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A solution of the falling cat problem is a curve in the configuration space that is horizontal with respect to the connection (that is, it is admissible by the physics) with prescribed initial and final configurations. Finding an optimal solution is an example of optimal motion planning. [11] [12]
A basic motion planning problem is to compute a continuous path that connects a start configuration S and a goal configuration G, while avoiding collision with known obstacles. The robot and obstacle geometry is described in a 2D or 3D workspace , while the motion is represented as a path in (possibly higher-dimensional) configuration space .
A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8 / 3 The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions.
The tautochrone problem is a special case of Abel's mechanical problem when () is a constant. Abel's solution begins with the principle of conservation of energy – since the particle is frictionless, and thus loses no energy to heat , its kinetic energy at any point is exactly equal to the difference in gravitational potential energy from its ...
In computational geometry, the point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon. It is a special case of point location problems and finds applications in areas that deal with processing geometrical data, such as computer graphics , computer vision , geographic ...
A double pendulum consists of two pendulums attached end to end.. In physics and mathematics, in the area of dynamical systems, a double pendulum, also known as a chaotic pendulum, is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. [1]
The horizontal velocity is the blue line, and the corresponding horizontal particle excursions are the red dots. The case for an oscillating far-field flow, with the plate held at rest, can easily be constructed from the previous solution for an oscillating plate by using linear superposition of solutions.
OMPL (Open Motion Planning Library) is a software package for computing motion plans using sampling-based algorithms.The content of the library is limited to motion planning algorithms, which means there is no environment specification, no collision detection or visualization.