TheVector-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 amplitudelimited 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

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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 waypointfollowing 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 postprocessing. Validity of the proposed approach has 266 J Intell Robot Syst (2018) 89:265-297 been confirmed by simulation studies and experimental motion execution with a laboratory-scale mobile robot.

Provably correct and computationally efficient path planning in the presence of various constraints is essential for autonomous driving and agile maneuvering of mobile robots. In this paper, we consider the planning of G 3-continuous planar paths with continuous and limited curvature in a motion environment that is bounded and contains obstacles modeled by a set of (non-convex) polygons. In practice, the curvature constraints often arise from mechanical limitations for the robot, such as limited steering and articulation angles in wheeled robots, or aerodynamic constraints in unmanned aerial vehicles. To solve the planning problem under those stringent constraints, we improve upon known path primitives, such as Reeds–Shepp (RS) and CC-steer (curvature-continuous) paths. Given the initial and final robot configuration, we developed extend-procedure computing paths that can approximate RS paths with arbitrary precision, but guaranteeing G 3-continuity. We show that satisfaction of all stated path constraints is guaranteed and, contrary to many other methods known from the literature, the method of checking for collisions between the planned path and obstacles is given by a closed-form analytic expression. Furthermore, we demonstrate that our approach is not conservative, i.e., it allows for precise maneuvers in tight environments under the assumption of a rectangular robot footprint. The presented extend procedure can be integrated into various motion-planning algorithms available in the literature. In particular, we utilized the Rapidly exploring Random Trees (RRT*) algorithm in conjunction with our extend procedure to demonstrate its feasibility in motion environments of nontrivial complexity and low computational cost in comparison to a G 3-continuous extend procedure based on η 3-splines.

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