The forward kinematics equation provides an updated pose at a given wheel speed. We can now think about the inverse problem.
Stand in pose (x, y, θ) at time t and determine the V-left and V-right control parameters so that the pose at time t + δt is (x', y', θ').
In differential drive systems, this problem may not always have a solution because this kind of robot can't be moved to any pose by simply setting the wheel velocity. It's because of the nonholonomic robots' constraints.
In nonholonomic robots, there are some ways to increase the constrained mobility if we allow a sequence of different (V-left, V-right) movements. If we insert the values from equations (12) and (15), we can identify some special movements that we can program:
- If V-right = V-left => nr = nl => R = ∞, ωδT = 0 =...