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## Tracking an omnidirectional evader with a differential drive robot, (2011)

Venue: | Autonomous Robots |

Citations: | 2 - 2 self |

### Citations

1133 | Planning Algorithms
- LaValle
- 2006
(Show Context)
Citation Context ...uer, we use the usual assignment of control inputs (Balkcom and Mason, 2002). The DDR controls its linear velocity u3 ∈ [−V maxp , V maxp ] and the rate of change of its motion direction u4. 3.2. Previous results. Previously (Murrieta-Cid et al., 2011) we presented the conditions under which it is possible for a differential drive robot (the pursuer) to track 374 U. Ruiz et al. an omnidirectional mobile evader at a constant distance. To make this paper self-contained, we include here a brief review of the most important results in that work. We have that the kinematic equations for a DDR (see LaValle, 2006) are given by u3 = Vp = (wr(t) + wl(t))R 2 , (2) u4 = θp = (wr(t) − wl(t))R 2b , (3) where u3 is the linear velocity, u4 is its angular velocity, wi is the angular velocity of the i-th wheel,R is the radius of the wheels, and b is the distance between the center of the robot and the wheel location. Without loss of generality, in what follows we will assume R = 1. Adding and subtracting Eqns. (2) and (3) and solving for u4, one obtains u4 = 1 b (wr − u3) (4) and u4 = 1 b (−wl + u3). (5) These equations mean that for a given value of wr (resp. wl) there is a linear relation between the controls... |

759 | Dynamic Noncooperative Game Theory - Basar, Olsder - 1995 |

156 | Searching for a mobile intruder in a polygonal region,
- Suzuki, Yamashita
- 1992
(Show Context)
Citation Context ...us work A lot of work has been done in the area of pursuit-evasion games (Hajek, 1965; Isaacs, 1965; Basar and Olsder, 1982), and three main problems have received a lot of attention. They include finding, tracking and capturing a mobile evader with one or several pursuers. In the finding problem (Isler et al., 2005; Hollinger et al., 2009), the objective is to establish some sort of visibility between the pursuer and the evader. In this case, the pursuer must sweep the environment so that the evader is not able to eventually sneak into an area that has already been explored. Deterministic (Suzuki and Yamashita, 1992; Guibas et al., 1999; Sachs et al., 2004; Tovar and LaValle, 2008) and probabilistic (Vidal et al., 2002; Hespanha et al., 2000; Chung, 2008) algorithms have been proposed to solve this problem. In the capturing problem, the pursuer tries to get closer than a given distance l to the evader. The goal of the evader is to keep the pursuer at all times farther from it than this capture distance. A classical problem is that of the homicidal chauffeur (Isaacs, 1965; Merz, 1971). In that game a faster pursuer (with respect to the evader) has as its objective to get closer than a given distance (the ... |

128 |
Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. Courier Dover Publications. 143 et al
- Isaacs
- 1999
(Show Context)
Citation Context ...manifold, no player controls it and this can be interpreted as a tied game. The motion strategies presented in this paper are applicable to several problems related to surveillance or capture: • They allow a DDR to maintain an omnidirectional evader within a limited sensing range defined by a maximal Lmax and a minimal Lmin sensing distances. • They allow a DDR to reduce the distance to the evader. In the remainder of the paper, we describe the conditions that make the tasks listed above possible. 2. Previous work A lot of work has been done in the area of pursuit-evasion games (Hajek, 1965; Isaacs, 1965; Basar and Olsder, 1982), and three main problems have received a lot of attention. They include finding, tracking and capturing a mobile evader with one or several pursuers. In the finding problem (Isler et al., 2005; Hollinger et al., 2009), the objective is to establish some sort of visibility between the pursuer and the evader. In this case, the pursuer must sweep the environment so that the evader is not able to eventually sneak into an area that has already been explored. Deterministic (Suzuki and Yamashita, 1992; Guibas et al., 1999; Sachs et al., 2004; Tovar and LaValle, 2008) and pr... |

106 | Algorithms for multi-robot observation of multiple targets
- Parker
- 2002
(Show Context)
Citation Context ...problem of evading surveillance. To drive the greedy motion planning algorithm, a local minimum risk function is applied, called the vantage time. In the work of O’Kane (2008), a robot has to track an unpredictable target with bounded speed. The robot’s sensors are manipulated to record general information about the target’s movements and avoid the need for detailed, potentially damaging information about the target’s position being available if the robot’s sensors are accessed by other agent. An interesting version of the problem involves multiple participants (several pursuers and evaders). Parker (2002) developed a method which attempts to minimize the total time in which the evaders escape surveillance. Jung and Sukhatme (2002) combined the application of mobile and static sensors. The authors used a metric for measuring the degree of occlusion, based on the average mean free path of a random line segment. Pursuit-evasion can be used in a variety of applications. For example, Tekdas and Yang (2010) noticed the similarity between pursuit-evasion games and mobile routing for networking. Applying this similarity, they proposed motion planning algorithms for robotic routers to maintain connecti... |

