Panagiotis Tsiotras

Stabilization and optimality results for the attitude control problem

In this paper we present some recent results on the description and control of the attitude motion of rotating rigid bodies We derive a new class of globally asymptotically stabilizing feedback control laws for the complete i e dynamics and kinematics attitude motion We show that the use of a Lyapunov function which involves the sum of a quadratic term in the angular velocities and a logarithmic term in the kinematic parameters leads to the design of linear controllers We also show that the feedback control laws for the kinematics minimize a quadratic cost in the state and control variables for all initial conditions For the complete system we construct a family of exponentially stabilizing control laws and we investigate their optimality characteristics The proposed control laws are given in terms of the classical Cayley Rodrigues parameters and the Modi ed Rodrigues parameters

Inverse optimal stabilization of a rigid spacecraft

The authors present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft. They employ the inverse optimal control approach which circumvents the task of solving a Hamilton-Jacobi equation and results in a controller optimal with respect to a meaningful cost functional. The inverse optimality approach requires the knowledge of a control Lyapunov function and a stabilizing control law of a particular form. For the spacecraft problem, they are both constructed using the method of integrator backstepping. The authors give a characterization of (nonlinear) stability margins achieved with the inverse optimal control law.

Further passivity results for the attitude control problem

In this paper we establish passivity for the system which describes the attitude motion of a rigid body in terms of minimal three-dimensional kinematic parameters. In particular, we show that linear asymptotically stabilizing controllers and control laws without angular velocity measurements follow naturally from these passivity properties. The results of this paper extend similar results for the case of the (nonminimal) Euler parameters.

Dynamic friction models for road/tire longitudinal interaction

Summary In this paper we derive a new dynamic friction force model for the longitudinal road/tire interaction for wheeled ground vehicles. The model is based on a dynamic friction model developed previously for contact-point friction problems, called the LuGre model. By assuming a contact patch between the tire and the ground we develop a partial differential equation for the distribution of the friction force along the patch. An ordinary differential equation (the lumped model) for the friction force is developed, based on the patch boundary conditions and the normal force distribution along the contact patch. This lumped model is derived to approximate closely the distributed friction model. Contrary to common static friction/slip maps, it is shown that this new dynamic friction model is able to capture accurately the transient behaviour of the friction force observed during transitions between braking and acceleration. A velocity-dependent, steady-state expression of the friction force versus the slip coefficient is also developed that allows easy tuning of the model parameters by comparison with steady-state experimental data. Experimental results validate the accuracy of the new tire friction model in predicting the friction force during transient vehicle motion. It is expected that this new model will be very helpful for tire friction modeling as well as for anti-lock braking (ABS) and traction control design.

Leader–follower cooperative attitude control of multiple rigid bodies

In this paper we extend our previous results on coordinated control of rotating rigid bodies to the case of teams with heterogenous agents. We assume that only a certain subgroup of the agents (the leaders) are vested with the main control objective, that is, maintain constant relative orientation amongst themselves. The rest of the team must meet relaxed control specifications, namely maintain their respective orientations within certain limits dictated by the orientation of the leaders. The proposed control laws respect the limited information each rigid body has with respect to the rest of its peers (leaders or followers) as well as with the rest of the team. Each rigid body is equipped with a control law that utilizes the Laplacian matrix of the associated communication graph, which encodes the communication links between the team members. Similarly to the linear case, the convergence of the multi-agent system relies on the connectivity of the communication graph.

Stability of time-delay systems: equivalence between Lyapunov and scaled small-gain conditions

It is demonstrated that many previously reported Lyapunov-based stability conditions for time-delay systems are equivalent to the robust stability analysis of an uncertain comparison system free of delays via the use of the scaled small-gain lemma with constant scales. The novelty of this note stems from the fact that it unifies several existing stability results under the same framework. In addition, it offers insights on how new, less conservative results can be developed.

Dynamic tire friction models for vehicle traction control

We derive a dynamic friction force model for road/tire interaction for ground vehicles. The model is based on a similar dynamic friction model for contact developed previously for contact-point friction problems, called the LuGre model. We show that the dynamic LuGre friction model is able to accurately capture velocity and road/surface dependence of the tire friction force.

