On structural instability of normal forms of affine control systems subject to static state feedback

AbstractSmooth affine control systems acted on by the feedback group are dealt with, from the viewpoint of the existence of structurally stable normal forms. Detailed analysis of the action of the approximate feedback group of order 1 has revealed that in most cases an obstacle to structural stability appears just in the action of this group

Towards constrained motion planning of mobile manipulators

Abstract-This paper addresses a constrained motion planning problem for mobile manipulators. The constraints are included into the system model by means of a sort of penalty function, and then processed in accordance with the endogenous configuration space approach. Main novelty of this paper lies in deriving a constrained Jacobian motion planning algorithm with the following features: inequality constraints are included into an extended kinematics model using a smooth approximation of the plus function, the model is then regularized against singularities, and the resulting imbalance in error equations is handled as a perturbation of an exponentially stable linear dynamic system. The operation of the constrained motion planning algorithm is illustrated by a motion planning problem of a mobile manipulator with bounds imposed on a platform variable. Performance of the algorithm is tested by computer simulations

On generic properties of linear systems: An overview

The topological space of linear, time-invariant systems is considered. A properly of linear systems is called generic if the systems equipped with this property occupy an open and dense subspace of the space of systems. Several generic properties of linear systems are reviewed, including controllability, observability, invertibility, structural stability, as well as some topological properties of orbits of the feedback group. A new estimate for the number of orbits of the feedback group is produced, and a differential geometric proof of the existence of generic controllability indices is given

Motion planning for parallel robots with non-holonomic joints

Presentado al 13th International Symposium on Advances in Robot Kinematics (ARK) celebrado en Austria del 24 al 28 de junio de 2012.Designing a robot manipulator with fewer actuators than the dimension of its configuration space – to reduce bulk, weight and cost – becomes feasible by introducing mechanical elements that lead to non-holonomic constraints. Unfortunately, the mechanical advantages of these non-holonomic designs are usually darkened by the complexity of their control. This paper deals with motion planning for parallel robots with non-holonomic joints shedding new light on their control strategies. As a case study, the motion planning problem is solved for a 3-ŬPU parallel robot, where Ŭ stands for a non-holonomic joint whose instantaneous kinematics are equivalent to that of a universal joint. It is thus shown how the three prismatic actuators can maneuver to reach any six-degree-of-freedom pose of the moving platform. The motion planning has been addressed as a control problem in the control system representation of the robot’s kinematics and a motion planning algorithm has been devised based on a Jacobian inversion of the end-point map of the representation. Performance of the algorithm is illustrated with numeric computations.The research of the first two authors was supported by a statutory grant from Wrocław University of Technology.Peer Reviewe

On dynamically consistent Jacobian inverse for non-holonomic robotic systems

This paper presents the dynamically consistent Jacobian inverse for non-holonomic robotic system, and its application to solving the motion planning problem. The system’s kinematics are represented by a driftless control system, and defined in terms of its input-output map in accordance with the endogenous configuration space approach. The dynamically consistent Jacobian inverse (DCJI) has been introduced by means of a Riemannian metric in the endogenous configuration space, exploiting the reduced inertia matrix of the system’s dynamics. The consistency condition is formulated as the commutativity property of a diagram of maps. Singular configurations of DCJI are studied, and shown to coincide with the kinematic singularities. A parametric form of DCJI is derived, and used for solving example motion planning problems for the trident snake mobile robot. Some advantages in performance of DCJI in comparison to the Jacobian pseudoinverse are discovered