Alexandre Pechev

Inverse Kinematics without matrix inversion

This paper presents a new singularity robust and computationally efficient method for solving the inverse kinematics (IK) problem. In this method, the transformation from Cartesian space to joint space is performed in a feedback loop and as a result the new feedback inverse kinematics (FIK) law operates as a filter and does not require matrix manipulations (inversion, singular value decomposition or a computation of a damping factor). While the computational demand is greatly reduced, the performance is comparable to the one delivered by the damped least squares (DLS) law. The new algorithm is capable of escaping and avoiding kinematic singularities and in this respect it outperforms pseudo-inverse based formulations.

Underactuated Satellite Attitude Control with Two Parallel CMGs

In this paper, we study the attitude stability and the disturbance attenuation properties for an underactuated spacecraft equipped with two parallel CMGs. We first present the actuator configuration and then compare this with typical fully actuated CMG-based configurations. The system model is then derived. Considering the pointing of an underactuated spacecraft, we derive a Lyapunov control law which is further modified to a dissipative controller to account for disturbances. Simulations are included to demonstrate the effectiveness of the proposed control law to attenuate perturbations and to render the underactuated attitude closed-loop system to a dissipative system.

Time-varying underactuated attitude control design with feedback linearization using two pairs of gas jet actuators

Research has shown that rigid spacecraft with two controls cannot be stabilized by continuous state feedback. In this paper, aiming at asymmetric spacecraft with two pairs of gas jet actuators, we design smooth time-varying controllers for the underactuated system. These optimal controllers are developed by introducing an assistant state variable and using feedback linearization techniques. Through this approach, the states of the closed-loop systems can converge with exponential rates and this is validated by numerical simulations. Compared with existing control designs for underactuated attitude systems, this approach is much simpler and can be also scaled to other applications.Copyright

Bounded gain-scheduled LQR satellite control using a tilted wheel

Generation of control torque for highly agile satellite missions is generally achieved with momentum exchange devices, such as reaction wheels and control moment gyros (CMGs) with high slew maneuverability. However, the generation of a high control torque from the respective actuators requires high power and thus a large mass. The work presented here proposes a novel type of control actuator that generates torques in all three principal axes of a rigid satellite using only a spinning wheel and a simple tilt mechanism. This newly proposed actuator has several distinct advantages including less mass and more simplicity than a conventional CMG and no singularities being experienced during nominal wheel operation. A new high performance bounded (HPB) linear quadratic regulator (LQR) control law has been presented that extends classical LQR by providing faster settling times, gain-scheduling the control input weightings to optimize its performance, and has much quicker computation times than classical LQR. This work derives a fundamental mathematical model of the actuator and demonstrates feasibility by providing three degree of freedom high fidelity simulations for the actuator using both classical LQR and HPB LQR.

3-D Wheel: A Single Actuator Providing Three-Axis Control of Satellites

CTIVE magnetic bearings (AMBs) offer many advantages for momentum wheels on small satellites compared with conventional bearings using ball or roller bearings. Conventional bearings require aformof lubricant, whichevaporates inthevacuum of space unless sealed, or to be made from a dry lubricant. The bearings will wear with time and may eventually fail, limiting the lifetime of the satellite. To minimize the wear on its bearings, the wheel may be operated at a low spin rate, limiting the angular momentumofthewheel.UsingAMBsmeansthatthereisnocontact between moving parts, and so lubrication is not required and wear is not an issue [1]. As the resolution of the cameras in small satellites approaches1mgroundresolution[2]microvibrationsonthesatellite increasinglyaffecttheimagequality.Thebandwidthandprecisionof an AMB-based momentum wheel allow it to damp such microvibrations. The number of degrees offreedom that are actively controlled can be chosen. The 3-D wheel presented here has 5 degrees of freedom actively controlled. Because the tilt angle of the wheel is actively controlled, it is possible to tilt the wheel, generating a gyroscopic output torque in a similar fashion to a control moment gyro (CMG). Unlike a CMG, the tilt axis of the 3-D wheel is not fixed, and the gyroscopic output torque can be steered to be anywhere in the plane normal to the spin axis of the wheel. A single wheel is therefore capable of generating an output torque about all three principle axes of the spacecraft. Because thewheel istilted using electromagnets, it can be tilted at a high rate, generating a large output torque. The bandwidth of the gyroscopic torque is higher than a conventional momentum wheel’s, making it ideal for the damping of microvibrations for highly sensitive payloads or for the rapid reorientation of spacecraft during maneuvers such as rendezvous and docking. In this Notewe present the design of the engineering model of the 3-D wheel that has been built: a tilting magnetically levitated momentum-wheel for small satellites. We discuss the design of the wheel and then present the results of testing this engineering model. The positionofthewheelcanbecontrolledtowithin2:5 � mandthe tilt angle can be controlled with an accuracy of 0.1 mrad. The bandwidthofthewheelandcontrolleris120 rad=s.Thewheelcanbe tilted at a maximum rate of 0:56 rad=s, which when the wheel is spinning at 5000 rpm generates a gyroscopic output torque of

