A* pathfinder obstacle collision problem

Have you considered adding a gradient cost to pixels near objects?

Perhaps one as simple as a linear gradient:

C = -mx + b

Where x is the distance to the nearest object, b is the cost right outside the boundary, and m is the rate at which the cost dies off. Of course, if C is negative, it should be set to 0.

Perhaps a simple hyperbolic decay

C = b/x

where b is the desired cost right outside the boundary, again. Have a cut-off to 0 once it reaches a certain low point.

Alternatively, you could use exponential decay

C = k e^(-hx)

Where k is a scaling constant, and h is the rate of decay. Again, having a cut-off is smart.

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Second suggestion

I've never applied A* to a pixel-mapped map; nearly always, tiles.

You could try massively decreasing the "resolution" of your tiles? Maybe one tile per ten-by-ten or twenty-by-twenty set of pixels; the tile's cost being the highest cost of a pixel in the tile.

Also, you could try de-valuing the shortest-distance heuristic you are using for A*.

You might try to enlarge the obstacles taking size of the robot into account. You could round the corners of the obstacles to address the blocking problem. Then the gaps that are filled are too small for the robot to squeeze through anyway.

I've done one such physical robot. My solution was to move one step backward whenever there is a left and right turn to do.

The red line is as I understand your problem. The Black line is what I did to resolve the issue. The robot can move straight backward for a step then turn right.