I ended up buying new motors for the robot, as the old ones (JGY-370) seemed getting stuck too easily. The new ones are JGB-37 (aliexpress). They seems to be strong to move around without any trouble. I ordered them with 12V / 18.5RPM.

The another good thing is that the area of support for robot weight is larger - as they are mounted in different manner than the old ones.

I also did work with lawn detect sensor. The idea came from ardumower. I was able to get it working so that it was able to detect my hand pretty far away (with sensor being smoothie bottle cap, radius around 40mm). But when mounted to the real electronics the measurements were not too good. I used 75OHM tv-cable with shielding to reduce the noise but no luck. It still detects if the grass touches the sensor, but its not able to differentiate stone tiling from short grass. Which makes it pretty much useless in my scenario.