Three-Axis Attitude Control of a Satellite in Zero Momentum Mode Using a Tilted Wheel Methodology

Generation of control torque for highly agile satellite missions is generally achieved with momentum exchange devices, such as reaction wheels and control moment gyros (CMGs) with high slew maneuverability. However, the generation of a high control torque from the respective actuators requires high power and thus a large mass. This paper proposes a novel type of control actuator that will generate torques in all three principal axes of a rigid satellite using only a spinning wheel and a simple tilt mechanism. The tilt mechanism will rotate the spin axis of the wheel (tilt the generated angular momentum vector) about two additional axes thereby generating high control torque about the axes orthogonal to the wheel spin axis. Torque will also be generated about the wheel spin axis through the increase or decrease of the wheel angular speed. This newly proposed actuator generates control torque through controlled precession of the spinning wheel while the tilt angle and the tilt rates are computed without the use of the popular pseudo-inverse calculation obtained with CMGs leading to no singularities being experienced during nominal wheel operation. This paper describes the fundamental mathematical dynamic model of the system and numerical simulations are used to demonstrate the agile three-axis attitude control capability that guarantees a highly efficient trade-off between torque capability, mass, and power consumption. The system actuator sizing is based on slew rates of up to two degrees per second.

Time-Varying Nonlinear Designs for Underactuated Attitude Control With Two Reaction Wheels

Reaction wheels are commonly employed for high precisision and agile pointing in spacecraft. In this paper, we consider the realization of three-axis stabilization with only two reaction wheels installed along two principle axes. In practise, the total angular momentum of the whole spacecraft periodically varies with time because of the existence of in-orbit disturbances. With regard to the time varying system, firstly, a time varying control law is presented for velocity dumping based on center manifold theory. Then a continuous nonlinear feedback controller with a periodic time varying term is also presented for the attitude. Numerical simulations are presented to illustrate the effectiveness of the designs.Copyright

Humanoid Robot Balance Control Using the Spherical Inverted Pendulum Mode

Human beings are highly efficient in maintaining standing balance under the influence of different perturbations. However, biped humanoid robots are far from exhibiting similar skills. This is mainly due to the limitations in the current control and modelling techniques used in humanoid robots. Even though approaches using the Linear Inverted Pendulum Model and the Preview Control schemes have shown improved results, they still suffer from shortcomings in the overall generated motion. We propose here a model and control approach that aims to overcome the limiting assumptions in the LIPM models, through using the ankle joint variables in modelling and control of the standing balance of the humanoid robot.

Modelling and data analysis of GPS reflections from low earth orbit

GPS-Reflectometry studies the forward scattering of GPS reflections for the purposes of determining surface characteristics. This can be used for measuring sea states, soil humidity and polar ice age. Theoretical and experimental studies have been mainly carried out on ground and airborne platforms. A space-borne platform, however, would provide broader spatial and temporal coverage for Earth Observation and disaster monitoring. Currently UK-DMC represents the only Low Earth Orbit (LEO) satellite able to routinely schedule GPS reflection observations from ocean surfaces. Earlier research work has shown that Delay-Doppler Maps (DDMs) derived from reflections from space, although weak, will vary with geometry and sea state. In this work we extend these results by developing a modelling technique that derives relationships between wind conditions, sea roughness and GPS reflections received from a LEO satellite. We present simulation results and two-dimensional fitting of experimental data to compare DDMs. A novel technique is also proposed for reversing experimental DDMs obtained from GPS-R back to spatial energy maps. Preliminary data inversion results have been included to demonstrate the feasibility of this new methodology.