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

Zhengyuan Chen, Ichiro Suzuki, Masafumi Yamashita

Research output: Contribution to journalArticle

4 Citations (Scopus)

### Abstract

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.

Original language English 721-729 9 IEEE Transactions on Robotics and Automation 13 5 https://doi.org/10.1109/70.631233 Published - Dec 1 1997

### Fingerprint

Robots
Variational techniques
Ordinary differential equations
Ethers
Differential equations
Trajectories

### All Science Journal Classification (ASJC) codes

• Control and Systems Engineering
• Electrical and Electronic Engineering

### Cite this

Time-optimal motion of two omnidirectional robots carrying a ladder under a velocity constraint. / Chen, Zhengyuan; Suzuki, Ichiro; Yamashita, Masafumi.

In: IEEE Transactions on Robotics and Automation, Vol. 13, No. 5, 01.12.1997, p. 721-729.

Research output: Contribution to journalArticle

Chen, Zhengyuan ; Suzuki, Ichiro ; Yamashita, Masafumi. / Time-optimal motion of two omnidirectional robots carrying a ladder under a velocity constraint. In: IEEE Transactions on Robotics and Automation. 1997 ; Vol. 13, No. 5. pp. 721-729.
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