This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: single-query -- instead of pre-computing a roadmap covering the entire free space, it uses the two input query configurations to explore as little space as possible; bi-directional -- it explores the robot's free space by building a roadmap made of two trees rooted at the query configurations; and lazy in checking collisions -- it delays collision tests along the edges of the roadmap until they are absolutely needed. Several observations motivated this strategy: (1) PRM planners spend a large fraction of their time testing connections for collision; (2) most connections in a roadmap are not on the final path; (3) the collision test for a connection is most expensive when there is no collision; and (4) any short connection between two collision-free configurations has high prior probability of being collision-free. The strengths of single-query and bi-directional sampling techniques, and those of delayed collision checking reinforce each other. Experimental results

Typical high-level directives for locomotion of human-like characters are useful for interactive games and simulations as well as for off-line production animation. In this paper, we present a new scheme for planning natural-looking locomotion of a biped figure to facilitate rapid motion prototyping and task-level motion generation. Given start and goal positions in a virtual environment, our scheme gives a sequence of motions to move from the start to the goal using a set of live-captured motion clips. Based on a novel combination of probabilistic path planning and hierarchical displacement mapping, our scheme consists of three parts: roadmap construction, roadmap search, and motion generation. We randomly sample a set of valid footholds of the biped figure from the environment to construct a directed graph, called a roadmap, that guides the locomotion of the figure. Every edge of the roadmap is associated with a live-captured motion clip. Augmenting the roadmap with a posture transition graph, we traverse it to obtain the sequence of input motion clips and that of target footprints. We finally adapt the motion sequence to the constraints specified by the footprint sequence to generate a desired locomotion.

This paper addresses the problem of motion planning (MP) in dynamic environments. It is first argued that dynamic environments impose a real-time constraint upon MP: it has a limited time only to compute a motion, the time available being a function of the dynamicity of the environment. Now, given the intrinsic complexity of MP, computing a complete motion to the goal within the time available is impossible to achieve in most real situations. Partial Motion Planning (PMP) is the answer to this problem proposed in this paper. PMP is a motion planning scheme with an anytime flavor: when the time available is over, PMP returns the best partial motion to the goal computed so far. Like reactive navigation scheme, PMP faces a safety issue: what guarantee is there that the system will never end up in a critical situation yielding an inevitable collision? The answer proposed in this paper to this safety issue relies upon the concept of Inevitable Collision States (ICS). ICS takes into account the dynamics of both the system and the moving obstacles. By computing ICS-free partial motion, the system safety can be guaranteed. Application of PMP to the case of a car-like system in a dynamic environment is presented.

We present an algorithm for computing stable collision-free motions for humanoid robots given fullbody posture goals. The motion planner is part of a simulation environment under development for providing high-level software control for humanoid robots. Given a robot's internal model of the environment and a statically-stable desired posture, we use a randomized path planner to search the configuration space of the robot for a collision-free path. Balance constraints are imposed on incremental search motions in order to maintain the overall dynamic stability of the computed trajectories. The algorithm is presented along with preliminary results using an experimental implementation on a dynamic model of the H5 humanoid robot.

We present an approach to path planning for humanoid robots that computes dynamically-stable, collision-free trajectories from full-body posture goals. Given a geometric model of the environment and a statically-stable desired posture, we search the configuration space of the robot for a collision-free path that simultaneously satisfies dynamic balance constraints. We adapt existing randomized path planning techniques by imposing balance constraints on incremental search motions in order to maintain the overall dynamic stability of the final path. A dynamics filtering function that constrains the ZMP (zero moment point) trajectory is used as a post-processing step to transform statically-stable, collision-free paths into dynamically-stable, collision-free trajectories for the entire body. Although we have focused our experiments on biped robots with a humanoid shape, the method generally applies to any robot subject to balance constraints (legged or not). The algorithm is presented along with computed examples using the humanoid robot "H6".

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Though motion planning has been studied extensively for rigid and articulated robots, motion planning for deformable objects is an area that has received far less attention. In this paper we present a framework for planning paths in completely deformable, elastic environments. In particular we apply a deformable model to the robot and obstacles in the environment and we present a kinodynamic planning algorithm suited for this type of deformable motion planning. The planning algorithm is based on the Rapidly-Exploring Random Tree (rrt) path planning algorithm. To the best of our knowledge, this is the first work that plans paths in totally deformable environments. Figure 1: Barriers Environment. Both the robot (the cube) and the obstacles (the plate barriers) in this environment are deformable. This image sequence is shown from left to right and from top to bottom. 1

Since differential constraints which restrict admissible velocities and accelerations of robotic systems are ignored in path planning, solutions for kinodynamic and non-holonomic planning problems from classical methods could be either inexecutable or inefficient. Motion planning with differential constraints (MPD), which directly considers differential constraints, provides a promising direction to calculate reliable and efficient solutions. A large amount of recent efforts have been devoted to various sampling-based MPD algorithms, which iteratively build search graphs using sam-pled states and controls. This thesis addresses several issues in analysis and design of these algorithms. Firstly, resolution completeness of path planning is extended to MPD and the first quantitative conditions are provided. The analysis is based on the relationship between the reachability graph, which is an intrinsic graph representation of a given problem, and the search graph, which is built by the algorithm. Because of sampling and other complications, there exist mismatches between these two graphs. If a solution exists in the reachability graph, resolution complete algorithms must con-struct a solution path encoding the solution or its approximation in the search graph

A new approach to high-speed, off-road navigation is presented. The interrelatedness of sensing horizon, prior map resolution, speed and efficiency is investigated over the space of off-road navigation. From this analysis, the space of off-road navigation is partitioned into three regimes (efficiency-limited, stoplimited and swerve-limited). Safeguarding through pre-planning and swerving emerges as an approach to achieve greater performance than possible with panic-stopping. The swerve-limited regime is characterized by high speeds that are achieved using plans derived in part from prior maps. Within the swerve-limited regime, sensing horizon is linearly proportional to robot speed. Thus an autonomous robot can operate at speeds beyond the point at which panic stopping is viable if it is safe to avoid obstacles by swerving. Navigating safely within this regime therefore explicitly requires some prior knowledge or assumption. The efficiency-limited regime is characterized by low speeds. Onboard sensing horizon is fixed given a specified prior map resolution and desired navigation efficiency. Typical applications include planetary exploration and mine-mapping For operation between the efficiency-limited and swerve-limited regimes, robot stopping distance limits speeds. In this stop-limited regime, sensing horizons increase quadratically as speed rises to ensure robot safety. Algorithms designed for navigation within the stop-limited regime generally require some cognizance of vehicle dynamics. Two implemented approaches to off-road navigation, one relevant for highspeed, long duration driving, and the other for planetary exploration, are contrasted and described in detail. These particular implementations exemplify the efficiency-limited and swerve-limited regimes and represent the state-of-theart in planetary exploration and high-speed navigation.