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A geometric procedure for robust decoupling control of contact forces in robotic manipulation

Paolo Mercorelli, Domenico Prattichizzo (2003)

Kybernetika

This paper deals with the problem of controlling contact forces in robotic manipulators with general kinematics. The main focus is on control of grasping contact forces exerted on the manipulated object. A visco-elastic model for contacts is adopted. The robustness of the decoupling controller with respect to the uncertainties affecting system parameters is investigated. Sufficient conditions for the invariance of decoupling action under perturbations on the contact stiffness and damping parameters...

An instrumental variable method for robot identification based on time variable parameter estimation

Mathieu Brunot, Alexandre Janot, Peter Young, Francisco Carrillo (2018)

Kybernetika

This paper considers the data-based identification of industrial robots using an instrumental variable method that uses off-line estimation of the joint velocities and acceleration signals based only on the measurement of the joint positions. The usual approach to this problem relies on a ‘tailor-made’ prefiltering procedure for estimating the derivatives that depends on good prior knowledge of the system's bandwidth. The paper describes an alternative Integrated Random Walk SMoothing (IRWSM) method...

Composite control of the n -link chained mechanical systems

Jiří Zikmund (2008)

Kybernetika

In this paper, a new control concept for a class of underactuated mechanical system is introduced. Namely, the class of n -link chains, composed of rigid links, non actuated at the pivot point is considered. Underactuated mechanical systems are those having less actuators than degrees of freedom and thereby requiring more sophisticated nonlinear control methods. This class of systems includes among others frequently used for the modeling of walking planar structures. This paper presents the stabilization...

Design of robust gain scheduled controller using L 2 gain performance

Vojtech Veselý, Martin Ernek (2018)

Kybernetika

This paper is devoted to robust gain scheduled PID controller design with L 2 performance for the linear time varying (LPV) uncertain system with polytopic uncertainties. The novel approach of robust controller design ensures that the obtained design procedure is convex with respect to both plant uncertainties (polytopic system) and gain scheduling parameters and gives less conservative results. Modified design procedure should be used to obtain a robust controller or robust switched controller (ideal,...

Entropy and complexity of a path in sub-riemannian geometry

Frédéric Jean (2003)

ESAIM: Control, Optimisation and Calculus of Variations

We characterize the geometry of a path in a sub-riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset A of a metric space is the minimum number of balls of a given radius ε needed to cover A . It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-riemannian manifold as the infimum of the lengths of all trajectories contained in an ε -neighborhood of the path,...

Entropy and complexity of a path in sub-Riemannian geometry

Frédéric Jean (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We characterize the geometry of a path in a sub-Riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset A of a metric space is the minimum number of balls of a given radius ε needed to cover A. It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-Riemannian manifold as the infimum of the lengths of all trajectories contained in an ε-neighborhood of the path,...

Flocking control of multi-agent systems with application to nonholonomic multi-robots

Qin Li, Zhong-Ping Jiang (2009)

Kybernetika

In this paper, we revisit the artificial potential based approach in the flocking control for multi-agent systems, where our main concerns are migration and trajectory tracking problems. The static destination or, more generally, the moving reference point is modeled by a virtual leader, whose information is utilized by some agents, called active agents (AA), for the controller design. We study a decentralized flocking controller for the case where the set of AAs is fixed. Some results on the velocity...

Geometry of non-holonomic diffusion

Simon Hochgerner, Tudor S. Ratiu (2015)

Journal of the European Mathematical Society

We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For G -Chaplygin systems, this yields a stochastic criterion for the existence of a smooth preserved measure. As an application of our results we consider the motion planning problem for the noisy two-wheeled robot and the noisy snakeboard.

LQR and MPC controller design and comparison for a stationary self-balancing bicycle robot with a reaction wheel

Kiattisin Kanjanawanishkul (2015)

Kybernetika

A self-balancing bicycle robot based on the concept of an inverted pendulum is an unstable and nonlinear system. To stabilize the system in this work, the following three main components are required, i. e., (1) an IMU sensor that detects the tilt angle of the bicycle robot, (2) a controller that is used to control motion of a reaction wheel, and (3) a reaction wheel that is employed to produce reactionary torque to balance the bicycle robot. In this paper, we propose three control strategies: linear...

Neutral wrenches of 3-parametric robot-manipulators of the spherical rank 1

Marta Bakšová (2011)

Applications of Mathematics

Let S E ( 3 ) be the Lie group of all Euclidean motions in the Euclidean space E 3 , let s e ( 3 ) be its Lie algebra and s e * ( 3 ) the space dual to s e ( 3 ) . This paper deals with structures of the subspaces of s e * ( 3 ) which are formed by all the forces whose power exerted on the robot effector is zero.

Non-cooperative game approach to multi-robot planning

Adam Gałuszka, Andrzej Świerniak (2005)

International Journal of Applied Mathematics and Computer Science

A multi-robot environment with a STRIPS representation is considered. Under some assumptions such problems can be modelled as a STRIPS language (for instance, a Block World environment) with one initial state and a disjunction of goal states. If the STRIPS planning problem is invertible, then it is possible to apply the machinery for planning in the presence of incomplete information to solve the inverted problem and then to find a solution to the original problem. In the paper a planning algorithm...

On asymptotic motions of robot-manipulator in homogeneous space

Anton Dekrét, Ján Bakša (2008)

Applications of Mathematics

In this paper the notion of robot-manipulators in the Euclidean space is generalized to the case in a general homogeneous space with the Lie group G of motions. Some kinematic subspaces of the Lie algebra 𝒢 (the subspaces of velocity operators, of Coriolis acceleration operators, asymptotic subspaces) are introduced and by them asymptotic and geodesic motions are described.

Parameter influence on passive dynamic walking of a robot with flat feet

Xiangze Lin, Haibo Du, Shihua Li (2013)

Kybernetika

The biped robot with flat feet and fixed ankles walking down a slope is a typical impulsive dynamic system. Steady passive gaits for such mechanism can be induced on certain shallow slopes without actuation. The steady gaits can be described by using stable non-smooth limit cycles in phase plane. In this paper, it is shown that the robot gaits are affected by three parameters, namely the ground slope, the length of the foot, and the mass ratio of the robot. As the ground slope is gradually increased,...

Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite riemannian metric

Claudio Altafini (2004)

ESAIM: Control, Optimisation and Calculus of Variations

For a riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the riemannian exponential...

Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric

Claudio Altafini (2010)

ESAIM: Control, Optimisation and Calculus of Variations

For a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential...

Robust neural network control of robotic manipulators via switching strategy

Lei Yu, Shumin Fei, Jun Huang, Yongmin Li, Gang Yang, Lining Sun (2015)

Kybernetika

In this paper, a robust neural network control scheme for the switching dynamical model of the robotic manipulators has been addressed. Radial basis function (RBF) neural networks are employed to approximate unknown functions of robotic manipulators and a compensation controller is designed to enhance system robustness. The weight update law of the robotic manipulator is based on switched multiple Lyapunov function method and the periodically switching law which is suitable for practical implementation...

Supporting locomotive functions of a six-legged walking robot

Krzysztof Walas, Dominik Belter (2011)

International Journal of Applied Mathematics and Computer Science

This paper presents a method for building a foothold selection module as well as methods for the stability check for a multi-legged walking robot. The foothold selection decision maker is shaped automatically, without expert knowledge. The robot learns how to select appropriate footholds by walking on rough terrain or by testing ground primitives. The gathered knowledge is then used to find a relation between slippages and the obtained local shape of the terrain, which is further employed to assess...

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