Sliding modes in constrained systems control

Abstract—In this paper, a sliding-mode-based design framework for fully actuated mechanical multibody system is discussed. The framework is based on the possibility to represent complex motion as a collection of tasks and to find effective mapping of the system coordinates that allows decoupling task and constraint control so one is able to enforce concurrently, or in certain time succession, the task and the constraints. The approach seems naturally encompassing the control of motion systems in interaction, and it allows application to bilateral control, multilateral control, etc. Such an approach leads to a more natural interpretation of the system tasks, simpler controller design, and easier establishment of the systems hierarchy. It allows a unified mathematical treatment of task control in the presence of constraints required to be satisfied by the system coordinates. In order to show the applicability of the proposed techniques, simulation and experimental results for high-precision systems in microsystem assembly tasks and bilateral control systems are presented

Motion control - A SMC approach

Motion control involves many diversified control problems of complex nonlinear systems. In this paper we will be addressing the SMC approach for multi-body mechanical systems control. The main feature of the SMC is constraint of the system motion into manifold in system state space. It will be shown that usage of the SMC methods is a natural way of addressing problems in motion control including constrained systems, redundant systems and functionally related systems to name some. The consistent application of the SMC methods leads to natural decomposition of system motion for redundant tasks and allows simple, straight forward dynamical decoupling of the multiple tasks

Reactive Planar Manipulation with Convex Hybrid MPC

This paper presents a reactive controller for planar manipulation tasks that leverages machine learning to achieve real-time performance. The approach is based on a Model Predictive Control (MPC) formulation, where the goal is to find an optimal sequence of robot motions to achieve a desired object motion. Due to the multiple contact modes associated with frictional interactions, the resulting optimization program suffers from combinatorial complexity when tasked with determining the optimal sequence of modes. To overcome this difficulty, we formulate the search for the optimal mode sequences offline, separately from the search for optimal control inputs online. Using tools from machine learning, this leads to a convex hybrid MPC program that can be solved in real-time. We validate our algorithm on a planar manipulation experimental setup where results show that the convex hybrid MPC formulation with learned modes achieves good closed-loop performance on a trajectory tracking problem

Sliding modes in electrical drives and motion control

In this paper application of Sliding Mode Control (SMC) to electrical drives and motion control systems is discussed. It is shown that in these applications simplicity in implementation makes concepts of SMC a very attractive design alternative. Application in electrical drives control is discussed for supply via different topologies of the supply converters. Motion control is discussed for single degree of freedom motion control systems as an extension of the control of mechanical coordinates in electrical drives. Extension to multi-body systems is discussed very briefly

SMC framework in motion control systems

Design of a motion control system should take into account both the unconstrained motion performed without interaction with environment or other system, and the constrained motion where system is in contact with environment or has certain functional interaction with another system. In this paper control systems design approach, based on siding mode methods, that allows selection of control for generic tasks as trajectory and/or force tracking as well as for systems that require maintain some functional relation like bilateral or multilateral systems, establisment of virtual relation among mobile robots or control of haptic systems is presented. It is shown that all basic motion control problems - trajectory tracking, force control, hybrid position/force control scheme and the impedance control - can be treated in the same way while avoiding the structural change of the controller and guarantying stable behavior of the system In order to show applicability of the proposed techniques simulation and experimental results for high precision systems in microsystems assembly tasks and bilateral control systems are presente

