Figure 4 - uploaded by Jing Xiao

Content may be subject to copyright.

# Five types of basic maneuver patterns, where the arrow shows the orientation of the robot. The robot changes motion directions from forward to backward or vice versa at each sharp intersection.

Source publication

Navigation of a car-like robot in environments with unknowns requires effective on-line planning of nonholonomic trajectories. We propose a set of basic maneuver patterns based on Bezier curves that allow either forward or backward motion as building blocks to create nonholonomic trajectories quickly, given a sequence of knot positions/points (e.g....

## Contexts in source publication

**Context 1**

... , P n , and P n+1 indicate a turn formed by two line segments. The figure also shows four types of transition curves, which are Bezier curves with P n as the common control point. We now describe how to use these four types of Bezier curves to construct maneuver patterns. For an arbitrary angle formed by P n-1 , P n , and P n+1 , as shown in Fig. 4, if is sufficiently large, the straightforward turning curve v 1 v 2 can be followed by a car-like robot to make the turn while satisfying inequality (4) under its velocity at P n-1 . Thus, the curve v 1 v 2 is a maneuver pattern, called maneuver 1. Now if there is an obstacle to block the maneuver along v 1 v 2 , a different ...

**Context 2**

... the curve v 1 v 2 is a maneuver pattern, called maneuver 1. Now if there is an obstacle to block the maneuver along v 1 v 2 , a different maneuver policy involving additional straight-line movements, called maneuver 2, can be used to achieve the same turn, as shown in Figure 4. Note that v 7 v 8 is executed by the robot by moving backward. ...

**Context 3**

... pair of patterns maneuver 1 and maneuver 2 provide two alternatives for a car to achieve the same turn while satisfying the nonholonomic constraint, i.e., inequality (4). If is too small so that the maneuver 1 and maneuver 2 patterns cannot be applied to the robot without violating the nonholonomic constraint, the patterns maneuver 3 and maneuver 4 (see Figure 4) can be used to make the turn by reversing the robot. The smaller is, the larger the angle is, and therefore, it is more likely that (4) will be satisfied. ...

## Similar publications

This paper presents a method for animating human characters, especially dedicated to walk planning problems. The method is integrated in a randomized motion planning scheme, including a local planner dedicated to human walk. This local planner inte- grates a character motion controller assuming realistic animations. The navigation of the character...

## Citations

... This is highly undesirable as it results in non-fluid trajectories [26]. Therefore, path planning based on circular arc, spline and Bezier curves can be mentioned to create a smooth path planning by getting rid of unwanted situations that adversely affect the movements of the autonomous mobile robot [27,28,15]. Path planning problems have attracted the attention of researchers in recent years, not only to shorten the road but also to ensure the smoothness and reliability of the path [23,29]. ...

Path planning algorithms are used in known environments to find the shortest, smooth and optimal way without collision from the starting point to the target point. However, excessive nodes and pointed spiking points that occur during this path planning process pose problems. Bezier curves offer highly effective possibilities for path forming problems. In this article, a new approach based on Bezier curves is proposed for solving such problems. First, grid maps are used to model the environment Second, a path is found between the start and endpoints using traditional algorithms. Third, the excess knots are discarded by pruning based on Bezier curves. Finally, the spikes are smoothed using Bezier curves to ensure smoothness and continuity. Looking at the results from the proposed approach, it has proven that its effectiveness in obtaining an optimum path between the starting and target points in known environments.

... However, it assumes that the deviations from the global path are small. If the deviations are large, the approach may fail, requiring the global path to be recomputed using the updated information (also see [9] and [1] for similar works). The assumption of availability of such a global path to the goal is invalid in this paper. ...

On-line motion planning in unknown environments is a challenging problem as it requires (i) ensuring collision avoidance and (ii) minimizing the motion time, while continuously predicting where to go next. Previous approaches to on-line motion planning assume that a rough map of the environment is available, thereby simplifying the problem. This paper presents a reactive on-line motion planner, Robust Autonomous Waypoint generation (RAW), for mobile robots navigating in unknown and unstructured environments. RAW generates a locally maximal ellipsoid around the robot, using semi-definite programming, such that the surrounding obstacles lie outside the ellipsoid. A reinforcement learning agent then generates a local waypoint in the robot's field of view, inside the ellipsoid. The robot navigates to the waypoint and the process iterates until it reaches the goal. By following the waypoints the robot navigates through a sequence of overlapping ellipsoids, and avoids collision. Robot's safety is guaranteed theoretically and the claims are validated through rigorous numerical experiments in four different experimental setups. Near-optimality is shown empirically by comparing RAW trajectories with the global optimal trajectories.

