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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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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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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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A Brain-Inspired Approach for Collision-Free Movement Planning in the Small Operational Space.

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    This study introduces a novel spiking neural network for precise visual guidance in small spaces, enabling collision-free movements for fragile objects through dual-channel control. The system mimics brain functions for accurate object manipulation and safety.

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    Area of Science:

    • Robotics and Neuroscience
    • Computational Intelligence
    • Biologically Inspired Systems

    Background:

    • Precise control of robotic systems in confined spaces is challenging due to the need for careful manipulation of fragile objects.
    • Existing visual guidance systems may lack the sophisticated processing required for complex, real-time adjustments in microscale environments.

    Purpose of the Study:

    • To propose a novel spiking neural network (SNN) architecture for visual guidance in small operational spaces.
    • To develop a dual-channel system for achieving collision-free movements by imitating multiple brain regions.
    • To enhance robotic manipulation capabilities for fragile objects.

    Main Methods:

    • Simulated primary and high-level visual cortices for feature extraction and distance measurement.
    • Emulated prefrontal cortex using liquid state machines for trajectory prediction and a feedforward network for movement planning.
    • Incorporated a cerebellar network for subconscious reactive control.
    • Implemented two distinct pathways: visual-servo control and collision-avoidance.
    • Utilized supervised learning for initial training and reinforcement learning for synaptic refinement.

    Main Results:

    • The proposed SNN structure effectively imitates brain region functions for visual guiding.
    • The dual-channel approach successfully achieves collision-free movements in small operational spaces.
    • Both simulation and experimental results validate the efficacy of the proposed method for precise robotic control.

    Conclusions:

    • The developed SNN-based system offers a biologically inspired solution for complex visual guidance tasks.
    • The dual-channel architecture provides robust control for handling fragile objects in confined environments.
    • This approach advances the integration of neuroscience principles into robotic control systems.