Likhachev, Maxim
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Publication Incremental Phi*: Incremental Any-Angle Path Planning on Grids(2009-07-11) Nash, Alex; Koenig, Sven; Likhachev, MaximWe study path planning on grids with blocked and unblocked cells. Any-angle path-planning algorithms find short paths fast because they propagate information along grid edges without constraining the resulting paths to grid edges. Incremental path-planning algorithms solve a series of similar path-planning problems faster than repeated single-shot searches because they reuse information from the previous search to speed up the next one. In this paper, we combine these ideas by making the any-angle path-planning algorithm Basic Theta* incremental. This is non-trivial because Basic Theta* does not fit the standard assumption that the parent of a vertex in the search tree must also be its neighbor. We present Incremental Phi* and show experimentally that it can speed up Basic Theta* by about one order of magnitude for path planning with the freespace assumption.Publication R* Search(2008-07-13) Likhachev, Maxim; Stentz, AnthonyOptimal heuristic searches such as A* search are widely used for planning but can rarely scale to large complex problems. The suboptimal versions of heuristic searches such as weighted A* search can often scale to much larger planning problems by trading off the quality of the solution for efficiency. They do so by relying more on the ability of the heuristic function to guide them well towards the goal. For complex planning problems, however, the heuristic function may often guide the search into a large local minimum and make the search examine most of the states in the minimum before proceeding. In this paper, we propose a novel heuristic search, called R* search, which depends much less on the quality of the heuristic function. The search avoids local minima by solving the whole planning problem with a series of short-range and easy-to-solve searches, each guided by the heuristic function towards a randomly chosen goal. In addition, R* scales much better in terms of memory because it can discard a search state-space after each of its searches. On the theoretical side, we derive probabilistic guarantees on the sub-optimality of the solution returned by R*. On the experimental side, we show that R* can scale to large complex problems.Publication Efficiently Using Cost Maps For Planning Complex Maneuvers(2008-05-19) Ferguson, Dave; Likhachev, MaximWe have recently developed an algorithm for generating complex dynamically-feasible maneuvers for autonomous vehicles traveling at high speeds over large distances. Our approach is based on performing anytime incremental search on a multi-resolution, dynamically-feasible lattice state space. It has been implemented on an autonomous passenger vehicle that competed in, and won, the Urban Challenge. Much of the speed and robustness of our approach owes to the clever design and use of grid-based cost maps that were used throughout the planning process. In this paper, we explain the design and use of these various grid-based cost maps.Publication Motion Planning in Urban Environments: Part II(2008-09-22) Ferguson, Dave; Howard, Thomas M; Likhachev, MaximWe present the motion planning framework for an autonomous vehicle navigating through urban environments. Such environments present a number of motion planning challenges, including ultra-reliability, high-speed operation, complex inter-vehicle interaction, parking in large unstructured lots, and constrained maneuvers. Our approach combines a model-predictive trajectory generation algorithm for computing dynamically-feasible actions with two higher-level planners for generating long range plans in both on-road and unstructured areas of the environment. In this Part II of a two-part paper, we describe the unstructured planning component of this system used for navigating through parking lots and recovering from anomalous on-road scenarios. We provide examples and results from ldquoBossrdquo, an autonomous SUV that has driven itself over 3000 kilometers and competed in, and won, the Urban Challenge.Publication Information Value-Driven Approach to Path Clearance with Multiple Scout Robots(2008-05-19) Likhachev, Maxim; Stentz, AnthonyIn the path clearance problem the robot needs to reach its goal as quickly as possible without being detected by enemies. The robot does not know the precise locations of enemies, but has a list of their possible locations. These locations can be sensed, and the robot can go through them if no enemy is present or has to take a detour otherwise. We have previously developed an approach to the path clearance problem when the robot itself had to sense possible enemy locations. In this paper we investigate the problem of path clearance when the robot can use multiple scout robots to sense the possible enemy locations. This becomes a high-dimensional planning under uncertainty problem. We propose an efficient and scalable approach to it. While the approach requires centralized planning, it can scale to very large environments and to a large number of scouts and allows the scouts to be heterogenous. The experimental results show the benefits of using our approach when multiple scout robots are available.Publication Time-bounded Lattice for Efficient Planning in Dynamic Environments(2009-05-12) Kushleyev, Aleksandr; Likhachev, MaximFor vehicles navigating initially unknown cluttered environments, current