voronoi Graph (GVG) is the collection of m-equidistant faces (i.e. generalized Voronoi edges) and m+1-equidistant faces (i.e. generalized Voronoi vertices, or, meet points). The GVD is the locus of points equidistant to two obstacles, whereas the GVG is the locus of points equidistant to m obstacles. Therefore, in ℜ m , the GVD is m–1-dimensional, and the GVG, 1- dimensional. In planar case, the GVG and GVD coincide (Aurenhammer & Klein, 2000). The Voronoi diagram is attractive in two respects: there are only O(n) edges in the Voronoi diagram, and it can be efficiently constructed in ƺ(nlogn) time, where n is the number of features. The Voronoi diagram can be searched for the shortest path in O(n 2 ) time by using the Dijkstra’s method. Another advantage of Voronoi method is the fact that the object’s initial connectedness is directly transferred to the diagram (Hwang & Ahuja, 1992). In (Canny, 1985) and (Choset & Burdick, 2000) the Voronoi diagram is used for planning robot paths. For higher-dimensional spaces than 2D, both the Visibility graph and the Voronoi diagram have higher complexities, and it is not obvious what to select for the features. For example, the Voronoi diagram among polyhedra is a collection of 2D faces, which is not a 1D roadmap (Agarwal et al., 1998). The Silhouette method has been developed at early stages of the motion planning discipline, and is complex to implement. Its time complexity is in O(2 m ), where m is the dimension of the C-space, and is mostly used in theoretical algorithms analyzing complexity, rather than developing practical algorithms. A path found from the silhouette curves makes the robot slide along obstacle boundaries (Canny, 1988). Probabilistic Roadmaps use randomization to construct a graph in C-space. Roadmap nodes correspond to collision-free configurations of the robot. Two nodes are connected by an Composite Models for Mobile Robot Offline Path Planning 239 edge if a path between the two corresponding configurations can be found by a ‘local planning’ method. Queries are processed by connecting the initial and goal configurations to the roadmap, and then finding a path in the roadmap between these two connection points (Kavraki et al., 1996). 1.2 The Potential Fields Method A robot in Potential Fields method is treated as a point represented in configuration space, and as a particle under the influence of an artificial potential field U whose local variations reflect the ‘structure’ of the free space (Khatib, 1986). In order to make the robot attracted toward its goal configuration while being repulsed from the obstacles, U is constructed as the sum of two elementary potential functions; attractive potential associated with the goal configuration q goal and repulsive potential associated with the C-obstacle region. Motion planning is performed in an iterative fashion. At each iteration, the artificial force induced by the potential function at the current configuration is regarded as the most appropriate direction of motion, and path planning proceeds along this direction by some increment. The most serious problem with the Potential Fields method is the presence of local minima caused by the interaction of attractive and repulsive potentials, which results in a cyclic motion. The routine method for getting free is to take a random step outwards the minimum well. Other drawbacks are (Koren & Borenstein, 1991): - No passage between closely spaced obstacles. - Oscillations in the presence of obstacles or in narrow passages. - Non-smooth movements of the robot when trying to extricate from a local minimum. - Overlapping of different obstacles’ repulsive potentials when they are adjacent to each other. - Difficulty in defining potential parameters properly. Nevertheless, the Potential Fields method remains as a major path-planning approach, especially when high degrees of freedoms are involved. This approach has improved later through a number of works such as (Sato, 1993), (Brook & Khatib, 1999) and (Alvarez et al., 2003) to overcome the problem of getting trapped in local minima. The next sections of this chapter introduce two new composite models for robot path planning, called V-P Hybrid, and V-V-P Compound. They are apt to cover the shortcomings of their original methods and are efficient both in time complexity and path quality. Although originally devised for two-dimensional workspaces, they can be extended straightforwardly to 3D spaces. Experiments have shown their strength in solving a wide variety of problems. 2. The V-P Hybrid Model In this section we present a new algorithm, called V-P Hybrid, where the concepts of Voronoi diagram and Potential fields are combined to integrate the advantages of each. In this approach, the initial path planning problem is decomposed to a number of smaller tasks, having intermediate milestones as temporary start and goal points. Through this iterative process the global path is incrementally constructed. For the path planning task, a number of assumptions are made: (i) the map of workspace is known a priori, (ii) the obstacles are static, and (iii) the robot is considered a point. For real world applications, the latter assumption can be attained by expanding the obstacles using the Minkowski Set Difference method. 240 Mobile Robots, Perception & Navigation The algorithm’s major steps are: (1) Preprocessing Phase; consisted of constructing a Pruned Generalized Voronoi Graph of the workspace, and then applying a Potential Field to it. This operation yields a network of Voronoi valleys (Sec. 2.1). (2) Search Phase; consisted of implementing a bidirectional steepest descent – mildest ascent search method to navigate through the network of Voronoi valleys. The search phase is designed to progressively build up a start-to-goal path (Sec. 2.2). Before explaining the details of the composite model, a mathematical representation of some variables is given: - n : Total number of obstacles’ vertices. - s : The Start configuration. - g : The Goal configuration. - G = (V, E): The Generalized Voronoi Graph (GVG) of the C free with the set of vertices (nodes) V(G) and edges E(G). - E(v, w): The edge connecting vertices v and w , ∀ v, w ∈ V(G). - N(v) = {w ⏐ E(v, w) ≠ ∅} : Neighboring vertices of the vertex v. - E(v): The set of all edges at vertex v. - d(v) = ⏐ E(v) ⏐ : The degree of vertex v, equal to the number of passing edges. 