95 |
On the piano mover’s problem: I. The case of a two-dimensional rigid polygonal body moving amidst polygonal barriers
- Schwartz, Sharir
- 1983
(Show Context)
Citation Context ...mple of those problems is monitoring children with mobile robots to prevent them straying out-with a prescribed area set by their guardian. The results can also be applied for capturing an evader, i.e., moving the pursuer closer than a given distance to the evader. 3. Preliminaries 3.1. System model. Figure 1 shows the geometric description of the system. In an Euclidean plane, the OA’s position is represented by (xe, ye) and the DDR’s position by (xp, yp). We will refer to the line segment connecting these positions as the (variable length) rod, using an analogy with the problem presented by Schwartz and Sharir (1983). The length L of this rod corresponds to the distance between both players (it can be interpreted as the measure of a range sensor). The angle θp denotes the angle of the pursuer’s wheels with respect to the x-axis, and φ represents the angle of the rod (sensor’s orientation) with respect to the x-axis. ψ corresponds to the motion direction of the evader. p x y y y x x p p e e L θ ψ φ e p Fig. 1. Geometric model of the pursuer-evader system. The evolution of the system is described by the following equations of motion: xe = u1 cosu2, ye = u1 sinu2, xp = u3 cos θp, yp = u3 sin θp, θp = u4... |

91 | Randomized pursuit-evasion in a polygonal environment.
- Isler, Kannan, et al.
- 2005
(Show Context)
Citation Context ...o maintain an omnidirectional evader within a limited sensing range defined by a maximal Lmax and a minimal Lmin sensing distances. • They allow a DDR to reduce the distance to the evader. In the remainder of the paper, we describe the conditions that make the tasks listed above possible. 2. Previous work A lot of work has been done in the area of pursuit-evasion games (Hajek, 1965; Isaacs, 1965; Basar and Olsder, 1982), and three main problems have received a lot of attention. They include finding, tracking and capturing a mobile evader with one or several pursuers. In the finding problem (Isler et al., 2005; Hollinger et al., 2009), the objective is to establish some sort of visibility between the pursuer and the evader. In this case, the pursuer must sweep the environment so that the evader is not able to eventually sneak into an area that has already been explored. Deterministic (Suzuki and Yamashita, 1992; Guibas et al., 1999; Sachs et al., 2004; Tovar and LaValle, 2008) and probabilistic (Vidal et al., 2002; Hespanha et al., 2000; Chung, 2008) algorithms have been proposed to solve this problem. In the capturing problem, the pursuer tries to get closer than a given distance l to the evader. ... |

83 | A visibility-based pursuit-evasion problem.
- Guibas, Latombe, et al.
- 1999
(Show Context)
Citation Context ...en done in the area of pursuit-evasion games (Hajek, 1965; Isaacs, 1965; Basar and Olsder, 1982), and three main problems have received a lot of attention. They include finding, tracking and capturing a mobile evader with one or several pursuers. In the finding problem (Isler et al., 2005; Hollinger et al., 2009), the objective is to establish some sort of visibility between the pursuer and the evader. In this case, the pursuer must sweep the environment so that the evader is not able to eventually sneak into an area that has already been explored. Deterministic (Suzuki and Yamashita, 1992; Guibas et al., 1999; Sachs et al., 2004; Tovar and LaValle, 2008) and probabilistic (Vidal et al., 2002; Hespanha et al., 2000; Chung, 2008) algorithms have been proposed to solve this problem. In the capturing problem, the pursuer tries to get closer than a given distance l to the evader. The goal of the evader is to keep the pursuer at all times farther from it than this capture distance. A classical problem is that of the homicidal chauffeur (Isaacs, 1965; Merz, 1971). In that game a faster pursuer (with respect to the evader) has as its objective to get closer than a given distance (the capture condition) to... |

