TY - JOUR

T1 - Time-optimal motion of two omnidirectional robots carrying a ladder under a velocity constraint

AU - Chen, Zhengyuan

AU - Suzuki, Ichiro

AU - Yamashita, Masafumi

N1 - Funding Information:
Manuscript received October 12, 1995; revised October 1, 1996. This work was supported in part by the National Science Foundation under Grant IRI-9307506, by the Office of Naval Research under Grant N00014-94-1-0284, by a Scientific Research Grant-in-Aid from the Ministry of Education, Science and Culture of Japan (09245222, 09680342, 08233219, 08680370), and an endowed chair supported by Hitachi Ltd., Faculty of Engineering Science, Osaka University. This paper was recommended for publication by Associate Editor V. Hayward and Editor A. Goldenberg upon evaluation of the reviewers’ comments.

PY - 1997

Y1 - 1997

N2 - We consider the problem of computing a time-optimal motion for two omnidirectional robots carrying a ladder from an initial position to a final position in a plane without obstacles. At any moment during the motion, the distance between the robots remains unchanged and the speed of each robot must be ether a given constant v, or 0. A trivial lower bound on time for the robots to complete the motion is the time needed for the robot farther away from its destination to move to the destination along a straight line at a constant speed of v. This lower bound may or may not be achievable, however, since the other robot may not have sufficient time to complete the necessary rotation around the first robot (that is moving along a straight line at speed v) within the given time. We first derive, by solving an ordinary differential equation, a necessary and sufficient condition under which this lower bound is achievable. If the condition is satisfied, then a time-optimal motion of the robots is computed by solving another differential equation numerically. Next, we consider the case when this condition is not satisfied, and show that a time-optimal motion can be computed by taking the length of the trajectory of one of the robots as a functional and then applying the method of variational calculus. Several optimal paths that have been computed using the above methods are presented.

AB - We consider the problem of computing a time-optimal motion for two omnidirectional robots carrying a ladder from an initial position to a final position in a plane without obstacles. At any moment during the motion, the distance between the robots remains unchanged and the speed of each robot must be ether a given constant v, or 0. A trivial lower bound on time for the robots to complete the motion is the time needed for the robot farther away from its destination to move to the destination along a straight line at a constant speed of v. This lower bound may or may not be achievable, however, since the other robot may not have sufficient time to complete the necessary rotation around the first robot (that is moving along a straight line at speed v) within the given time. We first derive, by solving an ordinary differential equation, a necessary and sufficient condition under which this lower bound is achievable. If the condition is satisfied, then a time-optimal motion of the robots is computed by solving another differential equation numerically. Next, we consider the case when this condition is not satisfied, and show that a time-optimal motion can be computed by taking the length of the trajectory of one of the robots as a functional and then applying the method of variational calculus. Several optimal paths that have been computed using the above methods are presented.

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U2 - 10.1109/70.631233

DO - 10.1109/70.631233

M3 - Article

AN - SCOPUS:0031257463

SN - 1042-296X

VL - 13

SP - 721

EP - 729

JO - IEEE Transactions on Robotics and Automation

JF - IEEE Transactions on Robotics and Automation

IS - 5

ER -