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Journal ArticleDOI

Sampling-based algorithms for optimal motion planning

01 Jun 2011-The International Journal of Robotics Research (SAGE Publications)-Vol. 30, Iss: 7, pp 846-894
TL;DR: In this paper, the authors studied the asymptotic behavior of the cost of the solution returned by stochastic sampling-based path planning algorithms as the number of samples increases.
Abstract: During the last decade, sampling-based path planning algorithms, such as probabilistic roadmaps (PRM) and rapidly exploring random trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g. as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g. showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e. such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.
Citations
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Journal ArticleDOI
13 Jun 2016
TL;DR: In this article, the authors present a survey of the state of the art on planning and control algorithms with particular regard to the urban environment, along with a discussion of their effectiveness.
Abstract: Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efficiency, and convenience of automotive transportation. Safety-critical tasks that must be executed by a self-driving vehicle include planning of motions through a dynamic environment shared with other vehicles and pedestrians, and their robust executions via feedback control. The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting. A selection of proposed techniques is reviewed along with a discussion of their effectiveness. The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements. The side by side comparison presented in this survey helps to gain insight into the strengths and limitations of the reviewed approaches and assists with system level design choices.

1,437 citations

Journal ArticleDOI
TL;DR: A review of motion planning techniques implemented in the intelligent vehicles literature, with a description of the technique used by research teams, their contributions in motion planning, and a comparison among these techniques is presented.
Abstract: Intelligent vehicles have increased their capabilities for highly and, even fully, automated driving under controlled environments. Scene information is received using onboard sensors and communication network systems, i.e., infrastructure and other vehicles. Considering the available information, different motion planning and control techniques have been implemented to autonomously driving on complex environments. The main goal is focused on executing strategies to improve safety, comfort, and energy optimization. However, research challenges such as navigation in urban dynamic environments with obstacle avoidance capabilities, i.e., vulnerable road users (VRU) and vehicles, and cooperative maneuvers among automated and semi-automated vehicles still need further efforts for a real environment implementation. This paper presents a review of motion planning techniques implemented in the intelligent vehicles literature. A description of the technique used by research teams, their contributions in motion planning, and a comparison among these techniques is also presented. Relevant works in the overtaking and obstacle avoidance maneuvers are presented, allowing the understanding of the gaps and challenges to be addressed in the next years. Finally, an overview of future research direction and applications is given.

1,162 citations

Posted Content
TL;DR: The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting and to gain insight into the strengths and limitations of the reviewed approaches.
Abstract: Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efficiency, and convenience of automotive transportation. Safety-critical tasks that must be executed by a self-driving vehicle include planning of motions through a dynamic environment shared with other vehicles and pedestrians, and their robust executions via feedback control. The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting. A selection of proposed techniques is reviewed along with a discussion of their effectiveness. The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements. The side-by-side comparison presented in this survey helps to gain insight into the strengths and limitations of the reviewed approaches and assists with system level design choices.

1,119 citations

Journal ArticleDOI
TL;DR: The technical aspect of automated driving is surveyed, with an overview of available datasets and tools for ADS development and many state-of-the-art algorithms implemented and compared on their own platform in a real-world driving setting.
Abstract: Automated driving systems (ADSs) promise a safe, comfortable and efficient driving experience. However, fatalities involving vehicles equipped with ADSs are on the rise. The full potential of ADSs cannot be realized unless the robustness of state-of-the-art is improved further. This paper discusses unsolved problems and surveys the technical aspect of automated driving. Studies regarding present challenges, high-level system architectures, emerging methodologies and core functions including localization, mapping, perception, planning, and human machine interfaces, were thoroughly reviewed. Furthermore, many state-of-the-art algorithms were implemented and compared on our own platform in a real-world driving setting. The paper concludes with an overview of available datasets and tools for ADS development.

851 citations

Journal ArticleDOI
TL;DR: CHOMP (covariant Hamiltonian optimization for motion planning), a method for trajectory optimization invariant to reparametrization, uses functional gradient techniques to iteratively improve the quality of an initial trajectory, optimizing a functional that trades off between a smoothness and an obstacle avoidance component.
Abstract: In this paper, we present CHOMP (covariant Hamiltonian optimization for motion planning), a method for trajectory optimization invariant to reparametrization. CHOMP uses functional gradient techniques to iteratively improve the quality of an initial trajectory, optimizing a functional that trades off between a smoothness and an obstacle avoidance component. CHOMP can be used to locally optimize feasible trajectories, as well as to solve motion planning queries, converging to low-cost trajectories even when initialized with infeasible ones. It uses Hamiltonian Monte Carlo to alleviate the problem of convergence to high-cost local minima (and for probabilistic completeness), and is capable of respecting hard constraints along the trajectory. We present extensive experiments with CHOMP on manipulation and locomotion tasks, using seven-degree-of-freedom manipulators and a rough-terrain quadruped robot.

682 citations

References
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Journal ArticleDOI
TL;DR: When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput /spl lambda/(n) obtainable by each node for a randomly chosen destination is /spl Theta/(W//spl radic/(nlogn)) bits persecond under a noninterference protocol.
Abstract: When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput /spl lambda/(n) obtainable by each node for a randomly chosen destination is /spl Theta/(W//spl radic/(nlogn)) bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission's range is optimally chosen, the bit-distance product that can be transported by the network per second is /spl Theta/(W/spl radic/An) bit-meters per second. Thus even under optimal circumstances, the throughput is only /spl Theta/(W//spl radic/n) bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signal-to-interference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance.

9,008 citations

Book
01 Sep 1985

7,736 citations

Journal ArticleDOI
TL;DR: This paper reformulated the manipulator con trol problem as direct control of manipulator motion in operational space—the space in which the task is originally described—rather than as control of the task's corresponding joint space motion obtained only after geometric and geometric transformation.
Abstract: This paper presents a unique real-time obstacle avoidance approach for manipulators and mobile robots based on the artificial potential field concept. Collision avoidance, tradi tionally considered a high level planning problem, can be effectively distributed between different levels of control, al lowing real-time robot operations in a complex environment. This method has been extended to moving obstacles by using a time-varying artificial patential field. We have applied this obstacle avoidance scheme to robot arm mechanisms and have used a new approach to the general problem of real-time manipulator control. We reformulated the manipulator con trol problem as direct control of manipulator motion in oper ational space—the space in which the task is originally described—rather than as control of the task's corresponding joint space motion obtained only after geometric and kine matic transformation. Outside the obstacles' regions of influ ence, we caused the end effector to move in a straight line with an...

6,515 citations