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 Probabilistic Planning with Clear Preferences on Missing Information(2008-11-04) Likhachev, Maxim; Stentz, AnthonyFor many real-world problems, environments at the time of planning are only partiallyknown. For example, robots often have to navigate partially-known terrains, planes often have to be scheduled under changing weather conditions, and car route-finders often have to figure out paths with only partial knowledge of traffic congestions. While general decisiontheoretic planning that takes into account the uncertainty about the environment is hard to scale to large problems, many such problems exhibit a special property: one can clearly identify beforehand the best (called clearly preferred) values for the variables that represent the unknowns in the environment. For example, in the robot navigation problem, it is always preferred to find out that an initially unknown location is traversable rather than not, in the plane scheduling problem, it is always preferred for the weather to remain a good flying weather, and in route-finding problem, it is always preferred for the road of interest to be clear of traffic. It turns out that the existence of the clear preferences can be used to construct an efficient planner, called PPCP (Probabilistic Planning with Clear Preferences), that solves these planning problems by running a series of deterministic low-dimensional A*-like searches. In this paper, we formally define the notion of clear preferences on missing information, present the PPCP algorithm together with its extensive theoretical analysis, describe several useful extensions and optimizations of the algorithm and demonstrate the usefulness of PPCP on several applications in robotics. The theoretical analysis shows that once converged, the plan returned by PPCP is guaranteed to be optimal under certain conditions. The experimental analysis shows that running a series of fast low-dimensional searches turns out to be much faster than solving the full problem at once since memory requirements are much lower and deterministic searches are orders of magnitude faster than probabilistic planning.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 Path Clearance(2009-06-01) Likhachev, Maxim; Stentz, AnthonyIn military scenarios, agents (i.e., troops of soldiers, convoys, and unmanned vehicles) may often have to traverse environments with only a limited intelligence about the locations of adversaries. We study a particular instance of this problem that we refer to as path clearance problem.This article presents a survey of our work on scalable and suitable for real-time use approaches to solving the path clearance problem. In particular, in the first part of the article, we show that the path clearance problem exhibits clear preferences on uncertainty. It turns out that these clear preferences can be used to develop an efficient algorithm called probabilistic planning with clear preferences (PPCP). The algorithm is anytime usable, converges to an optimal solution under certain conditions, and scales well to large-scale problems. We briefly describe the PPCP algorithm and show how it can be used to solve the path clearance problem when no scouts are present. In the second part of the article, we show several strategies for how to use the PPCP algorithm in case multiple scouting unmanned aerial vehicles (UAVs) are available. The experimental analysis shows that planning with PPCP results in a substantially smaller execution cost than when ignoring uncertainty, and employing scouts can decrease this execution cost even further.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.