%0 Journal Article
%T Time-optimal Trajectories for a Car-like Robot<br>车型机器人的时间最优轨迹
%A WANG Hui-Fang
%A CHEN Yang-Zhou
%A <br>王慧芳
%A 陈阳舟
%J 自动化学报
%D 2008
%I 
%X This paper provides a new geometric method for achieving the sufficient family of the time-optimal trajectories to connect any two configurations of the robot in a 3-dimensional manifold based on the geometric optimal control theory.We provide a new perspective for analyzing this special type of nonlinear problems.Based on the structural characteristics of the switching functions and their derivatives from the Pontryagin's minimum principle(PMP)and the Lie algebra,we build a special coordinate system and introduce a new vector.We discover the one-to-one mapping between the rotation trajectory of this new vector and the optimal control trajectory.Furthermore,we define a switching vector that denotes the position and rotation direction of this vector,and reach a conclusion that the specified initial and final switching vectors can uniquely determine an optimal trajectory.In addition,it is the first time a condition that can be used directly for selecting a time-optimal trajectory is provided.
%K Geometric optimal control theory
%K robotics
%K time-optimal trajectory
%K Pontryagin's minimum principle(PMP)
%K Lie algebra<br>Geometric
%K optimal
%K control
%K theory
%K robotics
%K time-optimal
%K trajectory
%K Pontryagin's
%K minimum
%K principle
%K (PMP)
%K Liealgebra
%K 车型机器人
%K 时间
%K 最优轨迹
%K Robot
%K time
%K condition
%K used
%K provided
%K addition
%K reach
%K initial
%K final
%K vectors
%K determine
%K optimal
%K trajectory
%K position
%K direction
%K discover
%K mapping
%K rotation
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=E76622685B64B2AA896A7F777B64EB3A&aid=49B2E3BDC5F2DEAFAC3527F0DD899BC1&yid=67289AFF6305E306&vid=339D79302DF62549&iid=E158A972A605785F&sid=A48DE16C07AAAB06&eid=30F3EEEA29E34EE7&journal_id=0254-4156&journal_name=自动化学报&referenced_num=0&reference_num=25