Motion planning for wheeled nonholonomic systems

This dissertation solves important cases of the motion planning problem for wheeled nonholonomic systems. Given initial and final positions and orientations of a mobile robot in its environment workspace, the problem is to generate a path specifying a continuous sequence of positions and orientations that do not collide with the workspace obstacles and to generate the control inputs needed to steer the robot along this path.; The two dual methods of geometric nonlinear control theory and exterior differential systems for transforming kinematic models of wheeled nonholonomic systems with two or more inputs into chained form or Goursat normal form are presented. Conversion to chained form using vector field methods only gives sufficient conditions, but is easy to apply. Conversion to Goursat normal form gives necessary and sufficient conditions, but requires using subtleties of exterior differential systems. Once the system is in chained form or Goursat normal form, various open-loop, point-to-point steering methods can easily be constructed to steer the mobile robot between any two given configurations. Algorithms are given for steering with sinusoidal, polynomial and piecewise constant control inputs. The examples used to illustrate the theory include a fire truck, or tiller truck, and a multiple-steering, multiple-trailer mobile robot. These systems are drift-free and the nonholonomic behavior comes from non-slipping constraints on the wheels.; For a mobile robot configured as a car pulling trailers connected by off-axle hitches, an upper bound is computed on the maximal distance that the trailers and kingpin hitches swing off the lead car's path when the car changes from a straight line to an arc of a circle, or vice versa. The trailers are shown to exponentially converge to their steady-state circular paths when the lead car is moving on a circular path. If the turning radius of the lead car is upper bounded, then a reduced visibility graph method is proposed to find a collision-free path. Otherwise, path planners from the literature for a car-like mobile robot are modified. The methodology presented in this dissertation guarantees that the trailers do not collide with the obstacles for forward motions of the lead car.