Tomasz Gawron

VFO stabilization of a unicycle robot with bounded curvature of motion

Parking a vehicle at a fixed configuration in the presence of motion curvature constraints is a well known problem of substantial practical meaning. It has been addressed in the robotic literature mostly in the context of planning an optimized path-to-goal or by computing open-loop controls for a vehicle. The paper presents a novel approach to the constrained set-point control for a mobile robot utilizing the Vector-Field-Orientation (VFO) feedback control law combined with controller-driven planning of at most three waypoint configurations. Thanks to specific properties of the VFO controller the method is mostly analytic, provides design flexibility for control optimization, and permits combination of both forward and backward motion of the robot. The concept is presented for the unicycle kinematics, which is a generic body-motion model of most popular mobile robot structures. Formal considerations presented in the paper have been validated by simulations.

VFO Path following Control with Guarantees of Positionally Constrained Transients for Unicycle-Like Robots with Constrained Control Input

The Vector-Field-Orientation (VFO) method is a control design concept which was originally introduced for the unicycle kinematics to solve two classical control tasks corresponding to the trajectory tracking and set-point control problems. A unified solution to both the tasks was possible by appropriate definitions of the so-called convergence vector field. So far, there has not been a version of the VFO control law for the third classical control task concerning the path following problem, which is particularly meaningful in the context of practical applications. The paper fills this gap by presenting a novel VFO path following controller devised for robots of unicycle-like kinematics with the amplitude-limited control input. Opposite to most path following controllers proposed in the literature, the new control law utilizes the recently introduced level curve approach which does not employ any parametrization of a reference path. In this way, the proposed solution is free of main limitations resulting from the need of unique determination of the shortest distance from a robot to the path. In contrast to other solutions, a formal analysis of the closed-loop dynamics presented in this paper provides sufficient conditions which guarantee constrained transients of robot motion with the position confined to a prescribed subset around a reference path. Theoretical results have been validated by numerical examples and experimentally verified with utilization of a laboratory-scale differentially driven robot.

The VFO-Driven Motion Planning and Feedback Control in Polygonal Worlds for a Unicycle with Bounded Curvature of Motion

Integrated motion planning and control for the purposes of maneuvering mobile robots under state- and input constraints is a problem of vital practical importance in applications of mobile robots such as autonomous transportation. Those constraints arise naturally in practice due to specifics of robot mechanical construction and the presence of obstacles in motion environment. In contrast to approaches focusing on feedback control design under the assumption of given reference motion or motion planning with neglection of subsequent feedback motion execution, we adopt a controller-driven motion planning paradigm, which has recently gained attention of many researchers. It postulates design of motion planning algorithms dedicated to specific feedback control policies, which compute a sequence of feedback control subtasks instead of classically planned open-loop controls or parametric paths. In this spirit, we propose a motion planning algorithm driven by the VFO (Vector Field Orientation) control law for the waypoint-following task. Presented analysis of the VFO control law reveals its beneficial properties, which are subsequently utilized to solve a generally nonlinear and non-convex optimal motion planning problem by formulating it as a mixed-integer linear program (MILP). The solution proposed in this paper yields a waypoint sequence, which is designed for execution by application of the VFO control law to drive a robot to a prescribed final configuration under an input constraint imposed by bounded curvature of robot motion and state constraints resulting from a convex decomposition of task space. Satisfaction of these constraints is guaranteed analytically and exactly, i.e., without utilization of numerical approximations. Moreover, for a given discrete set of possible waypoint orientations, the proposed algorithm computes plans optimal w.r.t. given cost functional, which can be any convex linear combination of quantities such as robot path length, curvature of robot motion, distance to imposed state constraints, etc. Furthermore, the planning algorithm exploits the possibility of both forward or backward movement of the robot to allow maneuvering in demanding environments. Generated waypoint sequences are a compact representation of a motion plan, which can be immediately executed with the VFO controller without any additional post-processing. Validity of the proposed approach has been confirmed by simulation studies and experimental motion execution with a laboratory-scale mobile robot.

A unified motion control and low level planning algorithm for a wheeled skid-steering robot

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.

VFO feedback control using positively-invariant funnels for mobile robots travelling in polygonal worlds with bounded curvature of motion

Feedback control of mobile robots guaranteeing preservation of state constraints resulting from obstacles in the environment and input constraints imposed by robot mechanical construction is essential in practical applications of robotic systems. The safety of motion execution is often ensured by a strategy of driving the robot through a sequence of funnels representing safe, positively invariant subsets of robot configuration space for utilized feedback control laws. In this paper, the VFO (Vector Field Orientation) control law is leveraged to develop such a feedback control strategy for a unicycle robot with bounded curvature of motion. The proposed definition of funnels arises naturally from analysis of the VFO control law under curvature constraints. Obstacles in the environment are handled by shrinking the funnels using additional artificial curvature constraints. An exact analytic method for computation of funnels is presented. To make the funnels positively-invariant and guarantee motion safety, the original VFO control law has been modified. In contrast to numerous methods available in the literature, proposed feedback control strategy ensures at least C1 continuity of the control signals during transitions between funnels. Effectiveness of our approach has been verified by simulations, during which the robot was driven through a sequence of funnels planned in the cluttered environment using the RRT* algorithm.

Planning \( {{\mathbb{G}}^3} \)-continuous paths for state-constrained mobile robots with bounded curvature of motion

The bounds on the mobile robot curvature of motion and path curvature continuity constraints usually result either from mechanical construction limitations or practical motion smoothness requirements. Most path planning primitives compatible with those constraints force planning algorithms to utilize costly numerical methods for computation of maximal path curvature or positional path constraints verification. In this paper a novel path primitive is proposed, which can be concatenated with the line and circle segments to form a path with bounded curvature such that its perfect realization by a unicycle robot guarantees continuous time-derivative of its curvature of motion. Satisfaction of prescribed curvature bounds and positional path constraints resulting from obstacles in the environment is formally guaranteed using explicit analytic formulas presented in the paper. It is shown that the proposed approach yields an arbitrarily precise \( {{\mathbb{G}}^3} \)-continuous approximation of the Reeds-Shepp paths. Presented analysis is further utilized to formulate the global path planning problem in a continuous domain as a tractable optimization problem. Computational effectiveness of the proposed method has been additionally verified by quantitative comparison of constraint satisfaction checking speed with the \( {\eta^3} \)-splines.