71 | Tracking targets using multiple robots: The effect of environment occlusion
- Jung, Sukhatme
- 2002
(Show Context)
Citation Context ...sented time-optimal strategies for the game of capturing an omnidirectional evader with a differential drive robot. The results presented here, although not time-optimal, have the advantage over those of Ruiz and Murrieta-Cid (2012) as well as Ruiz et al. (2013) of allowing solution of two problems: capturing an OA evader with a DDR pursuer and maintaining surveillance at a bounded variable distance of an OA with a DDR. In the tracking problem, the goal is maintaining visibility of the evader at all times, usually in an environment with obstacles (LaValle et al., 1997; Gonzalez et al., 2002; Jung and Sukhatme, 2002; Bandyopadhyay et al., 2006; Bhattacharya and Hutchinson, 2010). In recent years there has been a growing interest in related problems within the community of autonomous robots (Jung and Sukhatme, 2002; Kowalczuk and Czubenko, 2011), and specifically in robot motion planning (LaValle et al., 1997; Gonzalez et al., 2002; Murrieta-Cid et al., 2007). LaValle et al. (1997) proposed game theory as a framework to formulate the tracking problem. Becker et al. (1995) presented an algorithm that operates by maximizing the probability of future visibility of the evader. This algorithm is also studied ... |

52 | Time optimal trajectories for bounded velocity differential drive vehicles,”
- Balkcom, Mason
- 2002
(Show Context)
Citation Context ... evolution of the system is described by the following equations of motion: xe = u1 cosu2, ye = u1 sinu2, xp = u3 cos θp, yp = u3 sin θp, θp = u4, (1) where u1 ∈ [0, V maxe ] and u2 ∈ [0, 2π) are the OA’s controls, and they represent its speed and motion direction, respectively. Note that we assume that u1 takes only positive values, but since u2 takes any value between [0, 2π) after a time t the evader can reach any position inside or in the boundary of a circle with radius u1t centered at the evader’s initial position. For the DDR pursuer, we use the usual assignment of control inputs (Balkcom and Mason, 2002). The DDR controls its linear velocity u3 ∈ [−V maxp , V maxp ] and the rate of change of its motion direction u4. 3.2. Previous results. Previously (Murrieta-Cid et al., 2011) we presented the conditions under which it is possible for a differential drive robot (the pursuer) to track 374 U. Ruiz et al. an omnidirectional mobile evader at a constant distance. To make this paper self-contained, we include here a brief review of the most important results in that work. We have that the kinematic equations for a DDR (see LaValle, 2006) are given by u3 = Vp = (wr(t) + wl(t))R 2 , (2) u4 = θp = (w... |

49 | Visibility-based pursuit-evasion in an unknown planar environment.
- Sachs, LaValle, et al.
- 2004
(Show Context)
Citation Context ...f pursuit-evasion games (Hajek, 1965; Isaacs, 1965; Basar and Olsder, 1982), and three main problems have received a lot of attention. They include finding, tracking and capturing a mobile evader with one or several pursuers. In the finding problem (Isler et al., 2005; Hollinger et al., 2009), the objective is to establish some sort of visibility between the pursuer and the evader. In this case, the pursuer must sweep the environment so that the evader is not able to eventually sneak into an area that has already been explored. Deterministic (Suzuki and Yamashita, 1992; Guibas et al., 1999; Sachs et al., 2004; Tovar and LaValle, 2008) and probabilistic (Vidal et al., 2002; Hespanha et al., 2000; Chung, 2008) algorithms have been proposed to solve this problem. In the capturing problem, the pursuer tries to get closer than a given distance l to the evader. The goal of the evader is to keep the pursuer at all times farther from it than this capture distance. A classical problem is that of the homicidal chauffeur (Isaacs, 1965; Merz, 1971). In that game a faster pursuer (with respect to the evader) has as its objective to get closer than a given distance (the capture condition) to a slower but more a... |

45 | Real-time combinatorial tracking of a target moving unpredictably among obstacles - Gonzalez-Banos, Lee, et al. |

