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The following MPPI implementation is adapted from this research paper
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The algorithm utilizes a monte carlo procedure by producing random noise (gaussian splatter) over a model prediction horizon
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Cost is calculated for each path in the set of paths based on a model of the robot
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Path integral: The chosen control command is a weighted sum of all the monte carlo paths
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A temperature value is provided to encourage exploration or exploitation
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The control command is applied to the robot and the process is repeated
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All-in-all, the control is the minimization of the expected cost of a trajectory weighted and combined with other trajectories:
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Note: The annimation may show slight overlap of robot and obstacle without detecting a collision. This is because of the drawing function giving an extra 0.5 width overlap from the actual obstacle border