### Browsing by Author "Leonard, Naomi E."

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Item Adaptive Friction Compensation for Bi-Directional Low-Velocity Position Tracking(1992) Leonard, Naomi E.; Krishnaprasad, Perinkulam S.; ISRThis paper presents a comparative investigation of friction- compensating control strategies designed to improve low-velocity position tracking performance in the presence of velocity reversals for servomechanisms. The methods considered include adaptive control and estimation-based control. Additionally, the various controller designs incorporate different friction models ranging from classical friction and Stribeck friction to the less popular Dahl friction model. This investigation of friction models is motivated by the fact that there is little consensus in the literature on how best to model friction for dynamic friction compensation. the control strategies are compared in an extensive test program involving sinusoidal position trajectory tracking experiments on a direct-drive dc motor. We focus attention on comparative experimental results of friction compensation especially with repeated velocity reversals. The results show that the adaptive experiments also yield insight into the appropriateness of the different friction models under the tested operating conditions. In particular, the Dahl model, typically ignored in the literature proves to be significant for the firction-compensating control problem with repeated zero- velocity crossings.Item Averaging and Motion Control of Systems on Lie Groups(1994) Leonard, Naomi E.; Krishnaprasad, P.S.; ISRIn this dissertation, we study motion control problems in the framework of systems on finite-dimentional Lie groups. Nonholonomic motion control problems are challenging because nonlinear controllability theory does not provide an explicit procedure for constructing controls and linearization techniques, typically effective for nonlinear system analysis, fail to be useful. Our approach, distinguished from previous motion control research, is to exploit the Lie group framework since it provides a natural and mathematically rich setting for studying nonholonomic systems. In particular, we use the framework to develop explicit, structured formulas that describe system behavior and from these formulas we derive a systematic say of synthesizing controls to achieve desired motion.As our main tool we derive averaging theory for left-invariant systems on finite-dimensional Lie groups. This theory provides basis- independent formulas which approximate system behavior on the Lie group to arbitrarily high order in given small () amplitude, periodically time-varying control inputs. We interpret the average formulas geometrically and exploit this interpretation to prove a constructive controllability theorem for the average system. The proof of this theorem provides a constructive control synthesis methodology for drift-free systems which we use to derive algorithms which synthesize sinusoidal open-loop controls. We apply the algorithms to several under-actuated mechanical control problems including problems in spacecraft attitude control, unicycle motion control and autonomous underwater vehicle control. We illustrate the effectiveness of the synthesized controls by simulation and experimentation. We show further that as a consequence of the geometry inherited from the average formulas, our algorithms can be used to produce motion controls that adapt to changes in control authority such as loss of an actuator.

We also apply our theory to synthesize controls for bilinear control systems on Rn possibly with drift. Our approach is to control the system state by controlling the state transition matrix which evolves on a matrix Lie group. We design and demonstrate a controller for an example system with drift, a simple switched electrical network.

