This paper addresses the feedback control design for a class of nonholonomic systems which are subject to inequality stateconstraints defining a constrained (viability) set K. Based on concepts from viability theory, the necessary conditions forselecting viable controls for a nonholonomic system are given, so that system trajectories starting in K always remain inK. Furthermore, a c...

In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical control systems, Discrete Mechanics and extensions to Classical Field Theory within a single framework. Various examples along the discussion illustrate the soundn...

In this paper, the problem of coordinated motion control of a nonholonomic mobile platform with a serial manipulator mounted on top of the platform is addressed. The redundancy resolution algorithm bases on a constraint optimization approach, where the non–holonomic behaviour of the platform is modeled into inequality constraints leading to a convex optimization problem.

A new technique for the control of mobile robots using a discrete event model is presented. Physical obstacles are represented by constraints on the motion of the robot. In the discrete event model, the discrete state of the system is de-ned by the currently active constraint. This paper uses dynamic constraints which depend upon the velocity as well as the position of the robot. Dynamic constr...

This paper addresses the design of position tracking control of mechanical systems with classical nonholonomic constraints incorporating actuator dynamics. An adaptive controller is designed at the actuator level and the controller guarantees that the configuration state of the system tracks the desired trajectory. A detailed numerical example is presented to illustrate the developed method.

For achieving trajectory tracking issue of the lower limb exoskeleton robot, a novel optimal robust control with cooperative game theory is proposed. The uncertainties are considered (possible time-varying, bounded and fast), fuzzy set creatively adopted to describe boundary. From view analytical mechanics, treated as constraints problem, including holonomic nonholonomic constraints, which need...

We present an approach to the problem of mobile robot motion planning in arbitrary cost fields subject to differential constraints. Given a model of vehicle maneuverability, a trajectory generator solves the two point boundary value problem of connecting two points in state space with a feasible motion. We use this capacity to compute a control set which connects any state to its reachable neig...

Lagrangian systems with constraints are common models of fundamental or idealized physical systems. Holonomic constraints, typified in the example of a freely moving rigid body, give rise to systems with certain special properties, such as symplectic Hamiltonian systems. Nonholonomic constraints arise in such systems as a disk which rolls without slipping. Holonomic and nonholonomic systems hav...

Traditionally, the energy shaping for mechanical systems requires elimination of holonomic and nonholonomic constraints. In recent years, it was argued that such might be unnecessary, leading to a possible simplification matching conditions in shaping. On other hand, partial feedback linearization (PFL) approach has been widely applied unconstrained systems, but there is no general result const...