A geometric solution to the dynamic disturbance decoupling for discrete-time nonlinear systems

summary:The notion of controlled invariance under quasi-static state feedback for discrete-time nonlinear systems has been recently introduced and shown to provide a geometric solution to the dynamic disturbance decoupling problem (DDDP). However, the proof relies heavily on the inversion (structure) algorithm. This paper presents an intrinsic, algorithm-independent, proof of the solvability conditions to the DDDP

Motion Coordination Problems with Collision Avoidance for Multi-Agent Systems

This chapter studies the collision avoidance problem in the motion coordination control strategies for multi-agent systems. The proposed control strategies are decentralised, since agents have no global knowledge of the goal to achieve, knowing only the position and velocity of some agents. These control strategies allow a set of mobile agents achieve formations, formation tracking and containment. For the collision avoidance, we add a repulsive vector field of the unstable focus type to the motion coordination control strategies. We use formation graphs to represent interactions between agents. The results are presented for the front points of differential-drive mobile robots. The theoretical results are verified by numerical simulation

Infinitesimal Brunovsky Form for Nonlinear Systems with Applications to Dynamic Linearization

We define the ``infinitesimal Brunovsky form'' for nonlinear systems in the infinite-dimensionnal differential geometric framework devellopped in ``A Differential Geometric Setting for Dynamic Equivalence and Dynamic Linearization'' (Rapport INRIA No XXXX, needed to understand the present note), and link it with endogenous dynamic linearizability, i.e. conjugation of the system to a linear one by a (infinite dimensional) diffeomorphism

Infinitesimal Brunovsky form for nonlinear systems, with applications to dynamic linearization

International audienceWe define, in an infinite-dimensional differential geometric framework, the "infinitesimal Brunovsky form" which we previously introduced in another framework and link it with equivalence via diffeomorphism to a linear system, which is the same as linearizability by "endogenous dynamic feedback".NB: this paper follows "A differential geometric setting for dynamic equivalence and dynamic linearization", by J.-B. Pomet, published in the same 1995 volume, which is its natural intrduction.This is a corrected version of the reports http://hal.inria.fr/inria-00074360 and http://hal.inria.fr/inria-0007436

Invariant codistributions and the feedforward form for discrete-time nonlinear systems

International audienc

Formation with Non-Collision Control Strategies for Second-Order Multi-Agent Systems

This article tackles formation control with non-collision for a multi-agent system with second-order dynamics. The nested saturation approach is proposed to solve the well-known formation control problem, allowing us to delimit the acceleration and velocity of each agent. On the other hand, repulsive vector fields (RVFs) are developed to avoid collisions among the agents. For this purpose, a parameter depending on the distances and velocities among the agents is designed to scale the RVFs adequately. It is shown that when the agents are at risk of collision, the distances among them are always greater than the safety distance. Numerical simulations and a comparison with a repulsive potential function (RPF) illustrate the agents’ performance

Formation Tracking with Orientation Convergence for Groups of Unicycles

This paper presents three trajectory tracking control strategies for unicycle-type robots based on a leader-followers scheme. The leader robot converges asymptotically to a smooth trajectory, while the follower robots form an undirected open-chain configuration at the same time. It is also shown that the orientation angles of all the robots converge to the same value. The control laws are based on a dynamic extension of the kinematic model of each robot. The output function to be controlled is the midpoint of the wheel axis of every robot. This choice leads to an ill-defined control law when the robot is at rest. To avoid such singularities, a complementary control law is enabled momentarily when the linear velocity of the unicycles is close to zero. Finally, numerical simulations and real-time experiments show the performance of the control strategies

Immersion of nonlinear systems into higher order systems

Two nonlinear systems having the same number of inputs, but not the same number of state variables, are considered. The problem of the existence of two invertible state feedback laws and a surjective mapping from the higher dimensional state space of one system into the lower dimensional state space of the second system is stated, such that the rst system dynamics reduces exactly to the second system dynamics. This problem generalizes the linear feedback equivalence problem of two systems and is fully solved in the special case of feedback linearizable systems

Formation Control for Second-Order Multi-Agent Systems with Collision Avoidance

This paper deals with the formation control problem without collisions for second-order multi-agent systems. We propose a control strategy which consists of a bounded attractive component to ensure convergence to a specific geometrical pattern and a complementary repulsive component to guarantee collision-free rearrangement. For convergence purposes, it is assumed that the communication graph contains at least a directed spanning tree. The avoidance complementary component is formed by applying repulsive vector fields with unstable focus structure. Using the well-known input-to-state stability property a control law for second-order agents is derived in a constructive manner starting from the first-order case. We consider that every agent is able to detect the presence of any other agent in the surrounding area and also can measure and share both position and velocity with his predefined set of neighbours. The resulting control law ensures the convergence to the desired geometrical pattern without collisions during the transient behaviour, as well as bounded velocities and accelerations. Numerical simulations are provided to show the performance and effectiveness of the proposed strategy