Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

Safe handling of dynamic highway and inner city scenarios with autonomous vehicles involves the problem of generating traffic-adapted trajectories. In order to account for the practical requirements of the holistic autonomous system, we propose a semi-reactive trajectory generation method, which can be tightly integrated into the behavioral layer. The method realizes long-term objectives such as velocity keeping, merging, following, stopping, in combination with a reactive collision avoidance by means of optimal-control strategies within the Frenet-Frame [12] of the street. The capabilities of this approach are demonstrated in the simulation of a typical high-speed highway scenario.

Optimal trajectory generation for dynamic street scenarios in a Frenét Frame

An algorithm is presented for wheeled mobile robot trajectory generation that achieves a high degree of generality and efficiency. The generality derives from numerical linearization and inversion of forward models of propulsion, suspension, and motion for any type of vehicle. Efficiency is achieved by using fast numerical optimization techniques and effective initial guesses for the vehicle controls parameters. This approach can accommodate such effects as rough terrain, vehicle dynamics, models of wheel-terrain interaction, and other effects of interest. It can accommodate boundary and internal constraints while optimizing an objective function that might, for example, involve such criteria as obstacle avoidance, cost, risk, time, or energy consumption in any combination. The algorithm is efficient enough to use in real time due to its use of nonlinear programming techniques that involve searching the space of parameterized vehicle controls. Applications of the presented methods are demonstrated for planetary rovers.

Optimal Rough Terrain Trajectory Generation for Wheeled Mobile Robots

We present an approach to the problem of differentially constrained mobile robot motion planning in arbitrary cost fields The approach is based on deterministic search in a specially discretized state space We compute a set of elementary motions that connects each discrete state value to a set of its reachable neighbors via feasible motions Thus, this set of motions induces a connected search graph The motions are carefully designed to terminate at discrete states, whose dimensions include relevant state variables (eg, position, heading, curvature, and velocity) The discrete states, and thus the motions, repeat at regular intervals, forming a lattice We ensure that all paths in the graph encode feasible motions via the imposition of continuity constraints on state variables at graph vertices and compliance of the graph edges with a differential equation comprising the vehicle model The resulting state lattice permits fast full configuration space cost evaluation and collision detection Experimental results with research prototype rovers demonstrate that the planner allows us to exploit the entire envelope of vehicle maneuverability in rough terrain, while featuring real-time performance © 2009 Wiley Periodicals, Inc

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Differentially constrained mobile robot motion planning in state lattices

We present a motion planner for autonomous highway driving that adapts the state lattice framework pioneered for planetary rover navigation to the structured environment of public roadways. The main contribution of this paper is a search space representation that allows the search algorithm to systematically and efficiently explore both spatial and temporal dimensions in real time. This allows the low-level trajectory planner to assume greater responsibility in planning to follow a leading vehicle, perform lane changes, and merge between other vehicles. We show that our algorithm can readily be accelerated on a GPU, and demonstrate it on an autonomous passenger vehicle.

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Motion planning for autonomous driving with a conformal spatiotemporal lattice

There are many situations for which a feasible nonholonomic motion plan must be generated immediately based on real-time perceptual information Parametric trajectory representations limit computation because they reduce the search space for solutions (at the cost of potentially introducing suboptimality) The use of any parametric trajectory model converts the optimal control formulation into an equivalent nonlinear programming problem In this paper, curvature polynomials of arbitrary order are used as the assumed form of solution Polynomials sacrifice little in terms of spanning the set of feasible controls while permitting an expression of the general solution to the system dynamics in terms of decoupled quadratures These quadratures are then readily linearized to express the necessary conditions for optimality Resulting trajectories are convenient to manipulate and execute in vehicle controllers and they can be computed with a straightforward numerical procedure in real time KEY WORDS—mobile robots, car-like robots, trajectory generation, curve generation, nonholonomic, clothoid, cornu spiral, optimal control

Reactive Nonholonomic Trajectory Generation via Parametric Optimal Control

Curvature polynomials of cubic order are ideal primitive trajectories for car-like robots Unlike the clothoids, which are linear curvature polynomials, cubic curves can be used to determine a unique trajectory to an arbitrary target posture using a single continuous primitive Such curves are also the lowest order curves which are continuous in the torque applied to steering mechanisms, so they generate trajectories which are relatively easily tracked by a real vehicle Like the clothoids, cubic curvature polynomials are relatively difficult to compute but are easy to execute A real-time numerical method to compute them is described

Trajectory generation for car-like robots using cubic curvature polynomials

Automated guided vehicles (AGVs) have been operating effectively in factories for decades. These vehicles have successfully used strategies of deliberately structuring the environment and adapting the process to the automation. The potential of computer vision technology to increase the intelligence and adaptability of AGVs is largely unexploited in contemporary commercially available vehicles. We developed an infrastructure-free AGV that uses four distinct vision systems. Three of them exploit naturally occurring visual cues instead of relying on infrastructure. When coupled with a highly capable trajectory generation algorithm, the system produces four visual servo controllers that guide the vehicle continuously in several contexts. These contexts range from gross motion in the facility to precision operations for lifting and mating parts racks and removing them from semi-trailers. To our knowledge, this is the first instance of an AGV that has operated successfully in a relevant environment for an extended period of time without relying on any infrastructure.

An Infrastructure-Free Automated Guided Vehicle Based on Computer Vision An Effort to Make an Industrial Robot Vehicle that Can Operate without Supporting Infrastructure

Bryan Nagy

Papers

Reactive Nonholonomic Trajectory Generation via Parametric Optimal Control

Trajectory generation for car-like robots using cubic curvature polynomials

An Infrastructure-Free Automated Guided Vehicle Based on Computer Vision An Effort to Make an Industrial Robot Vehicle that Can Operate without Supporting Infrastructure