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When two or more objects collide with each other, they can stick together to form one single composite object (after collision). The total mass of the object after the collision is the sum of the masses of the original objects, and it moves with a velocity dictated by the conservation of momentum. Although the system's total momentum remains constant, the kinetic energy decreases, and thus such a collision is an inelastic collision. Most of the collisions between objects in daily life are...
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An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...
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Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...
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It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
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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.
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When two objects come in direct contact with each other, it is called a collision. During a collision, two or more objects exert forces on each other in a relatively short amount of time. A collision can be categorized as either an elastic or inelastic collision. If two or more objects approach each other, collide and then bounce off, moving away from each other with the same relative speed at which they approached each other, the total kinetic energy of the system is said to be conserved. This...
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Swarm formation morphing for congestion-aware collision avoidance.

Jawad N Yasin1, Mohammad-Hashem Haghbayan1, Muhammad Mehboob Yasin2

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This study introduces a new method for swarm formations to evade obstacles efficiently. The approach minimizes delays and energy use by optimizing agent distribution during evasion and recovery.

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Area of Science:

  • Robotics
  • Multi-agent systems
  • Swarm intelligence

Background:

  • Swarm formations face challenges in obstacle avoidance.
  • Overpopulation on one side of an obstacle leads to delays and increased energy consumption.
  • Efficient re-formation after obstacle evasion is crucial for mission success.

Purpose of the Study:

  • To present a novel methodology for optimal swarm formation distribution during obstacle evasion.
  • To reduce agent waiting delays and minimize overall mission time and energy consumption.
  • To develop distinct strategies for the disturbance (evasion) and convergence (re-formation) phases.

Main Methods:

  • Dividing the problem into a disturbance phase (optimal morphing to avoid obstacles) and a convergence phase (resuming formation shape).
  • Developing a methodology for the disturbance phase that tests formation morphing combinations using trajectory, velocity, and coordinate data.
  • Utilizing a thin-plate splines (TPS) inspired temperature function minimization for the convergence phase to optimally restore the formation.

Main Results:

  • The proposed methodology effectively manages swarm distribution around obstacles.
  • The approach significantly reduces agent waiting delays and optimizes traversal time.
  • Experimental results demonstrate substantial energy savings compared to traditional methods in simulated scenarios.

Conclusions:

  • The novel methodology provides an optimal solution for swarm formation obstacle avoidance.
  • The two-phase approach (disturbance and convergence) ensures efficient evasion and timely re-formation.
  • The method leads to reduced energy consumption and improved overall mission efficiency for robotic swarms.