Problems of control of a hopping apparatus
01 Apr 1998-Journal of The Franklin Institute-engineering and Applied Mathematics (Pergamon)-Vol. 335, Iss: 3, pp 579-593
TL;DR: It is shown, that a similar approach may be applied to the synthesis of a control system of hopping apparatus which would be supplied by a telescopic leg as well as by two segment legs.
Abstract: A problem of a control of the hopping apparatus model is considered. Relations determined by a program mode of movement are presented. The problem of synthesis of a stabilization system is reduced to a periodic linear quadratic problem. Flexibility of such a procedure of synthesis is noted. In particular, it is shown, that a similar approach may be applied to the synthesis of a control system of hopping apparatus which would be supplied by a telescopic leg as well as by two segment legs. Examples of synthesis of a control system of hopping apparatus are considered. The results of the simulation of the apparatus start process are presented.
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TL;DR: In this article, the basic problems that arise in designing systems of control of such facilities are considered, and the equations of model motion are derived, a specified trajectory is parametrized, and a stabilization algorithm is synthesized (including linear, nonlinear, adaptive, and robust controllers).
Abstract: Problems of control of robots (manipulators and wheeled transport robots) that are considered as controllable systems of rigid bodies with holonomic and nonholonomic constraints are reviewed. The basic problems that arise in designing systems of control of such facilities are considered. Namely, the equations of model motion are derived, a specified trajectory is parametrized, and a stabilization algorithm is synthesized (including linear, nonlinear, adaptive, and robust controllers). Some model examples are given to illustrate the efficiency of the algorithms considered.
29 citations
TL;DR: In this article, the static output-feedback control problem for a periodic discrete-time system is solved using standard MATLAB routines, and the efficiency of the approach proposed to design optimal static outputfeedback controllers is demonstrated by examples.
Abstract: Relations are derived that allow standard MATLAB routines to be used to solve the static output-feedback control problem for a periodic discrete-time system. The efficiency of the approach proposed to design optimal static output-feedback controllers is demonstrated by examples
22 citations
TL;DR: A review of the results obtained at the S. P. Timoshenko Institute of Mechanics in synthesis of robust controllers for linear stationary and periodic systems with uncertainty is given in this article.
Abstract: A review is made of the results obtained at the S. P. Timoshenko Institute of Mechanics in synthesis of robust controllers for linear stationary and periodic systems with uncertainty. The emphasis is on algorithms for construction of the Lyapunov function by solving the matrix Riccati equation and linear matrix inequalities. To illustrate the algorithms proposed, stabilization systems with uncertainty are synthesized for an A4D aircraft and a hopping vehicle. The numerical implementation of the algorithms involves no difficulties, since they are oriented toward standard MATLAB routines
20 citations
Journal Article•
TL;DR: In this article, the problem of designing a regulator, optimal by a quadratic performance criterion, on an infinite time interval is examined for a linear periodic system, where the control plant's motion is described by a system of linear periodic finite-difference equations.
Abstract: The problem of designing a regulator, optimal by a quadratic performance criterion, on an infinite time interval is examined for a linear periodic system. It is assumed that the control plant's motion is described by a system of linear periodic finite-difference equations. Controllable plants whose motion is described by differential and by finite-difference equations on different parts of the period are analyzed as well. The optimal regulator design problem is reduced to the determination of a periodic solution of an appropriate Riccati equation. An algorithm for constructing such a solution is derived. It is noted that this result can be used in periodic optimization problems /1/ and in the design of a stabilization system for a pacing apparatus.
18 citations
TL;DR: In this paper, the authors considered a legged machine walking with a statically unstable gait as a controlled system of solids with variable constraints and demonstrated that if the dynamic processes due to constraint variation are taken into account in the synthesis of a control system, then it is possible to substantially increase the performances of control algorithms and to reduce loads on actuating mechanisms.