33 | An intelligent observer, - Becker, Gonzalez-Banos, et al. - 1995 |

29 | Efficient multi-robot search for a moving target
- Hollinger, Singh, et al.
(Show Context)
Citation Context ...rectional evader within a limited sensing range defined by a maximal Lmax and a minimal Lmin sensing distances. • They allow a DDR to reduce the distance to the evader. In the remainder of the paper, we describe the conditions that make the tasks listed above possible. 2. Previous work A lot of work has been done in the area of pursuit-evasion games (Hajek, 1965; Isaacs, 1965; Basar and Olsder, 1982), and three main problems have received a lot of attention. They include finding, tracking and capturing a mobile evader with one or several pursuers. In the finding problem (Isler et al., 2005; Hollinger et al., 2009), the objective is to establish some sort of visibility between the pursuer and the evader. In this case, the pursuer must sweep the environment so that the evader is not able to eventually sneak into an area that has already been explored. Deterministic (Suzuki and Yamashita, 1992; Guibas et al., 1999; Sachs et al., 2004; Tovar and LaValle, 2008) and probabilistic (Vidal et al., 2002; Hespanha et al., 2000; Chung, 2008) algorithms have been proposed to solve this problem. In the capturing problem, the pursuer tries to get closer than a given distance l to the evader. The goal of the evader is... |

21 | Surveillance strategies for a pursuer with finite sensor 126
- Murrieta-Cid, Muppirala, et al.
- 2007
(Show Context)
Citation Context ...maintaining surveillance at a bounded variable distance of an OA with a DDR. In the tracking problem, the goal is maintaining visibility of the evader at all times, usually in an environment with obstacles (LaValle et al., 1997; Gonzalez et al., 2002; Jung and Sukhatme, 2002; Bandyopadhyay et al., 2006; Bhattacharya and Hutchinson, 2010). In recent years there has been a growing interest in related problems within the community of autonomous robots (Jung and Sukhatme, 2002; Kowalczuk and Czubenko, 2011), and specifically in robot motion planning (LaValle et al., 1997; Gonzalez et al., 2002; Murrieta-Cid et al., 2007). LaValle et al. (1997) proposed game theory as a framework to formulate the tracking problem. Becker et al. (1995) presented an algorithm that operates by maximizing the probability of future visibility of the evader. This algorithm is also studied more formally by LaValle et al. (1997). Fabiani et al. (2002) present an approach that takes into account the positioning uncertainty of the robot pursuer. The approach presented by Murrieta-Cid et al. (2005) computes a motion strategy by maximizing the shortest distance to escape, i.e., the shortest distance the evader needs to move in order to es... |

19 | Pursuit Games, - Hajek - 1965 |

17 | A sampling-based motion planning approach to maintain visibility of unpredictable targets,
- Murrieta-Cid, Tovar, et al.
- 2005
(Show Context)
Citation Context ...g and Sukhatme, 2002; Kowalczuk and Czubenko, 2011), and specifically in robot motion planning (LaValle et al., 1997; Gonzalez et al., 2002; Murrieta-Cid et al., 2007). LaValle et al. (1997) proposed game theory as a framework to formulate the tracking problem. Becker et al. (1995) presented an algorithm that operates by maximizing the probability of future visibility of the evader. This algorithm is also studied more formally by LaValle et al. (1997). Fabiani et al. (2002) present an approach that takes into account the positioning uncertainty of the robot pursuer. The approach presented by Murrieta-Cid et al. (2005) computes a motion strategy by maximizing the shortest distance to escape, i.e., the shortest distance the evader needs to move in order to escape the pursuer’s visibility region. Gonzalez et al. (2002) propose a technique to track an evader without the need for a global map. Instead, a range sensor is used to construct a local map of the environment, and a combinatorial algorithm is then employed to compute a motion for the pursuer at each iteration. In our previous work (Murrieta-Cid et al., 2007) we specifically considered the case in which both the pursuer and the evader are omnidirection... |

16 |
The Homicidal Chauffeur: A Differential Game,
- Merz
- 1971
(Show Context)
Citation Context ...that the evader is not able to eventually sneak into an area that has already been explored. Deterministic (Suzuki and Yamashita, 1992; Guibas et al., 1999; Sachs et al., 2004; Tovar and LaValle, 2008) and probabilistic (Vidal et al., 2002; Hespanha et al., 2000; Chung, 2008) algorithms have been proposed to solve this problem. In the capturing problem, the pursuer tries to get closer than a given distance l to the evader. The goal of the evader is to keep the pursuer at all times farther from it than this capture distance. A classical problem is that of the homicidal chauffeur (Isaacs, 1965; Merz, 1971). In that game a faster pursuer (with respect to the evader) has as its objective to get closer than a given distance (the capture condition) to a slower but more agile evader, in order to run it over. The pursuer is a vehicle with a minimal turning radius. The game takes place in the Euclidean plane without obstacles, and the evader aims to avoid the capture condition. The problem tackled in this paper and its proposed solution are different to the homicidal chauffeur issue. Note that the change in the mechanical model for the pursuer (if this role is taken by the DDR, which can rotate in pla... |

