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Relative Velocity in Two Dimensions01:11

Relative Velocity in Two Dimensions

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Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame. The concept of relative velocity can be used to describe motion in two dimensions. Consider a particle P and two reference frames S and S′. The position of the origin of S′ as measured in S is , the position of P as measured in S′ is , and the position of P as measured in S is , which can be evaluated by...
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Relative Motion Analysis using Rotating Axes-Problem Solving01:29

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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...
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Relative Velocity in One Dimension01:10

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The understanding of the concept of reference frames is essential to discuss relative motion in one or more dimensions. When we say that an object has a certain velocity, we must state the velocity with respect to a given reference frame. In most examples, this reference frame has been Earth. For instance, if a statement reads that a person is sitting in a train moving at 10 m/s east, then it implies that the person on the train is moving relative to the surface of Earth at this velocity,...
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Equation of Motion: General Plane motion - Problem Solving01:16

Equation of Motion: General Plane motion - Problem Solving

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Consider a lawn roller with a mass of 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. A force of 200 N is applied to this roller, angled at 60 degrees from the horizontal plane. What will be the angular acceleration of the lawn roller?
The friction between the roller and the ground is characterized by two coefficients. The static friction coefficient is 0.15, while the kinetic friction coefficient is 0.1. These values are crucial in understanding the interaction between...
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Absolute Motion Analysis- General Plane Motion01:24

Absolute Motion Analysis- General Plane Motion

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Visualize a drone, with its propellers spinning rapidly, hovering mid-air. The fascinating movements and operations of this drone can be comprehended by applying the principle of general plane motion.
As the drone's propellers rotate, an upward force is generated that counteracts the force of gravity, enabling the drone to lift off from the ground. This initial movement of the drone is along a straight path, representing a form of translational motion. In this phase, every point on the...
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Projectile Motion: Equations01:26

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Projectile motion is commonly observed in our day-to-day life. For example, a basketball thrown by a player, an arrow shot from a bow, and kids jumping into the pool, all undergo projectile motion.
Any projectile motion problem can be solved by using the following strategy:
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Updated: Aug 21, 2025

Trajectory Data Analyses for Pedestrian Space-time Activity Study
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Computationally efficient and sub-optimal trajectory planning framework based on trajectory-quality growth rate

Reiya Takemura1, Genya Ishigami1

  • 1Faculty of Science and Technology, Graduate School of Integrated Design Engineering, Keio University, Tokyo, Japan.

Frontiers in Robotics and AI
|November 17, 2022
PubMed
Summary

Planetary rovers need efficient algorithms due to power limits. This study introduces a framework that reduces computational cost by 47.6% while maintaining 63.8% trajectory optimality for rover navigation.

Keywords:
RRTanytime algorithmcomputationally efficientplanetary roversub-optimal algorithmtrajectory planning

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Area of Science:

  • Robotics
  • Planetary Science
  • Artificial Intelligence

Background:

  • Planetary exploration rovers require autonomous systems with limited onboard computing power and strict power supply constraints.
  • Computationally efficient algorithms are crucial for rover autonomous systems to manage processing performance effectively.

Purpose of the Study:

  • To present a computationally efficient and sub-optimal trajectory planning framework for planetary exploration rovers.
  • To address the trade-off between trajectory optimality and computational burden in rover navigation.

Main Methods:

  • Exploited an incremental search algorithm for trajectory planning, analyzing the trajectory-quality growth rate (TQGR) to balance optimality and computational cost.
  • Developed a machine learning model offline to predict the planning stop criterion based on terrain features.
  • Implemented an online motion planning approach that interrupts incremental search using the predicted criterion to achieve sub-optimal trajectories with reduced computational load.

Main Results:

  • The proposed framework reduced computational cost by an average of 47.6% while preserving 63.8% of trajectory optimality in simulations across diverse terrain data.
  • The framework demonstrated robust performance even when the planning stop criterion prediction was not precise.

Conclusions:

  • The developed trajectory planning framework offers a computationally efficient solution for planetary rover navigation under constrained resources.
  • The integration of machine learning for predicting stop criteria enhances the adaptability and efficiency of autonomous rover operations in varied terrains.