In this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well-understood in the particular case of nonholonomic (or driftless) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is app...

In this paper, we present an iterative steering algorithm for nonholonomic systems (also called driftless control-affine systems) and we prove its global convergence under the sole assumption that the Lie Algebraic Rank Condition (LARC) holds true everywhere. That algorithm is an extension of the one introduced in [21] for regular systems. The first novelty here consists in the explicit algebra...

We propose in this paper a constructive procedure that transforms locally, even at singular configurations, the kinematics of a car towing trailers into Kumpera-Ruiz normal form. This construction converts the nonholonomic motion planning problem into an algebraic problem (the resolution of a system of polynomial equations), which we illustrate by steering the two-trailer system in a neighborho...

In this thesis we propose a vision-based robot navigation system that constructs a high level topological representation of the world. A robot using this system learns to recognize rooms and spaces by building a hidden Markov model of the environment. Motion planning is performed by doing bidirectional heuristic search with a discrete set of actions that account for the robot's nonholonomic con...

We report on new applications of the Poincaré and Sundman timetransformations to the simulation of nonholonomic systems. These transformations are here applied to nonholonomic mechanical systems known to be Hamiltonizable (briefly, nonholonomic systems whose constrained mechanics are Hamiltonian after a suitable time reparameterization). We show how such an application permits the usage of vari...

-7803-5886-4/00/$10.00© 2000 IEEE 247 one. Being converted to the chained form, a tractor and all trailers can be stabilized to desired positions via. esla.I)lished nonholonomie motion control strategies for the chained form[5, 6, 7]. S0rdalen, Naka~ mura and Chung[8] developed "t, he nonholonomic manipulator," whose kinematic model is similar to those of trailer systems. The real-world tra~jec...

Challenges persist in nonholonomic robot navigation for dynamic environments. This paper presents a framework for nonholonomic robot navigation in dynamic environment based on the model of Generalized Velocity Obstacles (GVO). The idea of velocity obstacles has been well studied and developed for obstacle avoidance since proposed in 1998. Though proved to be successful, most studies assume equa...

This paper puts forward a formal basis for behavior-based robotics, using techniques that have been successful in control-theory-based approaches for steering and stabilizing robots that are subject to nonholonomic constraints. In particular, behaviors for robots are formalized in terms of kinetic state machines, a motion description language, and the interaction of the kinetic state machine wi...

In roadmap-based methods, such as the Probabilistic Roadmap Method (PRM) in deterministic environments or the Feedbackbased Information RoadMap (FIRM) in partially observable probabilistic environments, a stabilizing controller is needed to guarantee node reachability in state or belief space. In belief space, it has been shown that the belief-node reachability can be achieved using stationary ...

This paper deals with humanoid walk planning in cluttered environments. It presents a heuristic and efficient optimization method that takes as input a path computed for the robot bounding box, and produces a path where a discrete set of configurations is reoriented using an A* search algorithm. The resulting trajectory is realistic and time-optimal. This method is validated in various scenario...