state-of-the-art planning algorithms are able to plan and re-plan dynamically-feasible paths efficiently and robustly. It is still a challenge, however, to deal well with the surroundings that are both cluttered and highly dynamic. Planning under these conditions is more difficult for two reasons. First, tracking and predicting the trajectories of moving objects (i.e., cars, humans) is very noisy. Second, the planning process is computationally more expensive because of the increased dimensionality of the state-space, with time as an additional variable. Moreover, re-planning needs to be invoked more often since the trajectories of moving obstacles need to be constantly re-estimated. In this paper, we develop a path planning algorithm that addresses these challenges. First, we choose a representation of dynamic obstacles that efficiently models their predicted trajectories and the uncertainty associated with the predictions. Second, to provide real-time guarantees on the performance of planning with dynamic obstacles, we propose to utilize a novel data structure for planning - a time-bounded lattice - that merges together short-term planning in time with longterm planning without time. We demonstrate the effectiveness of the approach in both simulations with up to 30 dynamic obstacles and on real robots.Publication Search-based Planning for a Legged Robot over Rough Terrain(2009-05-12) Vernaza, Paul; Likhachev, Maxim; Bhattacharya, Subhrajit; Kushleyev, Aleksandr; Lee, Daniel D; Chitta, SachinWe present a search-based planning approach for controlling a quadrupedal robot over rough terrain. Given a start and goal position, we consider the problem of generating a complete joint trajectory that will result in the legged robot successfully moving from the start to the goal. We decompose the problem into two main phases: an initial global planning phase, which results in a footstep trajectory; and an execution phase, which dynamically generates a joint trajectory to best execute the footstep trajectory. We show how R* search can be employed to generate high-quality global plans in the high-dimensional space of footstep trajectories. Results show that the global plans coupled with the joint controller result in a system robust enough to deal with a variety of terrains.Publication Motion Planning in Urban Environments: Part I(2008-09-22) Ferguson, Dave; Howard, Thomas M; Likhachev, MaximWe present the motion planning framework for an autonomous vehicle navigating through urban environments. Such environments present a number of motion planning challenges, including ultra-reliability, high-speed operation, complex inter-vehicle interaction, parking in large unstructured lots, and constrained maneuvers. Our approach combines a model-predictive trajectory generation algorithm for computing dynamically-feasible actions with two higher-level planners for generating long range plans in both on-road and unstructured areas of the environment. In this Part I of a two-part paper, we describe the underlying trajectory generator and the on-road planning component of this system. We provide examples and results from ldquoBossrdquo, an autonomous SUV that has driven itself over 3000 kilometers and competed in, and won, the Urban Challenge.Publication Path Planning With Adaptive Dimensionality(2011-01-01) Gochev, Kalin; Cohen, Benjamin; Safonova, Alla; Butzke, Jonathan; Likhachev, MaximPath planning quickly becomes computationally hard as the dimensionality of the state-space increases. In this paper, we present a planning algorithm intended to speed up path planning for high-dimensional state-spaces such as robotic arms. The idea behind this work is that while planning in a highdimensional state-space is often necessary to ensure the feasibility of the resulting path, large portions of the path have a lower-dimensional structure. Based on this observation, our algorithm iteratively constructs a state-space of an adaptive dimensionality–a state-space that is high-dimensional only where the higher dimensionality is absolutely necessary for finding a feasible path. This often reduces drastically the size of the state-space, and as a result, the planning time and memory requirements. Analytically, we show that our method is complete and is guaranteed to find a solution if one exists, within a specified suboptimality bound. Experimentally, we apply the approach to 3D vehicle navigation (x, y, heading), and to a 7 DOF robotic arm on the Willow Garage’s PR2 robot. The results from our experiments suggest that our method can be substantially faster than some of the state-ofthe-art planning algorithms optimized for those tasks.Publication A Reasoning Framework for Autonomous Urban Driving(2008-06-04) Ferguson, Dave; Baker, Christopher; Likhachev, Maxim; Dolan, JohnUrban driving is a demanding task for autonomous vehicles as it requires the development and integration of several challenging capabilities, including high-level route planning, interaction with other vehicles, complex maneuvers, and ultra-reliability. In this paper, we present a reasoning framework for an autonomous vehicle navigating through urban environments. Our approach combines route-level planning, context-sensitive local decision making, and sophisticated motion planning to produce safe, intelligent actions for the vehicle. We provide examples from an implementation on an autonomous passenger vehicle that has driven over 3000 autonomous kilometers and competed in, and won, the Urban Challenge.