Geometric continuous-curvature path planning for automatic parallel parking

Abstract

International audienceThis paper deals with path planning for car-like vehicle in parallel parking problems. Our path planning method uses simple geometry of the vehicle kinematic model. The presented strategy consists in two parts: create a simple geometric path for the parallel parking in one or more maneuvers, formed by circle arcs and then transform it to a continuous-curvature path with the use of clothoids. Accordingly, a car-like vehicle can follow such path without reorienting its front wheels at stop. The proposed planning method is independent of the initial position and of the orientation of the vehicle. Control inputs for steering angle and longitudinal velocity are generated so that the vehicle can park by following them

A unified motion planning method for parking an autonomous vehicle in the presence of irregularly placed obstacles

“…The rationale behind this issue is that, the instantaneous curvature jðtÞ ¼ sin /ðtÞ l as well as its derivative djðtÞ dt ¼ xðtÞÁcos /ðtÞ l should be bounded so as to avoid generating non-smooth trajectories. Commonly, non-smooth trajectories are not recommended due to the resulting undesirable wear of tires [12]. Given that /ðtÞ is mechanically limited, if there is no boundaries imposed on xðtÞ, one cannot guarantee that djðtÞ dt is bounded, and then the continuous-curvature property cannot be guaranteed.…”

“…Imposing bounds on xðtÞ has been widely applied with the aim of planning continuous-curvature trajectories in a number of previous publications (e.g., [12,15,16,27]). The rationale behind this issue is that, the instantaneous curvature jðtÞ ¼ sin /ðtÞ l as well as its derivative djðtÞ dt ¼ xðtÞÁcos /ðtÞ l should be bounded so as to avoid generating non-smooth trajectories.…”

“…The prevailing motion planning methods on the basis of complete environmental knowledge can be broadly classified into three categories: geometric-based methods, heuristic-based methods, and methods based on control theories. Geometric-based approaches commonly compute reference paths first and then generate trajectories following the obtained paths (e.g., [12][13][14][15][16]). Here, a path refers to a geometric curve y ¼ f ðxÞ in the xy coordinate frame, whereas a trajectory attaches the time course along a path, i.e., the determination of x ¼ xðtÞ [17].…”

Simultaneous dynamic optimization: A trajectory planning method for nonholonomic car-like robots

“…To avoid the undesirable wearing of tires [40][41][42], many studies have planned continuous-curvature trajectories. One way to generate continuous-curvature trajectories is imposing bounds on xðtÞ [35].…”

Laser-Based Control Law for Autonomous Parallel and Perpendicular Parking

“…Among the different planning techniques it is possible to distinguish between geometric approaches, with either constant turning radius [4], [5] using saturated feedback controllers, or continuous-curvature planning using clothoids [6]; heuristic approaches [7] and machine learning techniques [8]. It is worth to note that parking maneuvers with forward motions are seldom considered, with [9] for the parallel parking case and [10] for the perpendicular case being some of the few works on this regard.…”