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Related Concept Videos

Orthogonal Trajectories01:26

Orthogonal Trajectories

Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
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One-Degree-of-Freedom System

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Kinematic Equations: Problem Solving01:15

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Related Experiment Video

Updated: Jul 7, 2026

Operation of the Collaborative Composite Manufacturing (CCM) System
10:09

Operation of the Collaborative Composite Manufacturing (CCM) System

Published on: October 1, 2019

Time-optimal trajectories for cooperative multi-manipulator systems.

S B Moon1, S Ahmad

  • 1Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|January 1, 1997
PubMed
Summary

We developed two methods for optimizing cooperative multi-manipulator system (CMMS) trajectories. One uses linear programming for time-optimal control, while the other efficiently distributes load for faster execution, enabling real-time applications.

Related Experiment Videos

Last Updated: Jul 7, 2026

Operation of the Collaborative Composite Manufacturing (CCM) System
10:09

Operation of the Collaborative Composite Manufacturing (CCM) System

Published on: October 1, 2019

Area of Science:

  • Robotics
  • Control Systems
  • Optimization

Background:

  • Cooperative multi-manipulator systems (CMMS) require efficient trajectory planning for complex tasks.
  • Existing methods may not fully utilize system dynamics or computational efficiency.

Purpose of the Study:

  • To present two novel schemes for time-optimal trajectory planning in CMMS carrying a common object.
  • To account for manipulator and object dynamics in trajectory optimization.

Main Methods:

  • Linear programming to achieve time-optimal execution using maximum joint motor torque capacities.
  • A computationally efficient sub-time-optimal approach involving load distribution among manipulators to maximize acceleration/deceleration.

Main Results:

  • The linear programming approach yields time-optimal trajectories by maximizing joint motor torques.
  • The load distribution method significantly reduces computation time, degenerating to a linear search for two robots.
  • The load distribution scheme enables real-time planning and control, and can yield truly time-optimal trajectories in specific cases.

Conclusions:

  • Two effective schemes for time-optimal trajectory planning in CMMS are presented.
  • The load distribution method offers computational efficiency and real-time applicability for CMMS control.
  • Both methods successfully incorporate manipulator and object dynamics for optimized task execution.