Lorenza Magnani

A stabilizing model-based predictive control algorithm for nonlinear systems

Using distinct prediction and control horizons, nonlinear model-based predictive control can guarantee: (i) computational efficiency, (ii) enlargement of the stability domain and (iii) local optimality.

Design and experimental validation of a second-order sliding-mode motion controller for robot manipulators

This article presents an original motion control strategy for robot manipulators based on the coupling of the inverse dynamics method with the so-called second-order sliding mode control approach. Using this method, in principle, all the coupling non-linearities in the dynamical model of the manipulator are compensated, transforming the multi-input non-linear system into a linear and decoupled one. Actually, since the inverse dynamics relies on an identified model, some residual uncertain terms remain and perturb the linear and decoupled system. This motivates the use of a robust control design approach to complete the control scheme. In this article the sliding mode control methodology is adopted. Sliding mode control has many appreciable features, such as design simplicity and robustness versus a wide class of uncertainties and disturbances. Yet conventional sliding mode control seems inappropriate to be applied in robotics since it can generate the so-called chattering effect, which can be destructive for the controlled robot. In this article, this problem is suitably circumvented by designing a second-order sliding mode controller capable of generating a continuous control law making the proposed sliding mode controller actually applicable to industrial robots. To build the inverse dynamics part of the proposed controller, a suitable dynamical model of the system has been formulated, and its parameters have been accurately identified relying on a practical MIMO identification procedure recently devised. The proposed inverse dynamics-based second-order sliding mode controller has been experimentally tested on a COMAU SMART3-S2 industrial manipulator, demonstrating the tracking properties and the good performances of the controlled system.

Second order sliding mode motion control of rigid robot manipulators

This paper presents a control strategy for robot manipulators, based on the coupling of the inverse dynamics method with the so-called second order sliding mode control approach. The motivation for using sliding mode control in robotics mainly relies on its appreciable features, such as design simplicity and robustness. Yet, the chattering effect, typical of the conventional sliding mode control, can be destructive. In this paper, this problem is suitably circumvented by adopting a second order sliding mode control approach characterized by a continuous control law. To design the inverse dynamics part of the proposed controller, a suitable dynamical model of the system has been formulated, and its parameters have been accurately identified. The proposed inverse dynamics-based second order sliding mode controller has been experimentally tested on a COMAU SMART3-S2 industrial manipulator, demonstrating the tracking properties and the good performances of the controlled system.

MIMO Closed Loop Identification of an Industrial Robot

This paper proposes a practical multi-input multi-output (MIMO) closed loop parameters identification procedure for robot manipulators. It is based on the weighted least squares (WLS) method, coupled with particular solutions to facilitate the estimation, reducing the noise effect. More precisely, a two steps procedure to reduce the condition number of the input data matrix with optimal trajectory planning, and a method to estimate the variances matrix to be used as a weight matrix for the WLS method are illustrated. Moreover, the identification problem is solved with reference to an MIMO coupled system. A closed loop identification is needed because the system is open loop unstable, and because the robot has to track an optimal reference input so as to correctly execute the identification procedure. Some solutions are also presented to overtake common identification problems, such as the bias of the estimated parameters, the presence of outliers, the necessity of balancing the kinematics of the third link, and the reduction of the sensitivity to noise of the estimate. The presented procedure has been successfully experimentally tested on a COMAU SMART3-S2 industrial manipulator used in a planar configuration.

Motion Control of Rigid Robot Manipulators via First and Second Order Sliding Modes

A motion control strategy for rigid robot manipulators based on sliding mode control techniques and the compensated inverse dynamics method is presented in this paper. The motivation for using sliding mode mainly relies on its appreciable features, such as simplicity and robustness versus matched uncertainties and disturbances. Furthermore the proposed approach avoids the estimation of the time-varying inertia matrix. As a preliminary step a first order sliding mode control law is presented. Then a second order strategy is discussed. In both cases the problem of chattering, typical of sliding mode control, is suitably circumvented. Simulations results demonstrates the good tracking properties of the proposed control strategy.

MIMO identification with optimal experiment design for rigid robot manipulators

This paper proposes a practical parameters identification procedure for robot manipulators. It is based on the well-known maximum likelihood method adopting particular techniques to facilitate the estimation: condition number reduction methods for the input data matrix with optimal trajectory planning, and two different methods for variances estimation. Moreover, the identification problem is solved with reference to the multi input multi output coupled system. A closed loop identification is needed because the system is open loop unstable, and, moreover, because to correctly execute the identification procedure, the robot has to track an optimal reference input. Some solutions are also presented to overtake common identification problems, such as bias of the estimated parameters, outliers detection and elimination, and noise sensitivity of the estimation. The presented procedure was successfully tested on a COMAU SMART3-S2 industrial manipulator demonstrating its efficiency.

A globally stabilizing hybrid variable structure control strategy

A hybrid variable structure control strategy for a class of second order systems is presented in this paper. It relies on a system state decomposition into regions, and on a suitable event-driven switching among the corresponding control laws. By enforcing conventional and unconventional sliding-mode behaviors, as well as avoiding the generation of limit cycles, the proposed strategy proves to globally asymptotically stabilize the origin of the system state space.

An Inverse Dynamics-Based Discrete-Time Sliding Mode Controller for Robot Manipulators

In the past years an extensive literature has been devoted to the subject of motion control of rigid robot manipulators. Many approaches have been proposed, such as feedback linearization [1], model predictive control [2], as well as sliding mode or adaptive control [3], [4], [5]. The basic idea of feedback linearization, known in the robotic context as inverse dynamics control [6], [7], is to exactly compensate all the coupling nonlinearities in the dynamical model of the manipulator in a first stage so that a second stage compensator may be designed based on a linear and decoupled plant. Although global feedback linearization is possible in theory, in practice it is difficult to achieve, mainly because the coordinate transformation is a function of the system parameters and, hence, sensitive to uncertainties which arise from joint and link flexibility, frictions, sensor noise, and unknown loads. This is the reason why the inverse dynamics approach is often coupled with robust control methodologies [1].

Models of the Influence of Coupled Spaces in Christian Churches

Ancient religious buildings usually contain articulated environments, such as lateral chapels, in which the effect of multiple acoustically coupled spaces can influence the sound field in the central volume. By introducing absorbent materials in a lateral chapel, the acoustic response of the whole church can be altered. If the effects of coupled spaces are described by geometrical acoustics, inaccurate results may be obtained since reverberation time is influenced by mutual power interactions through the coupling areas or separating walls. Two methods are considered, to determine the simplest way to obtain accurate values of reverberation time for these situations. The results of the simulations are compared with experimental values and indicate areas of applicability of the tested methods.

A stabilizing receding horizon controller for nonlinear discrete time systems

This note presents a new state-feedback receding horizon (RH) control algorithm for nonlinear systems guaranteeing closed-loop stability of the origin. This method can be viewed as a realistic approximation of the infinite-horizon optimal controller, while not requiring a heavy computational burden.