2.1 Preprocessing Phase The V-P Hybrid model starts solving the problem by constructing the Generalized Voronoi Graph (GVG) of the C-space. The Start and Goal configurations are then connected to the main Voronoi graph through shortest lines which are also included in the diagram. Fig. 1(a) provides an example of GVG. Fig. 1. (a) Generalized Voronoi Graph (GVG). (b) Algorithm for pruning the GVG. The main reason for incorporating the Voronoi concept in the Hybrid algorithm is its property of lying on the maximum clearance from the obstacles. This property helps the robot to navigate at a safe distance from obstacles, making it less prone to be trapped in local minimum wells. The next step is to exclude redundant or unpromising edges from the GVG. This is done through the pruning operation, where the Voronoi edges which either touch obstacle boundaries or have vertices with a degree (d(v)) equal to 1 are iteratively truncated. The pruning procedure is explained in Fig. 1(b). Also, the result of this operation performed on Procedure PRUNE(G, s, g) P={ v ⏐ v ∈ V(G) \ {s, g}, d(v) = 1 } if (P = ∅) then Stop V(G) ł V(G) \ P E(G) ł E(G) \ E(v, N(v)), v ∈ P PRUNE(G, s, g) end [...]... RA-3, (19 87) , pp 672 -681 Sato, K (1993) Deadlock-free motion planning using the Laplace potential field, Advanced Robotics, Vol 7, No 5, 1993, pp 449-462 Yeung, D.Y & Bekey, G.A (19 87) A decentralized approach to the motion planning problem for multiple mobile robots, Proceedings of IEEE International Conference on Robotics and Automation (ICRA ‘ 87) , pp 177 9- 178 4 13 Global Navigation of Assistant Robots. .. for multiple robots motion planning Especially, the Visibility component of the Compound model can be readily applied to mobile robots teams with vision capabilities 5 References Agarwal, P.K.; de Berg, M.; Matousek, J & Schwarzkopf, O (1998) Constructing levels in arrangements and higher order Voronoi diagrams, SIAM Journal on Computing, Vol 27, 1998, pp 654-6 67 Alvarez, D.; Alvarez, J.C.; & González,... 1992), pp 224-241 Brock, O & Khatib, O (1999) High-speed navigation using the global dynamic window approach, Proceedings of IEEE International Conference on Robotics and Automation (ICRA ‘99) Canny, J.F (1985) A voronoi method for the piano movers’ problem, Proceedings of IEEE International Conference on Robotics and Automation (ICRA ’85) 262 Mobile Robots, Perception & Navigation Canny, J.F (1998)... illustrated in Fig 7 248 Mobile Robots, Perception & Navigation The main differences between the V-V-P Compound and V-P Hybrid models are the width of the potential valleys and their filling technique Additionally, the V-V-P model employs a Visibility module to obtain shorter paths than the V-P model The description of algorithm’s phases is presented in the next subsections Fig 7 The overall process... speech) and touch screen for simple command selection 264 Mobile Robots, Perception & Navigation Fig 1 Global architecture of the SIRAPEM System This chapter describes the navigation module of the SIRAPEM project, including localization, planning and learning systems A suitable framework to cope with all the requirements of this application is Partially Observable Markov Decision Processes (POMDPs) These... Fig 18(b) to display the shape of the generated path for a maze-like problem The meeting point of the approaching trajectories is shown by a color contrast The search took 7 seconds and five iterations 258 Mobile Robots, Perception & Navigation (a) (b) Fig 18 (a) The final start-to-goal path (b) Maze-like problem solved by the V-V-P algorithm 3.4 Time Complexity As discussed in the Sec 2.4, the time... (September 2003), Taiwan, pp 2928-2933 Masehian, E & Amin-Naseri, M.R (2004) A Voronoi diagram – visibility graph – potential fields compound algorithm for robot path planning, Journal of Robotic Systems, Vol 21, No 6, (June 2004), pp 275 -300 Oommen, J.B.; Iyengar, S.S.; Rao, N.S.V & Kashyap, R.L (19 87) Robot navigation in unknown terrains using visibility graphs: Part I: The disjoint convex obstacle case,... been widely used in robotics, and especially in robot navigation The robots DERVISH (Nourbakhsh et al., 1995), developed in the Stanford University, and Xavier (Koenig & Simmons, 1998), in the Carnegie Mellon University, were the first robots successfully using this kind of navigation strategies for localization and action planning Other successful robots guided with POMDPs are those proposed by (Zanichelli,... iteration 1, navigating from the Goal point towards the temporary goal, which is now the endpoint of Traj(s) The Traj(g) stops at the first encountered junction, which becomes the new 244 Mobile Robots, Perception & Navigation temporary goal Fig 5(d) illustrates iteration 2, navigating from endpoint of Traj(s) toward the temporary goal The two trajectories Traj(s) and Traj(g) are now get connected, and... the 2D method The robot should scan the space inside the Region(αMIB) to find “tangent surfaces” The Potential calculations for gridpoints is still tractable in 3D workspace, and the 260 Mobile Robots, Perception & Navigation search phase can be performed similar to the 2D V-V-P method; the Visibility and Potential Field modules will execute alternately, and the valley filling procedure will change . Vol. 17, pp. 73 1 74 7 Durrant-Whyte, H.F. (1988). Sensor models and multisensor integration. International Journal of Robotics Research, Vol. 7, No. 9, pp. 97 113 Fioretti, S.; Leo, T. &. Kalman Filter. 232 Mobile Robots, Perception & Navigation 5. Concluding remarks This chapter has presented a concise look at the problems and methods relative to the mobile robot localization Intelligent Robots and Systems, pp. 546–551, Lausanne, Switzerland 236 Mobile Robots, Perception & Navigation Zhu, R.; Zhang, Y. & Bao, Q. (2000). A novel intelligent strategy for improving