## On Motion Planning in Changing, Partially-Predictable Environments (1997)

Venue: | International Journal of Robotics Research |

Citations: | 23 - 4 self |

### BibTeX

@ARTICLE{Lavalle97onmotion,

author = {Steven M. Lavalle and Rajeev Sharma},

title = {On Motion Planning in Changing, Partially-Predictable Environments},

journal = {International Journal of Robotics Research},

year = {1997},

volume = {16},

pages = {775--805}

}

### OpenURL

### Abstract

We present a framework for analyzing and computing motion plans for a robot that operates in an environment that both varies over time and is not completely predictable. We first classify sources of uncertainty in motion planning into four categories, and argue that the problems addressed in this paper belong to a fundamental category that has received little attention. We treat the changing environment in a flexible manner by combining traditional configuration space concepts with a Markov process that models the environment. For this context, we then propose the use of a motion strategy, which provides a motion command for the robot for each contingency that it could be confronted with. We allow the specification of a desired performance criterion, such as time or distance, and determine a motion strategy that is optimal with respect to that criterion. We demonstrate the breadth of our framework by applying it to a variety of motion planning problems. Examples are computed...

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Citation Context ...e geometry of the robot. 1 1 Introduction Substantial interest in the field of robot motion planning has led to a variety of approaches that use different models of the robot and its environment (see =-=[30, 37, 59]-=- for surveys). For many problems, the success of a motion planning approach depends to a large extent on the manner in which various forms of uncertainty are modeled and treated. One important uncerta... |

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Citation Context ...om sensor measurements or motion history. With a nondeterministic uncertainty model, the robot might have sufficient information to infer that q lies in some subset Q ae C free . For example, in [9], =-=[17]-=-, [38], [43] this representation of uncertainty is used to guarantee that the robot recognizably terminates in a goal region. With a probabilistic model, the robot might infer a posterior probability ... |

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Citation Context ...ainty. The other popular representation expresses uncertainty in the form of a posterior probability density. This often leads to the construction of motion plans through average-case analysis (e.g., =-=[14, 18, 23, 60]-=-) Uncertainty can be introduced into a motion planning problem in a number of ways. We organize this uncertainty into four basic sources for discussion: ffl Uncertainty in configuration sensing (Type ... |

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Citation Context ...e geometry of the robot. 1 1 Introduction Substantial interest in the field of robot motion planning has led to a variety of approaches that use different models of the robot and its environment (see =-=[30, 37, 59]-=- for surveys). For many problems, the success of a motion planning approach depends to a large extent on the manner in which various forms of uncertainty are modeled and treated. One important uncerta... |

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Citation Context ...e geometry of the robot. 1 1 Introduction Substantial interest in the field of robot motion planning has led to a variety of approaches that use different models of the robot and its environment (see =-=[30, 37, 59]-=- for surveys). For many problems, the success of a motion planning approach depends to a large extent on the manner in which various forms of uncertainty are modeled and treated. One important uncerta... |

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Citation Context ...s presentation. Detailed treatment of information spaces in optimal control theory can be found in [1, 35], and their application to motion planning with uncertainty in control and sensing appears in =-=[39]-=-. Suppose that the robot is equipped with a sensor that produces an observation o k at each stage, k 2 f1; : : : ; Kg. We assume that a noise or error model for the sensor can be specified as P (o k j... |

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Citation Context ...stic model, the robot might infer a posterior probability density, p(e), over environments, which is conditioned on sensor observations, initial conditions, or additional knowledge (e.g., [14], [15], =-=[28]-=-, [68]). Type EP uncertainty. Suppose again that the space of environments, E , is known by the robot; however, in addition, the robot knows its current environment e 2 E . Predictable motion commands... |

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Citation Context ...ainty. The other popular representation expresses uncertainty in the form of a posterior probability density. This often leads to the construction of motion plans through average-case analysis (e.g., =-=[14, 18, 23, 60]-=-) Uncertainty can be introduced into a motion planning problem in a number of ways. We organize this uncertainty into four basic sources for discussion: ffl Uncertainty in configuration sensing (Type ... |

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Citation Context ...cterizes the observations that are likely to be made for a given environment mode. The form P (o k je k ) is typically used in a variety of robotics applications that involve statistical sensor error =-=[25, 26, 41]-=-, and in general for stochastic control theory [35]. We begin with a prior probability distribution over E, denoted by P (e 1 ) (which could, for instance, be uniform). We next develop an incremental ... |

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Citation Context ...er the case in which x k 2 C free is at a distance of at least kvk\Deltat from the obstacles. If A chooses action u k 6= ; from state x k , then 1 x k+1 = 2 6 6 6 4 x k [1] + kvk\Deltat cos(u k ) x k =-=[2]-=- + kvk\Deltat sin(u k ) e k+1 3 7 7 7 5 ; (3) in which the environment mode e k+1 is known to be sampled from P (e k+1 jx k ; u k ). We can thus consider a finite-valued random variable X k+1 with cor... |

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Citation Context ...ities with the concept of a global navigation function in motion planning [37, 56]. Also, various forms of dynamic programming have been successfully applied in several other motion planning contexts =-=[2, 29, 48, 69]-=-; for instance, the wavefront expansion method that is described in [37] can be viewed as a special form of dynamic programming. It turns out that the optimal action u k , does not depend on the stage... |

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18 |
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Citation Context ...itutes of large body of work in which bounded uncertainties are propagated and combined with configuration-sensing uncertainty, to guarantee that the robot will achieve a goal (e.g., [9], [13], [17], =-=[20]-=-, [38], [43]). With a probabilistic model, future configurations can be described by a posterior density over configurations, p(q), that is conditioned on the initial configuration and the executed mo... |

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Citation Context ...ities with the concept of a global navigation function in motion planning [37, 56]. Also, various forms of dynamic programming have been successfully applied in several other motion planning contexts =-=[2, 29, 48, 69]-=-; for instance, the wavefront expansion method that is described in [37] can be viewed as a special form of dynamic programming. It turns out that the optimal action u k , does not depend on the stage... |

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Citation Context ...ities with the concept of a global navigation function in motion planning [37, 56]. Also, various forms of dynamic programming have been successfully applied in several other motion planning contexts =-=[2, 29, 48, 69]-=-; for instance, the wavefront expansion method that is described in [37] can be viewed as a special form of dynamic programming. It turns out that the optimal action u k , does not depend on the stage... |

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Citation Context ...aining constitutes of large body of work in which bounded uncertainties are propagated and combined with configuration-sensing uncertainty, to guarantee that the robot will achieve a goal (e.g., [9], =-=[13]-=-, [17], [20], [38], [43]). With a probabilistic model, future configurations can be described by a posterior density over configurations, p(q), that is conditioned on the initial configuration and the... |

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Citation Context ...ence about its environment. With a nondeterministic uncertainty model, the robot might have sufficient information to infer that the environment e belongs to some subset F ae E. For example, in [50], =-=[53], the envi-=-ronment is restricted to a plane populated with unknown polygonal obstacles, which are then discovered using visual "scans" to build a visibility graph for motion planning. In [44], unknown ... |

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Citation Context ... Environment Sensing Environment Predictability Figure 1: Four sources of uncertainty in the motion planning problem. configuration-sensing uncertainty with probabilistic representations include [6], =-=[71]-=-. Type CP uncertainty. Suppose that both C free and the current configuration, q 2 C free are given. Motion commands can be given to the robot, but with Type CP uncertainty the future configurations c... |