A path planning problem for a wheeled robot is considered. The problem consists in constructing a trajectory that approximates a given ordered sequence of points on the plane and satisfies certain smoothness requirements and curvature constraints. Such a problem arises, for example, when it is required to follow in an automated mode a path stored as a discrete set of points measured in the course of the first passage of this path in a manual mode. Due to errors inherent in the data points, the shape of the curve approximating the desired path may turn out inappropriate or even unacceptable from the control standpoint. The shape of the curve can be improved by applying the so-called fairing, which consists in moving the original data points with the aim to minimize some functional. Adequate small variations of the data points (within the measurement error) preserve the proximity of the resulting path to the original data points and, at the same time, may considerably improve its shape. In the paper, a new global fairing method for improving shape of curves consisting of elementary B-splines is proposed. The improvement is achieved through minimization of jumps of the spline third derivative. The problem of finding desired variations reduces to solving a quadratic programming problem with simple constraints. The discussion is illustrated by numerical examples

Abstract—A control synthesis problem for a wheeled robot moving on uneven terrain is studied. The terrain is assumed to be described by a sufficiently smooth function that does not vary too much at distances of the order of the platform size, which makes it possible to employ a planar robot model. The terrain model is not a priori known, and the information on the local terrain configuration is made available for the robot through measuring its pitch and roll angles. The control goal is to bring the robot to a given curvilinear path and to stabilize robot’s motion along it. A change of variables is found by means of which the system of differential equations governing controlled motion of the robot reduces to the form that admits feedback linearization. A numerical example presented demonstrates advantages of the synthesized control compared to that derived without regard to the terrain unevenness. It is shown that the latter is generally not capable of stabilizing robot’s motion with a desired accuracy.

The path following problem for a wheeled robot with constrained resource moving along a given curvilinear path is studied. With the help of an earlier introduced change of variables, the path following problem is reduced to that of stability of the zero solution, and a control law linearizing the system in the case of the unconstrained control resource is synthesized. For the closedloop system, the problem of finding the best ellipsoidal approximation of the attraction domain of the target path is set. To take into account the control constraint, an approach based on absolute stability theory is used. In the framework of this approach, construction of an approximating ellipse reduces to solving a parameterized system of linear matrix inequalities. The LMI system in the considered case can be solved analytically. Owing to this, construction of the best ellipsoidal approximation is reduced to solv ing a standard constrained optimization problem for a function of two variables. The proposed method is further extended to finding the best ellipsoidal approximation with an additional constraint on the maximum deviation from the target path. The discussion is illustrated by numerical example

The paper deals with the tracking output variable of nonlinear SISO-system for a given signal with some accuracy under unmatched external disturbances and functional uncertainties within the restrictions on state variables and control.