The control of nonholonomic and underactuated systems with symmetry is illustrated by the problem of controlling a bicycle. We derive a controller which, using steering and rear-wheel torque, causes a model of a riderless bicycle to recover its balance from a near fall as well as converge to a time parameterized path in the ground plane. Our construction utilizes new results for both the deriva...

we design a two-stage scheme to consider trajectory planning problem of two mobile manipulators for cooperative transportation of a rigid body in presence of static obstacles. within the first stage, regarding the static obstacles we develop a method that searches the workspace for the shortest possible path between start and goal configurations by constructing a graph on a portion of the confi...

This paper presents several classical mechanical systems with nonholonomic constraints from the point of view of sub-Riemannian geometry. For those systems that satisfy the bracket generating condition the system can move continuously between any two given states. However, the paper provides a counterexample to show that the bracket generating condition is not also a sufficient condition for co...

We consider nonholonomic mobile manipulators built from an na joint robotic arm and a nonholonomic mobile platform with two independently driven wheels. Actually, there is no efficient kinematic formalism for these systems which are generally characterized by their high number of actuators. So, kinematic modelling is presented with particular emphasis on redundancy. Whereas kinematic redundancy...

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...

This is the second paper in a series of works devoted to nonholonomic Ricci flows. By imposing non–integrable (nonholonomic) constraints on the Ricci flows of Riemannian metrics we can model mutual transforms of generalized Finsler–Lagrange and Riemann geometries. We verify some assertions made in the first partner paper and develop a formal scheme in which the geometric constructions with Ricc...

This paper deals with coordinated tasks for mobile nonholonomic manip-ulators. The systems are composed of a nonholonomic mobile platform and a simple kinematic chain holonomic arm. First, concepts such that redundancy and singular conngurations are deened. Then, reduced diierential models are introduced. It is then possible to work with a set of independant task coordinates. Applications follo...

The paper presents a new method of performing integrator backstepping in systems that are discontinuous, either due to their inherent structure or because of the applied control input. The proposed technique is applied to the stabilization problem of the dynamic system of a nonholonomic mobile robot. Simulation studies indicate that the methodology can also help alleviate the problem of chatter...

We show that the Suslov nonholonomic rigid body problem studied in [10, 13, 26] can be regarded almost everywhere as a generalized Chaply-gin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifol...

Several aspects of Dirac reduction are compared and formulated from the same geometric point of view. A link with nonholonomic reduction is found. The theory of optimal momentum maps and reduction is extended from the category of Poisson manifolds to that of closed Dirac manifolds. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in det...