... Hence, researchers have developed several techniques to reduce the computation time to achieve planning within allowable time limit. In our review, we will be primarily focusing on techniques involving grid and lattice-based planning paradigms (Pivtoraiko et al. 2009;Kelly et al. 2006;Li and Xiao 2009) that were developed to enhance the capability as well as performance of the classical discrete search algorithms such as A* (Hart et al. 1968), D* Lite (Koenig and Likhachev 2002), Anytime Dynamic A* (Likhachev et al. 2005), etc. ...

The growing variety and complexity of marine research and application oriented tasks requires unmanned surface vehicles (USVs) to operate fully autonomously over long time horizons even in environments with significant civilian traffic. In order to address this challenge, we have developed a lattice-based 5D trajectory planner for USVs. The planner estimates collision risk and reasons about the availability of contingency maneuvers to counteract unpredictable behaviors of civilian vessels. The planner also incorporates avoidance behaviors of the vessels into the search for a dynamically feasible trajectory to minimize collision risk. In order to be computationally efficient, it dynamically scales the control action primitives of a trajectory based on the distribution and concentration of civilian vessels while preserving the dynamical feasibility of the primitives. We present a novel congestion metric to compare the complexity of different scenarios when evaluating the performance of the planner. Our results demonstrate that the basic version of the risk and contingency-aware planner (RCAP) significantly decreases the number of collisions compared to a baseline, velocity obstacles based planner, especially in complex scenarios with a high number of civilian vessels. The adaptive version of the planner (A-RCAP) improves the computational performance of RCAP by 500 %. This leads to a high replanning rate, which allows shorter traversal distances and smaller arrival times, while ensuring comparable incidence of collisions.

... For geometry-based trajectory generation, different geometric elements have been employed, such as line segments and arcs [9], clothoids [10], β-spline [11], Bézier curves [12], [13], [14], etc. However, only a few works have been conducted on trajectory generation while considering curvature and velocity constraints. ...

To generate local trajectory between initial states and target states for autonomous vehicles, a feasible trajectory generation algorithm based on quartic Bézier curve is proposed. The problem of trajectory generation is firstly seperated into generating continuous and bounded curvature profile to shape the trajectory and generating linear velocity profile to execute the trajectory. The curvature profile generation is further converted to an optimization problem with only 3 parameters owing to the specific properties of quartic Bézier curve. Sequential quadratic programming is employed to find optimal solution with respect to specific objective function. To avoid sideslip and ensure velocity-continuity and acceleration limits, the framework of linear velocity profile generation is also proposed. A simple profile with constant acceleration is also provided as an example. Simulation results on lane keeping and changing and path following demonstrate the capability and the real-Time performance of the proposed algorithm.

... Trajectory planning using maneuver automatons [68] and related motion primitives [69], [22], [70] has lately become very popular for unmanned aerial and ground vehicles trajectory planning. This is mainly due to the discretization of a continuous state-action space into a manageable discrete space suitable for fast and dynamically feasible search. ...

The capability of following a moving target in an environment with obstacles is required as a basic and necessary function for realizing an autonomous unmanned surface vehicle (USV). Many target following scenarios involve a follower and target vehicles that may have different maneuvering capabilities. Moreover, the follower vehicle may not have prior information about the intended motion of the target boat. This paper presents a trajectory planning and tracking approach for following a differentially constrained target vehicle operating in an obstacle field. The developed approach includes a novel algorithm for computing a desired pose and surge speed in the vicinity of the target boat, jointly defined as a motion goal, and tightly integrates it with trajectory planning and tracking components of the entire system. The trajectory planner generates a dynamically feasible, collision-free trajectory to allow the USV to safely reach the computed motion goal. Trajectory planning needs to be sufficiently fast and yet produce dynamically feasible and short trajectories due to the moving target. This required speeding up the planning by searching for trajectories through a hybrid, pose-position state space using a multi-resolution control action set. The search in the velocity space is decoupled from the search for a trajectory in the pose space. Therefore, the underlying trajectory tracking controller computes desired surge speed for each segment of the trajectory and ensures that the USV maintains it. We have carried out simulation as well as experimental studies to demonstrate the effectiveness of the developed approach.

