FIR filters for online trajectory planning with time- and frequency-domain specifications

In this paper, the use of FIR (Finite Impulse Response) filters for planning minimum-time trajectories for robots or automatic machines under constraints of velocity, acceleration, etc. is presented and discussed. In particular, the relationship between multi-segment polynomial trajectories, i.e. trajectories composed of several polynomial segments, each one possibly characterized by constraints on one or more specific derivatives (i.e. velocity, acceleration, jerk, etc.), and FIR filters disposed in a cascade configuration is demonstrated and exploited in order to design a digital filter for online trajectory planning. The connection between analytic functions and dynamic filters allows a generalization of these trajectories, usually obtained by second- or third-order polynomial functions (e.g. trapezoidal velocity and double S velocity trajectories), to a generic order with only a modest increase of the complexity. As a matter of fact, the computation of trajectories with higher degree of continuity simply requires additional FIR filters in the chain. Moreover, the modular structure of the planner provides a direct frequency characterization of the motion law. In this way, it is possible to define the trajectories by considering constraints expressed in the frequency-domain besides the classical time-domain specifications, such as bounds on velocity, acceleration, and so on. Two examples illustrate the main features of the proposed trajectory planner, in particular with respect to the problems of multi-point trajectories generation and residual vibrations suppression

Correction of Force Errors for Flexible Manipulators in Quasi-Static Conditions

This paper deals with the problem of controlling the interactions of flexible manipulators with their environment. For executing a force control task, a manipulator with intrinsic (mechanical) compliance has some advantages over the rigid manipulators commonly employed in position control tasks. In particular, stability margins of the force control loop are increased, and robustness to uncertainties in the model of the environment is improved for compliant arms. On the other hand, the deformations of the arm under the applied load give rise to errors, that ultimately reflect in force control errors. This paper addresses the problem of evaluating these errors, and of compensating for them with suitable joint angle corrections. A solution to this problem is proposed in the simplifying assumptions that an accurate model of the arm flexibility is known, and that quasi-static corrections are of interest.MIT Artificial Intelligence Laborator

Output-Based Control of Robots with Variable Stiffness Actuation

The output-based control of a redundant robotic manipulator with relevant and adjustable joint stiffness is addressed. The proposed controller is configured as a cascade system that allows the decoupling of the actuators dynamics from the arm dynamics and the consequent reduction of the order of the manipulator dynamic model. Moreover, the proposed controller does not require the knowledge of the whole robot state: only the positions of the actuators and of the joints are necessary. This approach represents a significant simplification with respect to previously proposed state feedback techniques. The problem of controlling simultaneously the position trajectory and the desired stiffness in both the joint and work space is investigated, and the relations between the manipulator redundancy and the selection of both the joint and work space stiffness of the manipulator are discussed. The effectiveness of the proposed approach is verified by simulations of a 3 degrees of freedom planar manipulator

Port Hamiltonian formulation of infinite dimensional systems I. Modeling

In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multivariable case. The resulting class of infinite dimensional systems is quite general, thus allowing the description of several physical phenomena, such as heat conduction, piezoelectricity and elasticity. Furthermore, classical PDEs can be rewritten within this framework. The key point is the generalization of the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables

Geometric Scattering in Robotic Telemanipulation

In this paper, we study the interconnection of two robots, which are modeled as port-controlled Hamiltonian systems through a transmission line with time delay. There will be no analysis of the time delay, but its presence justifies the use of scattering variables to preserve passivity. The contributions of the paper are twofold: first, a geometrical, multidimensional, power-consistent exposition of telemanipulation of intrinsically passive controlled physical systems, with a clarification on impedance matching, and second, a system theoretic condition for the adaptation of a general port-controlled Hamiltonian system with dissipation (port-Hamiltonian system) to a transmission line

Multi-variable port Hamiltonian model of piezoelectric material

In this paper, the dynamics of a piezoelectric material is presented within the new framework of multi-variable distributed port Hamiltonian systems. This class of infinite dimensional system is quite general, thus allowing the description of several physical phenomena, such as heat conduction, elasticity, electromagnetism and, of course, piezoelectricity. The key point is the generalization of the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables. In this way, the dynamics of the system results from the interconnection of a proper set of elements, each of them characterized by a particular energetic behavior, while the interaction with the environment is described in terms of mechanical and electrical boundary ports

A Repetitive Control Scheme Based on B-Spline Trajectories Modification

In many applications of interest in industrial robotics, tasks are cyclic and must be repeated over and over. In this context, it seems natural to exploit the intrinsic properties of repetitive control schemes, where the cyclic nature of "disturbances" and/or unmodeled dynamic effects can be exploited to reduce the tracking errors. In this paper, we propose a new repetitive control scheme, where the main idea consists in the modification of the reference trajectory in order to compensate for the periodic undesired effects. By exploiting the dynamic filters for the B-spline generation, it is possible to integrate the trajectory planning within a repetitive control scheme able to modify in real-time the reference signal with the aims of nullify interpolation errors. By means of an extensive experimental activity on a servo mechanism pros and cons of the proposed approach are analyzed