Marcel Bergerman

Robust Joint and Cartesian Control of Underactuated Manipulators

Underactuated manipulators are robot manipulators composed of both active and passive joints in serial chain mechanisms. The study of underactuation is significant for the control of a variety of rigid-body systems, such as free-floating robots in space and gymnasts, whose structure include passive joints. For mechanisms with large degrees of freedom, such as hyper-redundant snake-like robots and multilegged machines, the underactuated structure allows a more compact design, weight decrease, and energy saving. Furthermore, when one or more joints of a standard manipulator fail, it becomes an underactuated mechanism; a control technique for such system will increase rhe reliability and fault-tolerance of current and future robots. The goal of this study is to present a robust control method for the control of underactuated manipulators subject to modeling errors and disturbances. Because an accurate modelling of the underactuated system is more critical for control issues than it is for standard manipulators, this method is significant in practice. Variable structure controllers are proposed in both joint space and Cartesian space, and a comprehensive simulation study is presented to address issues such as computation, robustness, and feasibility of the methods. Experimental results demonstrate the actual applicability of the proposed methods in a real two-degrees-of-freedom underactuated manipulator. As it will be shown, the proposed variable structure controller provides robustness against both disturbances and parametric uncertainties, a characteristic not present on previously proposed PID-based schemes.

Mapping a Space Manipulator to a Dynamically Equivalent Manipulator

In this paper, we discuss the problem of how a free-floating space manipulator can be mapped to a conventional, fixed-base manipulator which preserves both its dynamic and kinematic properties. This manipulator is called Dynamically Equivalent Manipulator (DEM). The DEM concept not only allows us to model a free-floating space manipulator system with simple, well-understood methods, but also to build a conventional manipulator system to experimentally study the dynamic performance and task execution of a space manipulator system, without having to resort to complicated experimental set-ups to simulate the space environment. This paper presents the theoretical development of the DEM concept, demonstrates the dynamic and kinematic equivalence, and presents simulation results to illustrate the equivalence under open-loop and closed-loop control strategies.

Linear {\mathcal H}_{\user2 \infty} Control

This chapter deals with linear robust control of robot manipulators. The approach we consider is based on the combination of two controllers, computed torque and linear ({mathcal{H}}_infty.) Experimental results using the UARM manipulator and CERob environment are presented to illustrate the validity of the method.

Experimental Set Up

This chapter describes the main features of the underactuted manipulators we use to validate the control approaches proposed throughout the book. It describes also a control environment for robots which we use to simulate the controllers and to operate the manipulators.

Nonlinear {\mathcal{H}}_{\varvec\infty} Control

This chapter deals with nonlinear ({mathcal{H}}_{infty}) control methodologies for robot manipulators. The nonlinear ({mathcal{H}}_{infty}) control considered guarantees an appropriate attenuation of the torque disturbance effect on the joint positions. We deal with two fundamental approaches for this class of controllers; the first is based on game theory and the second is based on linear parameter-varying (LPV) techniques. We provide solutions based on state and output feedback controls.

Adaptive Nonlinear {{\mathcal{H}}}_{\user2{\infty}} Control

In this chapter, we present adaptive nonlinear ({mathcal{H}}_{infty}) controllers for robot manipulators. Similarly to the controllers presented in Chap. 3, the ones here guarantee robustness to parametric uncertainty and external disturbances. They go beyond, however, by allowing us to estimate the parametric uncertainties and the unmodeled dynamics. These adaptive control laws are added into the standard nonlinear ({mathcal{H}}_{infty}) control approach whose derivation is based on the nominal model of the manipulator. Two adaptive control strategies are considered in this chapter, the first one based on linear parameterizations and the second one based on neural networks estimates.

Robust Control of Cooperative Manipulators

In this chapter we present three nonlinear ({mathcal{H}}_{infty}) control techniques for underactuated cooperative manipulators. Two are based on a quasi-linear parameter varying (quasi-LPV) representation of the nonlinear system with solutions based on game theory. These controllers take into account a fundamental characteristic of cooperative manipulator control, namely, that squeeze force control is designed independently of position control. In these cases, only the position control problem is reflected in the ({mathcal{H}}_{infty}) performance index. The third controller uses a neural network-based adaptive control law to estimate the parametric uncertainties of the system. In this case, the ({mathcal{H}}_{infty}) performance index includes both the position and squeeze force errors of the cooperative manipulators.

Underactuated Robot Manipulators

In this chapter we present the application of the ({mathcal{H}}_{infty}) and adaptive ({mathcal{H}}_{infty}) control methodologies to underactuated robotic manipulators, or manipulators with more joints than actuators. We begin by presenting a taxonomy to classify the different types of underactuation. Next, we present both model-based and non-model-based controller design approaches that guarantee robustness while the manipulator follows a desired trajectory.

Underactuated Cooperative Manipulators

In this chapter we present control strategies for cooperative manipulators with passive joints. These systems differ from the ones presented earlier because, here, one must control not only the position of the common load being manipulated by the various robots, but also the internal forces in the object to ensure it will not be damaged during the operation. Therefore, we use a hybrid motion and squeeze force controller. The strategy decouples the motion and squeeze force control problems via a Jacobian matrix that describes the relationship between the velocities of the load and the velocities of the actuated joints. The inertia matrices of the underactuated robots are not utilized, so as to reduce the possible influence of modeling errors in the controller performance. At the end of this chapter we also present a method to compute the dynamic load-carrying capacity of cooperative system with passive joints, which is an important measure of the maximum payload that can be manipulated over a given trajectory.

Markov Jump Linear Systems-Based Control

In this chapter we deal with the problem of fault tolerant control of robotic manipulators. We present a fault-modeling framework based on Markovian jump linear systems. An important feature of this approach is that it does not require that the manipulator be stopped when a fault is detected, i.e., the manipulator can continue moving until all joints have reached their respective desired positions. We deal here with free joint faults, when joint actuators lose their ability to apply torque and only the joint’s on/off brake is operative. We present experimental results based on ({{mathcal{H}}}_2,;{{mathcal{H}}}_{infty},) and mixed ({{mathcal{H}}}_2/{{mathcal{H}}}_{infty}) control-based approaches.