The paper deals with non-standard motion tasks specified for a two-wheeled nonholonomic robot. It is assumed that wheels cannot fully rotate which reduces a set of feasible movements significantly. In spite of these constraints, it is expected that position of the robot can be changed without violating nonholonomic constraints. Such a possibility comes from the small time local controllability (STLC) of the kinematics described on four-dimensional configuration manifold. In order to solve these specific tasks a feedback taking advantage of the transverse function approach is designed. Consequently, the system can be virtually released from non-holonomic constraints. The transverse function also defines a virtual geometry constraint which makes it possible to limit wheels rotation.Properties of the designed controller are illustrated by results of numerical simulations in various motion task scenarios.

In this paper a unified motion control and planning algorithm dedicated for the waypoint following task realized by a skid-steering is presented. In order to reduce excessive slip effects between robot wheels and ground it is assumed that the vehicle moves with bounded velocities and accelerations. The motion controller has been designed using formal methods to ensure asymptotically stable tracking of feasible reference trajectories. To account for practical motion tasks the trajectory tracking algorithm is complemented by a motion planner, which utilizes the differential flatness property of unicycle-like kinematics. During the motion planning stage an auxiliary trajectory connecting points in the configuration space and satisfying assumed phase constraints is generated. The resulting motion execution system has been implemented on a laboratory-scale skid-steering mobile robot, which served as platform for experimental validation of presented algorithms.

The paper considers application of a controller using transverse functions to solving the regulation and trajectory tracking problem for a multi-body vehicle which consists of a unicycle-like tractor with three trailers. In order to facilitate the controller design, the kinematics of the system is partially defined on the Lie group. The control solution is based on configuration and input transformation of an open-loop error dynamics to the invariant system with a drift. The properties of the closed-loop control system are examined based on the results of numerical simulations considering the selected motion tasks.

The paper considers the convergence problem for a two input affine nonholonomic driftless system with three-dimensional state. The problem is solved using time-invariant static-state feedback and polar transformation which is singular at the origin. The given solution, in general, is local, and the feasible domain is dependent on the properties of the control system. Theoretical considerations are illustrated for the particular system and the results of numerical simulations are presented.

The paper presents a comparison of selected smooth and time-differentiable control laws used for stabilization of nonholonomic two-wheeled mobile robot. The significant part of the research is concentrated on application of these algorithms in resolving parallel parking problem. Some remarks concerning tuning of the controllers and their robustness to the delay in control loop are given