Institute for Systems Research Technical Reports
Permanent URI for this collectionhttp://hdl.handle.net/1903/4376
This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
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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.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 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 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 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 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.