Item Averaging and Motion Control On Lie Groups(1993) Leonard, Naomi E.; Krishnaprasad, Perinkulam S.; ISRThe deeper investigation of problems of feedback stabilization and constructive controllability has drawn increased attention to the question of structuring control systems. Thus, for instance, it is interesting to know how to combine periodic open loop controls with intermittent feedback corrections to achieve prescribed behavior in robotic motion planning systems. As a first step towards understanding this type of question, it would be useful to obtain some insight into the average behavior of a periodically forced system. In the present paper we are primarily interested in periodic forcing of left-invariant systems on Lie groups such as would arise in spacecraft attitude control. We prove averaging theorems applicable to systems evolving on general matrix Lie groups with particular focus on the attitude control problem. The results of this paper also yield useful formulae for motion planning of a variety of other systems such as an underwater vehicle which can be modeled as a control system evolving on the Lie group SE (3).Item Comparative Study of Friction-Compensating Control Strategies for Servomechanisms(1991) Leonard, Naomi E.; Krishnaprasad, Perinkulam S.; ISRThis paper describes a comparative investigation of friction- compensating control strategies designed to improve low-velocity position tracking performance for servomechanisms. Several control methods are considered including adaptive control and estimation-based control. Additionally, the various controller designs incorporate different friction models ranging from classical friction and Stribeck friction to the less popular Dahl friction model. This investigation of friction models is motivated by the fact that there is little consensus in the literature on how best to model friction for dynamic friction compensation. The control strategies are compared in an extensive test program involving position tracking experiments on a direct- drive de motor. This effort addresses the current lack of comparative experimental results on friction compensation. The results show that the adaptive and estimation-based controllers outperform more traditional linear controllers. The experiments also yield insight into the appropriateness of the different friction models under the tested operating conditions. In particular, the Dahl model is observed to provide a reliable representation of friction behavior near zero velocity.Item Control Synthesis and Adaptation for an Underactuated Autonomous Underwater Vehicle(1994) Leonard, Naomi E.; ISRThe motion of an autonomous underwater vehicle (AUV) is controllable even with reduced control authority such as in the event of an actuator failure. In this paper we describe a technique for synthesizing controls for underactuated AUV's and show how to use this technique to provide adaptation to changes in control authority. Our frame-work is a motion control system architecture which includes both feedforward control as well as feedback control. We confine ourselves to kinematic models and exploit model nonlinearities to synthesize controls. Our results are illustrated for two examples, the first a yaw maneuver of an AUV using only roll and pitch actuation, and the second a ﲰarking maneuver for an AUV. Experimental results for the yaw maneuver example are described.Item High-Order Averaging on Lie Groups and Control of an Autonomous Underwater Vehicle(1993) Leonard, Naomi E.; Krishnaprasad, Perinkulam S.; ISRIn this paper we extend our earlier results on the use of periodic forcing and averaging to solve the constructive controllability problem for drift-free left-invariant systems on Lie groups with fewer controls than state variables. In particular, we prove a third-order averaging theorem applicable to systems evolving on general matrix Lie groups and show how to use the resulting approximations to construct open loop controls for complete controllability of systems that require up to depth- two Lie brackets to satisfy the Lie algebra controllability rank condition. The motion control problem for an autonomous underwater vehicle is modeled as a drift-free left-invariant system on the matrix Lie group SE (3). In the general case, when only one translational and two angular control inputs are available, this system satisfies the controllability rank condition using depth-two Lie brackets. We use the third-order averaging result and its geometric interpretation to construct open loop controls to arbitrarily translate and orient an autonomous underwater vehicle.Item Motion Control of Drift-Free, Left-Invariant Systems on Lie Groups(1994) Leonard, Naomi E.; Krishnaprasad, Perinkulam S.; ISRIn this paper we address the constructive controllability problem for drift free, left-invariant systems on finite-dimensional Lie groups with fewer controls than state dimension. We consider small (e) amplitude, low-frequency, periodically time-varying controls and derive average solutions for system behavior. We show how the pth-order average formula can be used to construct open-loop controls for point-to-point maneuvering of systems that require up to ( p - 1) iterations of Lie brackets to satisfy the Lie algebra controllability rank condition. In the cases p =2,3, we give algorithms for constructing these controls as a function of structure constants that define the control authority, i.e., the actuator capability, of the system. The algorithms are based on a geometric interpretation of the average formulas and produce sinusoidal controls that solve the constructive controllability problem with O (ep) accuracy in general (exactly if the Lie algebra is nipotent). The methodology is applicable to a variety of control problems and is illustrated for the motion control problem of an autonomous underwater vehicle with as few as three control inputs.Item Motion Control of Drift-Free, Left-Invariant Systems on Lie Groups, Part II: A General Constructive Control Algorithm(1994) Leonard, Naomi E.; Krishnaprasad, Perinkulam S.; ISRIn this paper we present a general algorithm for constructing open-loop controls to solve the complete constructive controllability problem for drift-free invariant systems on Lie groups that satisfy the Lie algebra controllability rank condition with up to ( p - 1) iterations of Lie brackets, p = 1,2,3. Specifically, given only the structure constants of the given system, an initial condition Xi, a final condition Xf and a final time tf, the algorithm specifies open-loop, small (e) amplitude sinusoidal controls such that the system starting from Xi, reaches Xf at t = tf, with O (ep) accuracy. The algorithm is based on the formulas and geometric interpretation of the average approximations to the solution given in Part I to this paper. To illustrate the effectiveness of the algorithms, we apply it to three problems: the spacecraft attitude control problem with only two controls available, the unicycle motion planning problem and the autonomous underwater vehicle motion control problem with only three controls available.