Abstract: Studies that consider a legged machine walking with a statically unstable gait as a controlled system of solids with variable constraints are generalized. The motion of such a system is described by both differential and difference equations. The method of optimization of periodic systems is used to synthesize control algorithms for such systems. It is demonstrated that if the dynamic processes due to constraint variation are taken into account in the synthesis of a control system, then it is possible to substantially increase the performances of control algorithms and to reduce loads on actuating mechanisms.
17 citations
References
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TL;DR: In this paper, the authors generalize the approach to a 3D one-legged machine that runs and balances on an open floor without physical support, and decompose control of the machine into three separate parts: one part that controls forward running velocity, another part controlling attitude of the body, and a third part controlling hopping height.
Abstract: In order to explore the balance in legged locomotion, we are studying systems that hop and run on one springy leg. Pre vious work has shown that relatively simple algorithms can achieve balance on one leg for the special case of a system that is constrained mechanically to operate in a plane (Rai bert, in press; Raibert and Brown, in press). Here we general ize the approach to a three-dimensional (3D) one-legged machine that runs and balances on an open floor without physical support. We decompose control of the machine into three separate parts: one part that controls forward running velocity, one part that controls attitude of the body, and a third part that controls hopping height. Experiments with a physical 3D one-legged hopping machine showed that this control scheme, while simple to implement, is powerful enough to permit hopping in place, running at a desired rate, and travel along a simple path. These algorithms that control locomotion in 3D are direct generalizations of those in 2D, with surpris...
382 citations
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TL;DR: In this paper, the authors explore the notion that the control of dynamically stable legged systems that locomote in 3-space can be decomposed into a planar part and an extra-planar part.
Abstract: This paper explores the notion that the control of dynamically stable legged systems that locomote in 3-space can be decomposed into a planar part and an extra-planar part. The planar part generates the large leg and body motions that raise and lower the legs to achieve stepping, that propel the system forward, and that maintain balance. The planar part of the control system deals only with 2D dynamics. The extra-planar part of the locomotion control system suppresses motion in those degrees of freedom that would cause deviation from the plane of motion. These degrees of freedom include roll of the body, yaw of the body, and translation perpendicular to the intended direction of travel.
149 citations
01 Nov 1983
TL;DR: A hybrid locomotion vehicle for use in remote maintenance of a nuclear power plant is proposed, and laboratory tests with a prototype vehicle demonstrate successful locomotion.
Abstract: A hybrid locomotion vehicle for use in remote maintenance of a nuclear power plant is proposed. The vehicle has five locomotion devices, each consisting of a supporting leg and a driving wheel. Each device has three degrees of freedom: leg lifting, wheel revolution, and wheel steering. These degrees of freedom and the inclusion of touch sensors for obstacle detection enable flexible locomotion such as stepping over rises and going up and down stairs in the plant. Two slope sensors set at orthogonal directions maintain vehicle posture through vertical leg motion. The control system, based on a microcomputer, supervises all of these motions. Laboratory tests with a prototype vehicle demonstrate successful locomotion.
32 citations
TL;DR: In this paper, a comprehensive set of formulae for the periodic solution of Riccati equations is obtained from some basic relations in estimation theory, and a set of numerically stable algorithms, square root formulations are introduced.
Abstract: From some basic relations in estimation theory, a comprehensive set of formulae are obtained for the periodic solution of Riccati equations. To obtain numerically stable algorithms, square root formulations are introduced. Both the discrete-time and continuous-time cases are considered. Closed-loop properties for periodic systems are also investigated. The results are applied to multirate measurement sampling. The control of a continuous stirred tank reactor serves as an illustrative example. The temperature measurements are then complemented by concentration analysis available at a slower rate than the basic sampling and control rate. The results give some guidelines about the benefits of multirate sampling.
29 citations
TL;DR: In this paper, the problem of designing a regulator, optimal by a quadratic performance criterion, on an infinite time interval is examined for a linear periodic system, where the control plant's motion is described by a system of linear periodic finite-difference equations.
19 citations