The following items must be considered in light of the nonholonomic nature of the kinematics of the vehicle.
Note how a small initial error in orientation results in a large eventual error in final position. Because kinematic equations of nonholonomic systems must be integrated, even small errors will grow with distance traveled, producing much larger terminal errors, unless OBSERVATIONS are available. The procedure used to combine integrals of wheel rotation with a sequence of observations to produce accurate position/orientation estimates is called "estimation."
Note that the nonholonomic constraints of the wheels preclude certain direct paths which would be allowed with a three degree-of-freedom holonomic device. In particular, any planned path for the wheelchair must be consistent with, or compatible with equations 1-3, the nonholonomic system contraints. At the same time, given that an admissible path can be found, the two-degree-of-freedom chair can reach a prescribed position/orientation combination which requires three degrees of freedom for the holonomic arm.(Quicktime Anim. 670 K or MPEG Anim. 700 K)
If an error in tracking the reference rotations occurs, returning to the reference ROTATION path will cause a holonomic robot to terminate at the desired pose, whereas, in general, a nonholonomic robot will terminate at an incorrect pose, under the same circumstance.
Other considerations include obstacle avoidance and precise positioning relative to certain critical bodies. An important distinction must be made between those bodies which must be neared with high precision (such as a desk) as part of the maneuver requirement, and those bodies which must be avoided as unforeseen obstacles (such as a misplaced office chair).
Continue to: Estimation
Return to: Nonholonomic Kinematics
