Second order anti-holonomic jets as anti-symmetric parts of second order semi-holonomic jets are introduced. The anti-holonomic nature of the Lie bracket is shown. A general result on universality of the Lie bracket is proved. 1. Introduction The concepts of non-holonomic (or iterated) and semi-holonomic jets, rst introduced by Ehresmann in 1], are commonly used in diierential geometry. In this...

The body of work called "Camera Space Manipulation" is an e ective and proven method of robotic control. Essentially, this technique identi es and re nes the input-output relationship of the plant using estimation methods and drives the plant open-loop to its target state. Three{dimensional "success" of the desired motion, i.e., the end e ector of the manipulator engages a target at a particula...

In this paper we present a theoretical and experimental result on the control of multi-agent non-holonomic systems. We design and implement a novel decentralized control scheme that achieves dynamic formation control and collision avoidance for a group of non-holonomic robots. First, we derive a feedback law using Lyapunov-type analysis that guarantees collision avoidance and tracking of a refe...

In the repetitive approach to the theory of jet bundles there are three methods of repetition, which yield non-holonomic, semi-holonomic, and holonomic jet bundles respectively. However the classical approach to holonomic jet bundles failed to be truly repetitive, for it must resort to such a non-repetitive coordinatedependent construction as Taylor expansion. The principal objective in this pa...

In this paper, the simple geometric kinematics of a three-wheeled holonomic mobile robot is proposed. Wheel architecture is developed for the holonomic mobile platform in order to provide omni-directional motions by three individually driven and steered wheels. Three types of basic motions are proposed for the path generation of the developed mobile robot. All paths of the mobile robot can be a...

Planning a path for a nonholonomic robot is a challenging topic in motion planning and it becomes more difficult when the desired path contains narrow passages. This kind of scenario can arise, for instance, when quadcopters search a collapsed building after a natural disaster. Choosing the quadcopter as the target platform, this paper proposes the Kinodynamic Aggressive Trajectory (KAT) motion...

To Ivan Koll a r on the occasion of his 60th birthday. The usual jets were introduced by C. Ehresmann as a fundamental tool in Diierential Geometry. They permit to globalize the theory of diierential systems and to give a formulation of the \innnite groups" of E. Cartan; this leads to the theory of Lie pseudogroups; initiated by C. Ehresmann, this theory was studied by many mathematicians (the ...

In order to obtain a framework in which both non-holonomic mechanical systems and non-holonomic mechanical systems with symmetry can be described, we introduce in this paper the notion of a Lagrangian system on a subbundle of a Lie algebroid.

We establish some cohomological bounds in $D$ -module theory that are known the holonomic case and folklore general. The method rests on a generalization of $b$ -function lemma for non-holonomic -modules.