## 1 Introduction
To produce a feasible path that avoids obstacles in a cluttered environment, waypoint navigation method has been a viable approach used to generate a sequence of waypoints connected via a path primitive [36; 37] for reactive trajectory generation, while the entire path satisfies the smoothness requirement or some other criterion and respects the kinodynamic constraints imposed on the vehicle motion such as the constraints on the instantaneous velocities that can be achieved [2; 22]. However, the path primitives have to be recomputed whenever some of the waypoints built between the start and the goal are changed. 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:  
1. 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]. 2. In many applications, the smoothness of trajectories is essential. Trajectories generated by HPF approaches are the integral curves of the gradient vector field of HPF. The trajectories that are smooth are readily executable. 3. Streamlines can be computed offline systematically based on prior obstacle information (distribution, i.e., shape, size, location, and number) without the waypoints and path primitives, thus, being more predictable. 4. Notably, the HPF-based path planner is a complete [7] and anytime algorithm [10], in which the streamlines generated cover the free regions of the workspace. [PERSON] 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. We elaborate on demonstrating the potential of the hydrodynamics-based motion planning approach of (1) subject to the curvature constraint. An obstacle avoidance system using three primitive streamline-based paths and a path selection strategy that makes the avoidance of small obstacle easier is proposed. For avoiding multiple obstacles, a pure pursuit algorithm [20; 21] is implemented in this paper for the purpose of enabling a smooth and safe transition using streamline changing between obstacles without violating the curvature constraint. The experiment is conducted for a constant speed circular non-holonomic mobile robot to navigate smoothly in real-world partially unknown environments cluttered with cylinder-shaped obstacles. The Dr. Robot X80 robot (Dr Robot Inc. in Markham, ON, Canada), which was equipped with a low-cost sonar and infrared sensors to detect obstacles during motion, is used as the navigation platform. The paper is organized as follows. Section 2 gives a brief introduction of a mobile robot with two independently driven wheels for the experiment. Section 3 mentions the harmonic potential field approach for avoiding cylindrical obstacles.