Given the rules for bumper design would constructing curved bumpers to fit a concave in front of a robot be allowed?
No. The bumpers may be flat or convex only. please re-read the definition of FRAME PERIMETER
To answer your question, there is actually two parts:
<R07> D. Each BUMPER segment must be backed by a piece of ¾-inch thick by 5-inch tall piece of plywood. Each piece of BUMPER backing must be a minimum of 6 inches long. Small clearance pockets and/or access holes in the BUMPER backing are permitted, as long as they do not significantly affect the structural integrity of the BUMPER.
Can you bend the backing, this question should probably be addressed by the Q&A forum. If I recall last year, they had issues with how that worked, but this is a new year and should proably be asked again.
<R07> Teams are required to use BUMPERS on their ROBOTS. BUMPERS have several advantages, such as reducing damage to ROBOTS when they contact other ROBOTS or ARENA elements, and being excluded from the calculation of ROBOT weight and volume constraints specified in Rule <R10>. The BUMPER location and design have been specified so that ROBOTS will make BUMPER-to-BUMPER contact during most collisions. If implemented as intended, a ROBOT that is pushed against a vertical wall in any normal NORMAL CONFIGURATION will always have the BUMPER be the first thing to contact the wall. To achieve this, BUMPERS must be constructed as described below and illustrated in Figure 8 – 1.
A. BUMPERS must provide complete protection of the entire FRAME PERIMETER of the ROBOT (i.e. BUMPERS must wrap entirely around the ROBOT). The BUMPERS must be located entirely within the BUMPER ZONE when the ROBOT is standing normally on a flat floor, and must remain there (i.e. the BUMPERS must not be articulated or designed to move outside of the BUMPER ZONE).
So the second part is certainly not legal - having the bumpers being “concave” violates the fact the bumpers must follow the Frame perimeter. There is a lot of discussion regarding the rules about what this means, I encourage you to do a search and you will find many discusssions regarding why this would not be a legal configuration.
Good Luck!
Best regards,
Steve