When a differential drive robot moves on a circular arc with constant speed, its kinematics gets me constant wheel velocities. This appears to suggest that once a circular motion is reached and curvature remains constant, no acceleration and hence no motor torques are required. It also fits my understanding that circular motion at constant speed requires no work, as the tangential displacement is orthogonal to the radial centripetal force.
Intuitively however, I cannot wrap my head around this - it seems to not match how such systems actually behave - the centripetal acceleration experienced very much limits how much it can accelerate tangentially. Furthermore I find it hard to believe that change in momentum achieved by changing the direction of velocity should come “for free”.
I only have a superficial understanding of mechanics, so I’m sure there are a lot of holes in my thought process and I would be grateful for someone to point them out.