Control of underactuated spacecraft with bounded inputs

Bounded feedback control laws are designed for stabilization and tracking of underactuated spacecraft. The flat outputs of the system are computed and are used to generate reference trajectories for the tracking problem.

Spacecraft adaptive attitude and power tracking with variable speed control moment gyroscopes

Control laws for an integrated powerlattitude control system (IPACS) for a satellite using variable-speed single-gimbal control moment gyroscopes (VSCMGs) are introduced. Whereas the wheel spin rates of the conventional CMGs are constant, the VSCMGs are allowed to have variable speeds. Therefore, VSCMGs have extra degrees of freedom and can be used to achieve additional objectives, such as energy storage, as well as attitude control. We use VSCMGs in conjunction with an IPACS system. The gimbal rates of the VSCMGs are used to provide the reference-tracking torques, whereas the wheel accelerations are used for both attitude and power reference tracking. The latter objective is achieved by storing or releasing the kinetic energy in the wheels. The control algorithms perform both the attitude and power tracking goals simultaneously. A model-based control and an indirect adaptive control for a spacecraft with uncertain inertia properties are developed. Moreover, control laws for equalization of the wheel speeds are also proposed. Wheel speed equalization distributes evenly the kinetic energy among the wheels, minimizing the possibility of wheel speed saturation and the occurrence of zero-speed singularities. Finally, a numerical example for a satellite in a low Earth, near-polar orbit is provided to test the proposed IPACS algorithm.

Singularity Analysis of Variable Speed Control Moment Gyros

Single-gimbal control moment gyros (CMGs) have many advantages over other actuators for attitude control of spacecraft. For instance, they act as torque amplifiers and, thus, are suitable for slew maneuvers. However, their use as torque actuators is hindered by the presence of singularities, that, when encountered, do not allow a CMG cluster to generate torques about arbitrary directions. One method to overcome this drawback is to use variable-speed single-gimbal control moment gyros (VSCMGs). Whereas the wheel speed of a conventional CMG is constant, VSCMGs are allowed to have variable wheel speed. Therefore, VSCMGs have extra degrees of freedom that can be used to achieve additional objectives, such as singularity avoidance and/or power tracking, as well as attitude control. The singularity problem of a VSCMGs cluster is studied in detail for the cases of attitude tracking, with and without a power tracking requirement. A null motion method to avoid singularities is presented, and a criterion is developed to determine the momentum region over which this method will successfully avoid singularities. This criterion can be used to size the wheels and develop appropriate momentum damping strategies tailored to the specific mission requirements. I. Introduction A CONTROL moment gyro (CMG) is a device used as an actuator for attitude control of spacecraft. It generates torques through angular momentum transfer to and from the main spacecraft body. This is achieved by changing the direction of the angular momentum vector of a gimballed flywheel. Because a CMG operates in a continuous manner, contrary to the gas jet’s on/off operation, it can achieve precise attitude control. Moreover, as with other momentum exchange devices, for example, reaction wheels, it does not consume any propellant, thus prolonging the operational life of the spacecraft. Single-gimbal CMGs essentially act as torque amplifiers. 1 This torque amplification property makes them especially advantageous as attitude control actuators for large space spacecraft and space structures, for example, a space station. In fact, single-gimbal and double-gimbal CMGs have been used for attitude control of the Skylab, the MIR and the International Space Station (ISS). An obstacle when using a CMG system in practice is the existence of singular gimbal angle states for which the CMGs cannot generate a torque along arbitrary directions. At each singular state, all admissible torque directions lie on a two-dimensional surface in the three-dimensional angular momentum space; therefore, the CMG system cannot generate a torque normal to this surface. The CMG singularities can be classified into two categories: 1) external or saturated singularities in which the total angular momentum sum of the CMGs lies on the maximum momentum envelope and 2) internal singularities in which the total momentum lies inside this envelope. The external singularities can be easily anticipated from the given CMG configuration and mission profile; therefore, they can be taken into account at the design step. A properly designed momentum management scheme can also relieve the external singularity problem. The internal CMG singularities, on the other hand, are in general difficult to anticipate. Avoiding such internal singularities has, thus, been a long-standing problem in the CMG