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Real-Time Motion Planning with Applications to Autonomous Urban IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 17, NO. 5, SEPTEMBER 2009 1105 Real-time Motion Planning with Applications to Autonomous Urban Driving Yoshiaki Kuwata, Member, IEEE, Justin Teo, Student Member, IEEE, Gaston Fiore, Student Member, IEEE, Sertac Karaman, Student Member, IEEE, Emilio Frazzoli, Senior Member, IEEE, and Jonathan P. How, Senior Member, IEEE Abstract—This paper describes a real-time motion planning expected to stay in the correct lane, maintain a safe speed at or algorithm, based on the Rapidly-exploring Random Tree (RRT) under specified speed limits, correctly yield to other vehicles at approach, applicable to autonomous vehicles operating in an intersections, pass other vehicles when safe to do so, recognize urban environment. Extensions to the standard RRT are predom- inantly motivated by: (i) the need to generate dynamically feasible blockages and execute U-turns when needed, and park in an plans in real-time, (ii) safety requirements, (iii) the constraints assigned space. dictated by the uncertain operating (urban) environment. The Developing a robotic vehicle that could complete the DUC primary novelty is in the use of closed-loop prediction in the was a major systems engineering effort, requiring the de- framework of RRT. The proposed algorithm was at the core of the velopment and integration of state-of-the-art technologies in planning and control software for Team MIT’s entry for the 2007 DARPA Urban Challenge, where the vehicle demonstrated the planning, control, and sensing [2], [3]. The reader is referred ability to complete a 60 mile simulated military supply mission, to [3] for a system-level report on the design and development while safely interacting with other autonomous and human driven of Team MIT’s vehicle, Talos. The focus of this paper is on vehicles. the motion planning subsystem (or “motion planner”) and the Index Terms—Real-time motion planning, dynamic and un- associated controller (which is tightly coupled with the motion certain environment, RRT, urban driving, autonomous, DARPA planner). The motion planner is an intermediate level planner, Urban Challenge. with inputs primarily from a high level planner called the Navigator, and outputs being executed by the low level con- troller. Given the latest environment information and vehicle I. INTRODUCTION states, the motion planner computes a feasible trajectory to In November 2007, several autonomous automobiles from reach a goal point specified by the Navigator. This trajectory all over the world competed in the DARPA Urban Challenge is feasible in the sense that it avoids static obstacles and other (DUC), which was the third installment of a series of races vehicles, and abide by the rules of the road. The output of the for autonomous ground robots [1]. Unlike previous events that motion planner is then sent to the controller, which interfaces took place on desert dirt roads, the DUC course consisted directly to the vehicle, and is responsible for the execution of mainly of paved roads, incorporating features like intersec- the motion plan. tions, rotaries, parking lots, winding roads, and highways, The main challenges in designing the motion planning typically found in urban/suburban environments. The major subsystem resulted from the following factors: (i) complex and distinguishing characteristic of the DUC was the introduction unstable vehicle dynamics, with substantial drift, (ii) limited of traffic, with up to 70 robotic and human-driven vehicles sensing capabilities, such as range and visibility, in an uncer- on the course simultaneously. This resulted in hundreds of tain, time-varying environment, and (iii) temporal and logical unscripted robot-on-robot (and robot on human-driven vehi- constraints on the vehicle’s behavior, arising from the rules of cle) interactions. With a longer term goal of fielding such the road. autonomous vehicles in environments with co-existing traffic Numerous approaches to address the motion planning prob- and/or traffic infrastructure, all vehicles were required to abide lem have been proposed in the literature, and the reader by the traffic laws and rules of the road. Vehicles were is referred to [1], [4]–[8], to name a few. For our motion planning system, we chose to build it on the Rapidly-exploring Y. Kuwata was with Department of Aeronautics & Astronautics, Mas- sachusetts Institute of Technology, Cambridge, MA, 02139 USA. He is now Random Trees (RRT) algorithm [9]–[11], which belongs to the with Jet Propulsion Laboratory, California Institute of Technology, Pasadena, class of incremental sampling-based methods [7, Section 14.4]. CA, 91109 USA. e-mail: [email protected]. The main reasons for this choice were: (i) sampling-based J. Teo, E. Frazzoli and J. How are with Department of Aeronautics & Astronautics, Massachusetts Institute of Technology, Cambridge, MA, 02139 algorithms are applicable to very general dynamical models, USA. e-mail: fcsteo, frazzoli, [email protected]. (ii) the incremental nature of the algorithms lends itself easily G. Fiore was with Department of Aeronautics & Astronautics, Mas- to real-time, on-line implementation, while retaining certain sachusetts Institute of Technology, Cambridge, MA, 02139 USA. He is now with School of Engineering and Applied Sciences, Harvard University, completeness guarantees, and (iii) sampling-based methods do Cambridge, MA, 02138 USA. e-mail: gafi[email protected]. not require the explicit enumeration of constraints, but allow S. Karaman is with Department of Mechanical Engineering, Mas- trajectory-wise checking of possibly very complex constraints. sachusetts Institute of Technology, Cambridge, MA, 02139 USA. e-mail: [email protected]. In spite of their generality, the application of incremental Manuscript received September 12, 2008; revised December 23, 2008. sampling-based motion planning methods to robotic vehicles IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 17, NO. 5, SEPTEMBER 2009 1106 with complex and unstable dynamics, such as the full-size r - u Vehicle x - Controller - - Landrover LR3 used for the race, is far from straightforward. Model For example, the unstable nature of the vehicle dynamics requires the addition of a path-tracking control loop whose performance is generally hard to characterize. Moreover, the Fig. 1. Closed-loop prediction. Given a reference command r, the controller momentum of the vehicle at speed must be taken into account, generates high rate vehicle commands u to close the loop with the vehicle making it impossible to ensure collision avoidance by point- dynamics. wise constraint checks. In fact, to the best of our knowledge, RRTs have been restricted either to simulation, or to kinematic (essentially driftless) robots (i.e., it can be stopped instanta- III. PLANNING OVER CLOSED-LOOP DYNAMICS neously by setting the control input to zero), and never been used in on-line planning systems for robotic vehicles with the above characteristics. The existing randomized planning algorithms solve for the This paper reports on the design and implementation of input to the vehicle u(t) either by sampling an input itself an efficient and reliable general-purpose motion planning or by sampling a configuration and reverse calculating u(t), system, based on RRTs, for our team’s entry to the DUC. typically with a lookup table [9], [10], [12]–[14]. This paper In particular, we present an approach that enables the on- presents the Closed-loop RRT (CL-RRT) algorithm, which line use of RRTs on robotic vehicles with complex, unstable extends the RRT by making use of a low-level controller and dynamics and significant drift, while preserving safety in the planning over the closed-loop dynamics. In contrast to the face of uncertainty and limited sensing. The effectiveness of existing work, CL-RRT samples an input to the stable closed- our motion planning system is discussed, based on the analysis loop system consisting of the vehicle and the controller [15]. of actual data collected during the DUC race. Figure 1 shows the forward simulation of the closed- loop dynamics. The low-level controller takes a reference II. PROBLEM FORMULATION command r(t) 2 Rnr . For vehicles with complex dynamics, This section defines the motion planning problem. The the dimension of the vehicle states nx can be quite large, vehicle has nonlinear dynamics but the reference command r typically has a lower dimension (i.e., nr nx). For example, in our application, the reference x_ (t) = f(x(t); u(t)); x(0) = x0; (1) command is a 2D path for the steering controller and a speed where x(t) 2 Rnx and u(t) 2 Rnu are the states and inputs command profile for the speed controller. The vehicle model in nx of the system, and x0 2 R is the initial states at t = 0. this case included 7 states, and the reference command consists The input u(t) is designed over some (unspecified) finite of a series of triples (x; y; vcmd), where x and y are the position horizon [0; tf ]. Bounds on the control input, and requirements of the reference path, and vcmd is the associated desired speed. of various driving conditions, such as static and dynamic For urban driving, the direction of the vehicle motion (forward obstacles avoidance and the rules of the road, can be captured or reverse) is also part of the reference command, although this with a set of constraints imposed on the states and the inputs direction needs to be defined only once per reference path. Given the reference command, CL-RRT runs a forward x(t) 2 Xfree(t); u(t) 2 U: (2) simulation using a vehicle model and the controller to compute The time dependence of Xfree expresses the avoidance con- the predicted state trajectory x(t). The feasibility of this output nx straints for moving obstacles. The goal region Xgoal ⊂ R is checked against vehicle and environmental constraints, such of the motion planning problem is assumed to be given by a as rollover and obstacle avoidance constraints.
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