11 | On the existence of Nash equilibrium for a two player pursuit-evasion game with visibility constraints
- Bhattacharya, Hutchinson
- 2010
(Show Context)
Citation Context ...ing an omnidirectional evader with a differential drive robot. The results presented here, although not time-optimal, have the advantage over those of Ruiz and Murrieta-Cid (2012) as well as Ruiz et al. (2013) of allowing solution of two problems: capturing an OA evader with a DDR pursuer and maintaining surveillance at a bounded variable distance of an OA with a DDR. In the tracking problem, the goal is maintaining visibility of the evader at all times, usually in an environment with obstacles (LaValle et al., 1997; Gonzalez et al., 2002; Jung and Sukhatme, 2002; Bandyopadhyay et al., 2006; Bhattacharya and Hutchinson, 2010). In recent years there has been a growing interest in related problems within the community of autonomous robots (Jung and Sukhatme, 2002; Kowalczuk and Czubenko, 2011), and specifically in robot motion planning (LaValle et al., 1997; Gonzalez et al., 2002; Murrieta-Cid et al., 2007). LaValle et al. (1997) proposed game theory as a framework to formulate the tracking problem. Becker et al. (1995) presented an algorithm that operates by maximizing the probability of future visibility of the evader. This algorithm is also studied more formally by LaValle et al. (1997). Fabiani et al. (2002) pr... |

11 | A complexity result for the pursuit-evasion game of maintaining visibility of a moving evader
- Murrieta-Cid, Monroy, et al.
(Show Context)
Citation Context ...scape, i.e., the shortest distance the evader needs to move in order to escape the pursuer’s visibility region. Gonzalez et al. (2002) propose a technique to track an evader without the need for a global map. Instead, a range sensor is used to construct a local map of the environment, and a combinatorial algorithm is then employed to compute a motion for the pursuer at each iteration. In our previous work (Murrieta-Cid et al., 2007) we specifically considered the case in which both the pursuer and the evader are omnidirectional; that led to a sufficient escape condition for the evader. Then (Murrieta-Cid et al., 2008) we again considered both players as omnidirectional systems moving in an Tracking an omnidirectional evader with a differential drive robot at a bounded variable distance 373 environment containing obstacles. Further (Murrieta-Cid et al., 2008), we specifically addressed the combinatorial problem inherent to any strategy that considers visiting several locations in an environment with obstacles, and we provided a complexity result for this problem. Bandyopadhyay et al. (2006) used a greedy approach for the problem of evading surveillance. To drive the greedy motion planning algorithm, a local... |

10 | On probabilistic search decisions under searcher motion constraints,
- Chung
- 2008
(Show Context)
Citation Context ... received a lot of attention. They include finding, tracking and capturing a mobile evader with one or several pursuers. In the finding problem (Isler et al., 2005; Hollinger et al., 2009), the objective is to establish some sort of visibility between the pursuer and the evader. In this case, the pursuer must sweep the environment so that the evader is not able to eventually sneak into an area that has already been explored. Deterministic (Suzuki and Yamashita, 1992; Guibas et al., 1999; Sachs et al., 2004; Tovar and LaValle, 2008) and probabilistic (Vidal et al., 2002; Hespanha et al., 2000; Chung, 2008) algorithms have been proposed to solve this problem. In the capturing problem, the pursuer tries to get closer than a given distance l to the evader. The goal of the evader is to keep the pursuer at all times farther from it than this capture distance. A classical problem is that of the homicidal chauffeur (Isaacs, 1965; Merz, 1971). In that game a faster pursuer (with respect to the evader) has as its objective to get closer than a given distance (the capture condition) to a slower but more agile evader, in order to run it over. The pursuer is a vehicle with a minimal turning radius. The gam... |

9 | V.Isler, “Robotic routers: Algorithms and implementation - Tekdas |

7 | On the value of ignorance: Balancing tracking and privacy using a two-bit sensor,” in - O’Kane - 2008 |

4 | Tracking an unpredictable target among occluding obstacles under localization uncertainties, Robotics and Autonomous Systems - Fabiani, Gonzalez, et al. - 2002 |

