Motion planning in a dynamic environment involves, solving both the path planning and velocity planning problems simultaneously, hence a difficult proposition. It is a combination of a kinematic problem of path planning and a dynamic problem which takes into consideration the robot dynamics, and the various differential constrains. Problems related to computational complexity and non availability of a solution exists in relation to dynamic environments for motion planning.
Steven M. LaValle, University of Illinois, provides a 4 part lecture series on, "Motion Planning in Dynamic Environments"
Part 2: Motion Planning - Finding the Path
Part 3: Dynamic Environments - Modeling Issues
Part 4: Dynamic Environments - Methods
The slides for the lecture are found here.
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