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Related Concept Videos

Three-Dimensional Force System:Problem Solving01:30

Three-Dimensional Force System:Problem Solving

A three-dimensional force system refers to a scenario in which three forces act simultaneously in three different directions. This type of problem is commonly encountered in physics and engineering, where it is necessary to calculate the resultant force on the system, which can then be used to predict or analyze the behavior of the object or structure under consideration.
To solve a three-dimensional force system, first resolve each force into its respective scalar components. Do this using...
Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
Relative Motion Analysis using Rotating Axes-Problem Solving01:29

Relative Motion Analysis using Rotating Axes-Problem Solving

Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
Here, in order to determine the magnitude of velocity and acceleration for point...
Two-Dimensional Force System: Problem Solving01:29

Two-Dimensional Force System: Problem Solving

Solving problems related to two-dimensional force systems is an essential aspect of mechanics and engineering. By applying the principles of vector analysis and force equilibrium, one can determine the effect of multiple forces acting on an object in a two-dimensional space.
The first step to solving a two-dimensional force system problem is to draw a free-body diagram of the object under consideration. This diagram helps identify all the external forces acting on the object, including their...
Vector Functions and Motion: Problem Solving01:30

Vector Functions and Motion: Problem Solving

Accurate position tracking is fundamental to the safe and effective operation of unmanned aerial vehicles (UAVs), particularly during precision maneuvers near complex structures. In this scenario, a drone is programmed to perform a high-precision inspection of a vertical structure, starting at position ((x, y, z) = (3, 0, 0)), with an initial velocity oriented in the positive z-direction. The trajectory of the drone is governed by a time-dependent acceleration function a(t), which is predefined...
Planar Rigid-Body Motion01:22

Planar Rigid-Body Motion

Understanding the movement of a rigid body in planar motion involves recognizing that every particle within this body is traversing a path that maintains a consistent distance from a specific plane. This concept is fundamental in the study of physics and mechanical engineering, and it allows us to comprehend better how objects move in space.
Planar motion is typically divided into three distinct categories. The first is rectilinear translation, demonstrated by a subway train that moves along...

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Related Experiment Video

Updated: Jun 8, 2026

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions
09:46

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

Published on: May 10, 2012

Multi-objective four-dimensional vehicle motion planning in large dynamic environments.

Paul P-Y Wu1, Duncan Campbell, Torsten Merz

  • 1Australian Research Centre for Aerospace Automation, Queensland University of Technology, Brisbane, Australia. p.wu@qut.edu.au

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|September 21, 2010
PubMed
Summary
This summary is machine-generated.

Multi-Step A* (MSA*) enhances autonomous vehicle planning by efficiently generating optimal paths in complex 4-D environments. This algorithm significantly reduces computation time for unmanned aerial vehicles (UAVs) while accommodating multiple objectives and constraints.

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Operation of the Collaborative Composite Manufacturing (CCM) System
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MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions
09:46

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

Published on: May 10, 2012

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
  • Artificial Intelligence
  • Aerospace Engineering

Background:

  • Autonomous unmanned aerial vehicles (UAVs) require robust motion planning in dynamic, uncertain 4-D environments.
  • Conventional planners struggle with multi-objective criteria, constraints (wind, fuel, obstacles), and variable trajectory parameters.

Purpose of the Study:

  • To introduce Multi-Step A* (MSA*), a novel search algorithm for multi-objective 4-D vehicle motion planning.
  • To address limitations of existing planners in handling complex environments and multiple decision criteria for UAVs.

Main Methods:

  • Developed MSA*, an A*-based algorithm for 4-D motion planning (3 spatial, 1 temporal dimension).
  • Employs variable length, angle, and velocity trajectory segments approximated by a grid-based cell sequence.
  • Utilizes variable successor operators for a multiresolution, memory-efficient lattice sampling structure.

Main Results:

  • MSA* finds cost-optimal solutions with variable trajectory segments, offering tolerance to uncertainty.
  • Achieves computational efficiency, enabling online replanning for UAVs.
  • Demonstrates average time reduction to one-quarter compared to vector neighborhood-based A* for equivalent path costs.

Conclusions:

  • MSA* provides an efficient and effective solution for multi-objective 4-D motion planning, particularly for UAVs.
  • The algorithm successfully balances computational performance with path optimality and adaptability to environmental uncertainties.