Robust on-off pulse control of flexible space vehicles

The on-off reaction jet control system is often used for attitude and orbital maneuvering of various spacecraft. Future space vehicles such as the orbital transfer vehicles, orbital maneuvering vehicles, and space station will extensively use reaction jets for orbital maneuvering and attitude stabilization. The proposed robust fuel- and time-optimal control algorithm is used for a three-mass spacing model of flexible spacecraft. A fuel-efficient on-off control logic is developed for robust rest-to-rest maneuver of a flexible vehicle with minimum excitation of structural modes. The first part of this report is concerned with the problem of selecting a proper pair of jets for practical trade-offs among the maneuvering time, fuel consumption, structural mode excitation, and performance robustness. A time-optimal control problem subject to parameter robustness constraints is formulated and solved. The second part of this report deals with obtaining parameter insensitive fuel- and time- optimal control inputs by solving a constrained optimization problem subject to robustness constraints. It is shown that sensitivity to modeling errors can be significantly reduced by the proposed, robustified open-loop control approach. The final part of this report deals with sliding mode control design for uncertain flexible structures. The benchmark problem of a flexible structure is used as an example for the feedback sliding mode controller design with bounded control inputs and robustness to parameter variations is investigated

An observer-based attitude and nutation control and flexible dynamic analysis for the NASA Magnetospheric Multiscale Mission

Current research with the NASA Goddard Space Flight Center (GSFC) involves the dynamic modeling and control of the NASA Magnetospheric Multiscale (MMS) Mission, a. Solar-Terrestrial Probe mission to study Earth\u27s magnetosphere. Four observer-based attitude and nutrition controllers are designed and evaluated to determine the most effective feedback control system as it applies to MMS. Also, a dynamic analysis of each of the four identical satellites\u27 two Axial Double Probe (ADP) booms is performed to provide an understanding of flexible boom dynamics. The Finite Element method is used in evaluating boom modes of vibration for confirmation of NASA GSFC theoretical analysis and use in flexible model development. The dynamic transient and modal extraction technique are investigated for vibration analysis of constrained and unconstrained bodies. A fully flexible boom and rigid spacecraft model is also developed for vibrational analysis under steady-state rotation and thruster loads. Results indicate, however, the need for future research in numerical analysis of propagating systems through finite element methods and in the stability of the observer-based control system. Linear and nonlinear observers are developed through simulations to estimate satellite attitude and angular body rates without the use of rate sensors. Control systems are then developed assuming perfect state measurements. Euler angles are used to describe satellite attitude in this research. Finally, linear and nonlinear (Sliding Mode Control) techniques are implemented in conjunction with the nonlinear observers to complete the observer-based control system. The results of this research show that, of the methods analyzed, both the Extended Kalman Filter and Sliding Mode Observer implemented with Sliding Mode Control yield the most satisfactory performance. These observer-based control systems both meet NASA design requirements while reducing thruster control effort and reducing the effects of measurement noise and spacecraft uncertainties/disturbances. More simulations, however, are needed to verify performance of the proposed observer-based control system over all possible ranges of operation

Stiffness pathologies in discrete granular systems: bifurcation, neutral equilibrium, and instability in the presence of kinematic constraints

The paper develops the stiffness relationship between the movements and forces among a system of discrete interacting grains. The approach is similar to that used in structural analysis, but the stiffness matrix of granular material is inherently non-symmetric because of the geometrics of particle interactions and of the frictional behavior of the contacts. Internal geometric constraints are imposed by the particles' shapes, in particular, by the surface curvatures of the particles at their points of contact. Moreover, the stiffness relationship is incrementally non-linear, and even small assemblies require the analysis of multiple stiffness branches, with each branch region being a pointed convex cone in displacement-space. These aspects of the particle-level stiffness relationship gives rise to three types of micro-scale failure: neutral equilibrium, bifurcation and path instability, and instability of equilibrium. These three pathologies are defined in the context of four types of displacement constraints, which can be readily analyzed with certain generalized inverses. That is, instability and non-uniqueness are investigated in the presence of kinematic constraints. Bifurcation paths can be either stable or unstable, as determined with the Hill-Bazant-Petryk criterion. Examples of simple granular systems of three, sixteen, and sixty four disks are analyzed. With each system, multiple contacts were assumed to be at the friction limit. Even with these small systems, micro-scale failure is expressed in many different forms, with some systems having hundreds of micro-scale failure modes. The examples suggest that micro-scale failure is pervasive within granular materials, with particle arrangements being in a nearly continual state of instability