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We have presented a simple, efficient randomized planner for kinodynamic motion planning in the presence the form

Randomized Kinodynamic Planning

I. J. Robotic Res., no. 5 (2001): 378-400

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摘要

LaValle & Ku ner (12) present an application of a randomized technique to the problem of kinodynamic planning. Their algorithm constructs Rapidly-exploring Random Trees (RRTs) in a high dimensional state space that encompasses both first order constraints resulting from the physically-based system dynamics as well as global kinematic cons...更多

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简介
  • In its simplest form, motion planning is a purely geometric problem: given the geometry of a robot and static obstacles, compute a collision-free path of the robot between two given configurations.
  • This formulation ignores several key aspects of the physical world.
  • The authors need to consider numerous other issues, some of which will be examined here
重点内容
  • In its simplest form, motion planning is a purely geometric problem: given the geometry of a robot and static obstacles, compute a collision-free path of the robot between two given configurations
  • Unlike obstruction by obstacles, such constraints cannot be represented as forbidden regions in the configuration space
  • Our work extends the probabilistic roadmap (PRM) framework originally developed for planning collision-free geometric paths [Kav[94], KS LO96, Sve97]
  • We prove that if the state ¥ time space is expansive, under suitable assumptions, our new randomized planner for kinodynamic planning with moving obstacles is probabilistically complete with a convergence rate exponential in the number of sampled milestones
  • We have presented a simple, efficient randomized planner for kinodynamic motion planning in the presence the form
  • The motion constraints are naturally enforced during the construction of the roadmap
方法
  • To further test the performance of the planner, the authors connected the planner described in the previous section to the air-cushioned robot in Figure 1.
  • In these tests, the authors examined the behavior of Algorithm 1 running in real-time mode on a system integrating control and sensing modules over a distributed architecture and operating in a physical environment with uncertainties and time delays.
  • They are initially propelled by hand from various locations and move frictionlessly on the table at roughly constant speed until they reach the boundary of the table, where they stop due to the lack of air bearing
结果
  • The authors experimented with the planner in many workspaces. Each one is a 10 m ¥ 10 m square region cwnai inarimvdtchiFl/g‘esisa,gttwtaauerntiraitefdchnrog8iodtmesbissashsmotftoareneowceetlmreseisrsnit.VWd0ghe.rfT8aeonhemmfgecl,iteottoawmtnnihoodphvituchak tamererŒoidte.osæstehabxerk eaertm.t wiEdæpeelneenvnShsti.`hirgujcoaEmniWln,mS#.vkeeTiaranchonthend!#m’psriWe(peSlpenckreot.edns!ˆTte‡toahn(fietnteihssadeltalwbocymwaoraaatlsbazprelrego;aelndtyhgiogseebtosasrnntofarcbccoeoolmentbstecaujstaiwenri tpeesmadermna/isntu‘ etsdoaŒt by a narrow passage.
  • The planner successfully produced complex maneuvers of the robot among static and moving obstacles in various situations, including obstacles moving directly toward the robot or perpendicular to the line connecting its initial and goal positions.
  • The planner assumes that obstacles move at constant linear velocities and do not collide with one other, an assumption which is likely to fail in practice
  • To address this last and important issue, the authors introduce on-the-fly replanning
结论
  • The authors have presented a simple, efficient randomized planner for kinodynamic motion planning in the presence the form

    ƒo f°m"ov!dWin“g&p(

    obstacles.
  • The authors' algorithm represents the motion constraints by and constructs a roadmap of sampled milestones in the state ¥.
  • An equation time space of of a robot.
  • It samples new milestones by first picking at random a point in the space of admissible control functions and mapping the point into the state space by integrating the equations of motion.
  • The motion constraints are naturally enforced during the construction of the roadmap.
  • The performance of the algorithm has been evaluated through both theoretical analysis and extensive experiments
表格
  • Table1: Performance statistics of the planner on the nonholonomic robot
  • Table2: Performance statistics of the planner on the air-cushioned robot
Download tables as Excel
基金
  • This work was supported by ARO MURI grant DAAH04-96-1-007, NASA TRIWG Coop-Agreement NCC2-333, Real-Time Innovations, and the NIST ATP program
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