this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints.

We present a randomized motion planner for robots that must avoid moving obstacles and achieve a specified goal under kinematic and dynamic constraints. The planner samples the robot's statetime space by picking control inputs at random and integrating the equations of motion. The result is a roadmap of sampled statetime points, called milestones, connected by short admissible trajectories. The planner does not precompute the roadmap as traditional probabilistic roadmap planners do; instead, for each planning query, it generates a new roadmap to find a trajectory between an initial and a goal statetime point. We prove in this paper that the probability that the planner fails to find such a trajectory when one exists quickly goes to 0, as the number of milestones grows. The planner has been implemented and tested successfully in both simulated and real environments. In the latter case, a vision module estimates obstacle motions just before planning starts; the planner is then allocated a small, fixed amount of time to compute a trajectory. If a change in the obstacle motion is detected while the robot executes the planned trajectory, the planner recomputes a trajectory on the fly. 1

We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman’s controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra which suits well to the fact that, in accordance with Willems ’ standpoint, flatness and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of planar curves. The three non-flat examples, the simple, double and variable length pendulums, are borrowed from nonlinear physics. A high frequency control strategy is proposed such that the averaged systems become flat. ∗This work was partially supported by the G.R. “Automatique ” of the CNRS and by the D.R.E.D. of the “Ministère de l’Éducation Nationale”. 1 1

Introduction A natural and well-studied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of the edges that comprise it. Efficient algorithms are well known for this problem, as briefly summarized below. The shortest path problem takes on a new dimension when considered in a geometric domain. In contrast to graphs, where the encoding of edges is explicit, a geometric instance of a shortest path problem is usually specified by giving geometric objects that implicitly encode the graph and its edge weights. Our goal in devising efficient geometric algorithms is generally to avoid explicit construction of the entire underlying graph, since the full induced graph may be very large (even exponential in the input size, or infinite). Computing an optimal

An autonomous robot o ers a challenging and ideal field for the study of intelligent architectures. Autonomy within a rational behavior could be evaluated by the robot's effectiveness and robustness in carrying out tasks in different and ill-known environments. It raises major requirements on the control architecture. Furthermore, a robot as a programmable machine brings up other architectural needs, such asthe ease and quality of its specification and programming. This paper describes an integrated architecture allowing a mobile robot to plan its tasks, taking into account temporal and domain constraints, to perform corresponding actions and to control their execution in real-time, while being reactive to possible events. The general architecture is composed of three levels: a decision level, an execution level and a functional level. The later is composed of modules that embed the functions achieving sensor data processing and e ector control. The decision level is goal and event-driven, it may have several layers, according to the application; their basic structure is a planner/supervisor pair that enables to integrate deliberation and reaction. The proposed architecture relies naturally on several representations, programming paradigms and processing approaches meeting the precise requirements specified for each level. We developed proper tools to meet these specifications and implement each level of the architecture: IxTeT a temporal planner, prs a procedural system for task refinement and supervision, Kheops for the reactive control of the functional level, and G en oM for the specification and integration of modules at that level. Validation of temporal and logical properties of the reactive parts of the system, through these tools, are presented. Instances of the proposed architecture have been already integrated into several indoor and outdoor robots. Examples from real world experimentations are provided and analyzed.

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this paper, we show how the machinery of exterior differential systems can be used to help solve nonholonomic motion planning problems. Since the Goursat normal form for exterior differential systems is dual to chained form for vector fields, we solve the problem of steering a mobile robot with n

. This paper develops a constructive method for finding a nilpotent basis for a special class of smooth nonholonomic distributions. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior differential systems. The results are applied to the problem of finding a set of nilpotent input vector fields for a nonholonomic control system, which can then used to construct explicit trajectories to drive the system between any two points. A kinematic model of a rolling penny is used to illustrate this approach. The methods presented here extend previous work using "chained form" and cast that work into a coordinate-free setting. 1. Introduction This work is motivated by the recent interest in trajectory generation for mechanical systems with nonholonomic constraints. Consider the problem of steering a mechanical system with n-dimensional configuration space M from an initial configuration x 0 to a final configuration x 1 , subject to a set of indep...

We present a new and complete multi-level approach for solving path planning problems for nonholonomic robots. At the first level a path is found that disrespects (some of) the nonholonomic constraints. At each next level a new path is generated, by transformation of the path generated at the previous level. The transformation is such that more nonholonomic constraints are respected than at the previous level. At the final level all nonholonomic constraints are respected. We present two techniques for these transformations. The first, which we call the Pick and Link technique, repeatedly picks pieces from the given path, and tries to replace these by more feasible ones. The second technique restricts the free configuration space to a "tube" around the given path, and a roadmap, capturing the free space connectivity within this tube, is constructed by the Probabilistic Path Planner. From this roadmap we retrieve a new, more feasible, path. In the intermediate levels we plan ...

This paper uses geometric methods to study basic problems in the mechanics and control of locomotion. We consider in detail the case of "undulatory locomotion," in which net motion is generated by coupling internal shape changes with external nonholonomic constraints. Such locomotion problems have a natural geometric interpretation as a connection on a principal fiber bundle. The properties of connections lead to simplified results for studying both dynamics and issues of controllability for locomotion systems. We demonstrate the utility of this approach using a novel "Snakeboard" and a multi-segmented serpentine robot which is modeled after Hirose's Active Cord Mechanism.