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Related Concept Videos

Kinematic Equations: Problem Solving01:15

Kinematic Equations: Problem Solving

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When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two...
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Kinematic Equations - II01:17

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The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
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Kinematic Equations - III01:18

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The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
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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.
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When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of motions are derived for such cases where the acceleration of the object is constant. The first kinematic equation gives an insight into the relationship between velocity, acceleration, and time. We can see, for example:
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Kinematic Equations for Rotation01:30

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In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
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An Efficient Online Trajectory Generation Method Based on Kinodynamic Path Search and Trajectory Optimization for

Hongyan Liu1,2,3, Daokui Qu1,2,4, Fang Xu1,2,4

  • 1State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China.

Entropy (Basel, Switzerland)
|May 28, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient online trajectory generation method for robot manipulators. It ensures safer human-robot collaboration in dynamic environments by creating smoother, collision-free paths faster than current methods.

Keywords:
B-splinehuman-robot interactionkinodynamic path searchreal-time collision avoidancereplanningtrajectory optimization

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Area of Science:

  • Robotics
  • Artificial Intelligence
  • Control Systems

Background:

  • Human-robot collaboration is increasing in shared workspaces, necessitating robust safety measures.
  • Traditional motion planning struggles with dynamic environments and uncertain obstacle movements.
  • Ensuring safety in human-robot coexistence is critical as robots operate outside fixed perimeters.

Purpose of the Study:

  • To develop an efficient online trajectory generation method for manipulator autonomous planning in dynamic environments.
  • To enhance safety and efficiency in human-robot interaction within shared workspaces.
  • To address the limitations of traditional motion planning in uncertain, dynamic settings.

Main Methods:

  • An efficient kinodynamic path search algorithm considering link constraints for initial trajectory generation.
  • B-spline convex hull property for trajectory optimization, minimizing collision cost, improving smoothness, and ensuring dynamic feasibility.
  • Constraint-relaxed link collision avoidance using quadratic programming to prevent link-obstacle and self-collisions.

Main Results:

  • The proposed method generates smoother, collision-free trajectories.
  • Achieves higher success rates and reduces planning time compared to state-of-the-art methods.
  • Demonstrated effectiveness through detailed simulation and real-world experiments.

Conclusions:

  • The developed online trajectory generation method significantly improves manipulator planning in dynamic environments.
  • It enhances safety and efficiency for human-robot collaboration.
  • The approach offers a viable solution for real-world applications requiring reliable robot navigation.