Kinodynamic Motion Planning for a Two-Wheel-Drive Mobile Robot

Abstract

Since a nonholonomic system such as a robot with two independent driving wheels includes complicated nonlinear terms generally, it is hard to realize a stable and tractable controller design. However, about a dynamic control method for the motion planning, it is guaranteed that a nonholonomic-controlled object can always be converged to an arbitrary point using a control method based on an invariant manifold. Based on it, the method called “kinodynamic motion planning” was proposed to converge the states of the two-wheeled mobile robot to the arbitrary target position while avoiding obstacles by combining the control based on the invariant manifold and the HPF. In this chapter, how to combine the invariant manifold control and the concept of the HPF is explained in detail, and the usefulness of the proposed approach is verified through some simulations.

A Real-Time Hydrodynamic-Based Obstacle Avoidance System for Non-holonomic Mobile Robots with Curvature Constraints

“…The gradient of the HPF or the streamline that defines the vector field of the path at every point can be computed efficiently; analytically for a simple obstacle shape such as a circle or numerically. There are a few simulations showing that a vehicle modeled as a point (fluid) particle could smoothly navigate without collision with the (circular, elliptical, rectangle, or arbitrary-shaped) obstacles [6,8,[11][12][13][14][15][16][17][18]26,30] by following streamlines from a variety of start points in an environment composed of multiple obstacles. To build an APF via hydrodynamics potential, Reference [15] proposed a panel method by first approximating an arbitrarily shaped obstacle by an enclosing polygon (set of panels).…”

“…Furthermore, the entire path could be lengthy because of many detours. HPF-based non-holonomic path planning for a mobile robot subject to kinodynamic constraints [17,22,26] takes advantages of features of streamlines that are very appropriate for building a directional navigation system: (i) Streamlines are rich, thus, enabling the selection of appropriate paths for the planner. The desired state trajectory to be followed by a robot is determined only by the input defined by HPFs, i.e., along a streamline-based trajectory compatible with the kinodynamic constraints of the motion, even in high-speed motion [12].…”

“…Lau et al [18] provide a streamline-based kinodynamic motion planning approach to avoid elliptical obstacles, guaranteeing that both velocity and curvature are within limits by adjusting the strength of a source and a sink if a portion of the 3D trajectory violates the kinematic constraints. Recent work [26] used the gradient of HPF as an additional input to alter the motion pattern of a two-wheeled drive mobile robot based on the stabilizing controller design using an invariant manifold to avoid the obstacles, thus, extending the guidance method of Reference [22] based on the HPF only. Along this line of HPF-based non-holonomic path planning work, this work starts with the point that the curvature constraint, viewed as a constrained input to (1), significantly restricts the selection or generation of allowable paths to be followed in a cluttered environment.…”