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I'm working with a 4DOF Parallel-Mechanism arm. I'm interested in writing planners for this arm (PRM or RRT) in the configuration space, but I'm not sure how to identify obstacles/collisions.

When writing planners for mobile robots in a 2d workspace, it was easy to define and visualize the workspace and obstacles in which the planner/robot was operating. This website (link) shows a great example of visualizing the workspace and configuration space for a 2DOF arm, but how can I do this for higher dimensions?

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This is one of the basic problems in planning robot trajectories: The transformation from Configuration-Space to Workspace via direct kinematic is unambiguous, while the inverse way from Workspace to Config-Space is ambivaltent (in all cases where Dim(Config-Space) > Dim(Workspace)).

So what almost all planers do (especially the sampling based ones like RRT) is sampling in Config-Space, transforming the sample to Workspace and performing a collision check there. If no collision occurs, add sample to planning-graph.

The same has to be done for longer trajectories in between the samples: Break them down to smaller subtrajectories (< Robot/Endeffector-Size) and do a collision check for each waypoint.

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