3 | A homicidal differential drive robot,
- Ruiz, Murrieta-Cid
- 2012
(Show Context)
Citation Context ...o run it over. The pursuer is a vehicle with a minimal turning radius. The game takes place in the Euclidean plane without obstacles, and the evader aims to avoid the capture condition. The problem tackled in this paper and its proposed solution are different to the homicidal chauffeur issue. Note that the change in the mechanical model for the pursuer (if this role is taken by the DDR, which can rotate in place) has as distinctive consequences that both the condition defining the winner and the motion strategies of the two players also change with respect to the homicidal chauffeur solution. Ruiz and Murrieta-Cid (2012) as well as Ruiz et al. (2013) presented time-optimal strategies for the game of capturing an omnidirectional evader with a differential drive robot. The results presented here, although not time-optimal, have the advantage over those of Ruiz and Murrieta-Cid (2012) as well as Ruiz et al. (2013) of allowing solution of two problems: capturing an OA evader with a DDR pursuer and maintaining surveillance at a bounded variable distance of an OA with a DDR. In the tracking problem, the goal is maintaining visibility of the evader at all times, usually in an environment with obstacles (LaValle et a... |

2 | Control of a team of mobile robots based on non-cooperative equilibria with partial coordination,
- Skrzypczyk
- 2005
(Show Context)
Citation Context ... a metric for measuring the degree of occlusion, based on the average mean free path of a random line segment. Pursuit-evasion can be used in a variety of applications. For example, Tekdas and Yang (2010) noticed the similarity between pursuit-evasion games and mobile routing for networking. Applying this similarity, they proposed motion planning algorithms for robotic routers to maintain connectivity between a mobile user and a base station. That work also includes a proof-of-concept implementation. Other possible interesting application of pursuit-evasion is the control of a team of robots (Skrzypczyk, 2005) with the goal of achieving a specific robot formation, for example, tracking the trajectory of an agent designed as the leader (Prodan et al., 2013). Our problem consists in determining motion strategies to always maintain surveillance of the evader (assuming surveillance at the beginning of the game). The evader is under pursuer surveillance whenever it is at a bounded variable distance to the pursuer. It is interesting to analyze this case because commercially available sensors have upper and lower range limits. In particular, even in the absence of obstacles, if the evader is farther or cl... |

1 | Intelligent decision-making system for autonomus robots,
- Kowalczuk, Czubenko
- 2011
(Show Context)
Citation Context ...2012) as well as Ruiz et al. (2013) of allowing solution of two problems: capturing an OA evader with a DDR pursuer and maintaining surveillance at a bounded variable distance of an OA with a DDR. In the tracking problem, the goal is maintaining visibility of the evader at all times, usually in an environment with obstacles (LaValle et al., 1997; Gonzalez et al., 2002; Jung and Sukhatme, 2002; Bandyopadhyay et al., 2006; Bhattacharya and Hutchinson, 2010). In recent years there has been a growing interest in related problems within the community of autonomous robots (Jung and Sukhatme, 2002; Kowalczuk and Czubenko, 2011), and specifically in robot motion planning (LaValle et al., 1997; Gonzalez et al., 2002; Murrieta-Cid et al., 2007). LaValle et al. (1997) proposed game theory as a framework to formulate the tracking problem. Becker et al. (1995) presented an algorithm that operates by maximizing the probability of future visibility of the evader. This algorithm is also studied more formally by LaValle et al. (1997). Fabiani et al. (2002) present an approach that takes into account the positioning uncertainty of the robot pursuer. The approach presented by Murrieta-Cid et al. (2005) computes a motion strate... |

1 |
Tracking an omnidirectional evader with a differential drive robot at a bounded variable distance 385
- Tovar, LaValle
- 2008
(Show Context)
Citation Context ...mes (Hajek, 1965; Isaacs, 1965; Basar and Olsder, 1982), and three main problems have received a lot of attention. They include finding, tracking and capturing a mobile evader with one or several pursuers. In the finding problem (Isler et al., 2005; Hollinger et al., 2009), the objective is to establish some sort of visibility between the pursuer and the evader. In this case, the pursuer must sweep the environment so that the evader is not able to eventually sneak into an area that has already been explored. Deterministic (Suzuki and Yamashita, 1992; Guibas et al., 1999; Sachs et al., 2004; Tovar and LaValle, 2008) and probabilistic (Vidal et al., 2002; Hespanha et al., 2000; Chung, 2008) algorithms have been proposed to solve this problem. In the capturing problem, the pursuer tries to get closer than a given distance l to the evader. The goal of the evader is to keep the pursuer at all times farther from it than this capture distance. A classical problem is that of the homicidal chauffeur (Isaacs, 1965; Merz, 1971). In that game a faster pursuer (with respect to the evader) has as its objective to get closer than a given distance (the capture condition) to a slower but more agile evader, in order to r... |