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Related Concept Videos

Collisions in Multiple Dimensions: Problem Solving01:06

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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.
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...
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Collisions in Multiple Dimensions: Introduction01:05

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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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Elastic Collisions: Case Study01:15

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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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Types of Collisions - II01:19

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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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Elastic Collisions: Introduction01:00

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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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Distributed Loads: Problem Solving01:21

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Beams are structural elements commonly employed in engineering applications requiring different load-carrying capacities. The first step in analyzing a beam under a distributed load is to simplify the problem by dividing the load into smaller regions, which allows one to consider each region separately and calculate the magnitude of the equivalent resultant load acting on each portion of the beam. The magnitude of the equivalent resultant load for each region can be determined by calculating...
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Human-machine shared driving for vehicle collision avoidance based on Hamilton-Jacobi reachability.

Shiyue Zhao1, Junzhi Zhang2, Rui Zhou3

  • 1School of Vehicle and Mobility, Tsinghua University, Beijing 10084, China; Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI 48105, USA.

Accident; Analysis and Prevention
|March 1, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a novel framework for shared collision avoidance, using reachability analysis to ensure machine intervention only when necessary. This approach prevents unavoidable collisions while minimizing disruption to the driver.

Keywords:
Collision avoidanceConflict minimizationHamilton-Jacobi reachabilityHuman-machine shared controlReinforcement learning

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Area of Science:

  • Robotics
  • Artificial Intelligence
  • Control Theory

Background:

  • Current shared control systems for collision avoidance often disrupt driver intent.
  • Existing methods can increase the risk of human-machine conflict.
  • There's a need for intelligent systems that intervene minimally and effectively.

Purpose of the Study:

  • To develop a shared control framework that aids drivers in critical collision scenarios.
  • To minimize human-machine conflicts during autonomous interventions.
  • To ensure collision avoidance by intervening only when theoretically unavoidable.

Main Methods:

  • Utilized Hamilton-Jacobi (HJ) reachability analysis to define a Collision Avoidance Reachable Set (CARS).
  • Employed offline data to precompute reachability distributions and CARS.
  • Developed a driver model and an authority allocation strategy to reduce conflicts.
  • Trained a Reinforcement Learning (RL) agent to enforce CARS constraints and minimize conflicts.

Main Results:

  • The Reachability-Aware RL framework effectively intervenes before the CARS boundary, preventing collisions.
  • The system demonstrated improved performance in maintaining the original driving task.
  • Robustness analysis confirmed flexibility across different driver attributes.

Conclusions:

  • The proposed HJ reachability-guided RL framework offers effective and minimally intrusive shared collision avoidance.
  • This method enhances safety by preventing entry into unavoidable collision states.
  • The approach shows promise for real-world vehicle platforms and diverse driving behaviors.