The paper deals with the robust energy-based stabilization of a wheeled inverted pendulum, which is an underactuated, unstable mechanical system subject to nonholonomic constraints. The equilibrium to be stabilized is characterized by the length of the driven path, the orientation, and the pitch angle. We use the method of Controlled Lagrangians which is applied in a systematic way, and is very...

We propose a first example of a simple classical field theory with nonholonomic constraints. Our model is a straightforward modification of a Cosserat rod. Based on a mechanical analogy, we argue that the constraint forces should be modeled in a special way, and we show how such a procedure can be naturally implemented in the framework of geometric field theory. Finally, we derive the equations...

Two linear algebra based strategies are presented to deal with general classical mechanics problems with constraints. Classical concepts such as holonomic and nonholonomic constraints, virtual displacements, principle of virtual work, Hamilton’s principle and method of Lagrange multipliers are critiqued.

This paper presents a sensor based algorithm for guiding a nonholonomic platform, such as a wheelchair, through a doorway. The controller uses information from a camera system and a laser range finder to perform image-based navigation. Simulations of the resultant switching controller are presented along with experimental results. A simple obstacle avoidance algorithm is also implemented on the...

A wheeled mobile manipulator system is modeled using Kane’s dynamic equations. Kane’s equations are constructed with minimum effort, are control oriented and provide both physical insight and fast simulations. The powerful tools of Kane’s approach for incorporating nonholonomic motion constraints and bringing noncontributing forces into evidence are exploited. Both nonholonomic constraints asso...

In this paper; we are interested principally in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints in order to develop a new synoptic control scheme as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new statespace representation and a new control scheme. We present also ...

In this paper, we present an analytical solution for the trajectory generation and tracking control design of mobile robots with nonholonomic constraints moving in a dynamic environment populated with obstacles. By explicitly defining complex potential primitives, the desired trajectory from a start position to the goal position can be generated following the negative gradient of complex potent...

This paper presents a new fuzzy Lyapunov controller for nonholonomic mobile vehicles. A symbiosis between classical backstepping techniques and fuzzy logic was realized. The control system ensures a good robustness with respect to outside perturbations. These perturbations can interact with the vehicle. They are sources of uncertainty for the system model and can perturb the validity of the non...

We address the motion planning problem for multiple cooperating manipulators on nonholonomic carts. The mobile manipulators possess the ability to manipulate and transport objects while holding them in a stable grasp. We present a general approach that allows the generation of optimal trajectories and actuator inputs for any given maneuver in the presence of obstacles. We assume a meaningful in...

This paper proposes a general approach to design convergent coordination control laws for multi-agent systems subject to motion constraints. The main contribution of this paper is to prove in a constructive way that a gradient-descent coordination control law designed for single integrators can be easily modified to adapt for various motion constraints such as nonholonomic dynamics, linear/angu...