... ,[7] ...

This paper proposes an improved Maximum Power Point Tracking method and design methods of unmanned solar vehicle system by parts of hardware, unmanned driving control and power conversion. The hardware design is offered on the weight reduction and structural reliability by using structural analysis software. The technique of curve fitting is applied to unmanned control system due to minimizing the vehicle's behavior. Furthermore, lateral controller applying actuator dynamics is robust enough to prevent performance degradation by measurement noise regarding position and heading angle. The power conversion system contains battery charger system and tapped-inductor boost converter. In the battery charger system, variable step-size MPPT is conducted for quick response of maximum power point tracking. The validity of the proposed algorithm are verified by simulations and experiments.

... t 가 0부터 1까지 변화할 때, P(0) = P 0 에서 시작하여 P(1) = P n 에서 끝나는 베지어 곡선을 그리게 되며, 각각의 조 절점은 전체 곡선 형상에 영향을 미친다. 베지어 곡선의 특 징은 아래와 같다 [15,16]. ...

This paper presents a sensor fusion-based estimation of heading and a Bezier curve-based motion planning for unmanned ground vehicle. For the vehicle to drive itself autonomously and safely, it should estimate its pose with sufficient accuracy in reasonable processing time. The vehicle should also have a path planning algorithm that enables to adapt to various situations on the road, especially at intersections. First, we address a sensor fusion-based estimation of the heading of the vehicle. Based on extended Kalman filter, the algorithm estimates the heading using the GPS, IMU, and wheel encoders considering the reliability of each sensor measurement. Then, we propose a Bezier curve-based path planner that creates several number of path candidates which are described as Bezier curves with adaptive control points, and selects the best path among them that has the maximum probability of passing through waypoints or arriving at target points. Experiments under various outdoor conditions including at intersections, verify the reliability of our algorithm.

Safe lane changing of the dynamic industrial park and port scenarios with autonomous trucks involves the problem of planning an effective and smooth trajectory. To solve this problem, we propose a new trajectory planning method based on the Dijkstra algorithm, which combines the Dijkstra algorithm with a cost function model and the Bezier curve. The cost function model is established to filter target trajectories to obtain the optimal target trajectory. The third-order Bezier curve is employed to smooth the optimal target trajectory. Road experiments are carried out with an autonomous truck to illustrate the effectiveness and smoothness of the proposed method. Compared with other conventional methods, the improved method can generate a more effective and smoother trajectory in the truck lane change.

The ability of autonomous vehicles to successfully replace human drivers depends on their capability to plan safe, efficient and usable paths in dynamically evolving traffic scenarios. This challenge gets more difficult when the autonomous vehicle has to drive through complex scenarios such as intersections which demand interactive behaviour between vehicles. Many autonomous vehicle demonstrations over the last few decades have highlighted the limitations in the current state-of-the-art of path planning solutions. They have been found to be inefficient and sometimes unsafe when tackling interactively demanding scenarios. The generic path planning solutions consists of three planners, a “global path planner”, a “behaviour planner” and a “local path planner. In this paper we establish that the “behaviour planner” is the limitation of a successful path planning solution, after reviewing the individual planners and the associated solutions. In this paper a new adaptive tactical behaviour planner is proposed to overcome the limitations. This planner is motivated by how expert human drivers behave in interactive scenarios, and is made up of a three module architecture. The paper describes the individual modules, and also highlights how they play a part in the overall behaviour selection for the autonomous vehicle. The paper is concluded by a discussion on how this proposed planner generates safe and efficient behaviours in complex dynamic traffic scenarios by considering a case of a roundabout not controlled by traffic signals.

This paper addresses the problem of real-time, non-holonomic motion planning in environments with moving
obstacles of unforeseen, arbitrary motion. An approach is introduced to generate feasible non-holonomic trajectory segments on the fly as the robot moves in such an environment, extending the real-time adaptive motion planning (RAMP) approach that is used for holonomic motion. It allows efficient on-line simultaneous planning and execution of non-holonomic trajectories and enables a robot to adapt to changes in the environment by smoothly switching trajectories while taking into account robot motion uncertainty. The effectiveness and efficiency of the method has been verified through real experiments with a mobile robot and several dynamic obstacles of unforeseen motion to the robot.