Planar Dynamic Model Research Articles

Stabilization and Control of a Spherical Robot on an Inclined Plane

In this study, the dynamics and control aspects of a spherical robot rolling without slipping on an inclined plane are investigated. The planar dynamic model of the robot rolling ahead on an inclined plane is derived using Lagrangian dynamics. Based on the equivalent control method and Lyapunov stability theorem, a decoupled sliding mode control approach is presented for stable control of the planar motion. Utilizing the constrained Lagrange method the three-dimensional dynamics of the robot rolling on an inclined plane are deduced. Based on input-output feedback linearization, we develop a trajectory tracking control algorithm for the three-dimensional motion of the robot. The validity of the proposed controllers is demonstrated through numerical simulations.

Alternative trajectory-tracking control approach for marine surface vessels with experimental verification

SUMMARYExperiments with a nonlinear trajectory-tracking controller for marine unmanned surface vessels are reported. The tracking controller is designed using a nonlinear robust model-based sliding mode approach. The marine vehicles can track arbitrary desired trajectories that are defined in Cartesian coordinate as continuous functions of time. The planar dynamic model used for the controller design consists of 3 degrees of freedom (DOFs) of surge, sway, and yaw. The vessel only has two actuators, so the vessel is underactuated. Therefore, only two outputs, which are functions of the 3-DOF, can be controlled. The Cartesian position of a control point on the vessel is defined as the output. The orientation dynamics is not directly controlled. It has been previously shown that the orientation dynamics, as the internal dynamics of this underactuated system, is stable. The result of field experiments show the effectiveness of tracking control laws in the presence of parameter uncertainty and disturbance. The experiments were performed in a large outdoor pond using a small test boat. This paper reports the first theoretical development and experimental verification of the proposed model-based nonlinear trajectory-tracking controller.

Landing, perching and taking off from vertical surfaces

An approach is presented whereby small, unmanned aircraft can land on walls. The approach is demonstrated with a plane that uses an ultrasonic sensor to initiate a pitch-up maneuver as it flies toward a wall. The plane contacts the wall with spines that engage asperities on the surface. A non-linear suspension absorbs the kinetic energy while keeping the spines attached. A planar dynamic model is used to evaluate pitch-up maneuvers and determine suspension parameters that satisfy constraints on the contact forces for a range of flight velocities. Simulations conducted using the model are compared with data obtained using high-speed video and a force plate embedded in a wall.

Free boundary effects on stability of two phase planar fluid motion in annulus. Part I: Migration of the stable mode

We study the linearized stability of a planar dynamical model describing two-phase perfect fluid circulating around a circle with a sufficiently large radius within a central gravitational field. The model is associated with the spatial and temporal structure of the zonally averaged global-scale atmospheric longitudinal circulation around the Earth. Two cases are studied separately; in the first one, the simulations were carried out using the rigid lid approximation at the upper boundary of the outer atmospheric layer. In the second one, the free boundary nonlinear conditions (kinematic and dynamic) were assumed on the outer atmospheric layer. For the both cases, a certain family of steady, explicit solutions which have circular streamlines was considered. The governing equations were linearized at these solutions to find the typical wave numbers of the interfacial wave perturbation to the basic state at which the destabilizing effect of shear, which overcomes the stabilizing effect of stratification, occurs. It is shown that for the both cases, the model always have the same two potentially unstable wave modes while there always exist two wave modes which are stable for any wavelengths. The behavior of the stable and unstable modes were compared for the both cases to investigate the effects of the free boundary on the mixing process at the interface.

Discrete dynamical modeling and analysis of the R– S flip-flop circuit

A simple discrete planar dynamical model for the ideal (logical) R– S flip-flop circuit is developed with an eye toward mimicking the dynamical behavior observed for actual physical realizations of this circuit. It is shown that the model exhibits most of the qualitative features ascribed to the R– S flip-flop circuit, such as an intrinsic instability associated with unit set and reset inputs, manifested in a chaotic sequence of output states that tend to oscillate among all possible output states, and the existence of periodic orbits of arbitrarily high period that depend on the various intrinsic system parameters. The investigation involves a combination of analytical methods from the modern theory of discrete dynamical systems, and numerical simulations that illustrate the dazzling array of dynamics that can be generated by the model. Validation of the discrete model is accomplished by comparison with certain Poincaré map like representations of the dynamics corresponding to three-dimensional differential equation models of electrical circuits that produce R– S flip-flop behavior.

The reliability and validity of a lift simulator and its functional equivalence with free weight lifting tasks

The combination of Workers' Compensation legal claims and the enactment of the Americans with Disabilities Act (1990) has created a need for more objective and realistic trunk muscle testing. The LIDOLift (Loredan, Inc.) is a computerized dynamometer which has the capabilities to test multijoint coordinated lifting tasks in isometric, isokinetic, and isoinertial modes of operation. The calibration of the electromechanical sensors produced R/sup 2/ values greater than 0.999. In the validation of the isokinetic mode, the normalized rms error from the set velocity was less than 1% at higher set velocities, after the accelerative portion of the lift. In the technical validation of the isoinertial mode, the measured force was significantly different than the predicted force based on an isoinertial model, Consequently, the simulated mass was found to be larger than the intended mass. However, the relative difference decreased as the intended mass increased. Next, an experimental protocol was utilized to determine the validity of the isoinertial mode in the work and joint spaces. A sagittal planar dynamic biomechanical model was used to provide the basis of comparison between lifts performed with the LIDOLift and with free weights. Analyses of covariance showed statistical differences for most work and joint space variables. However, the relative difference between the two for some variables may be functionally negligible. Important guidelines for clinical protocols using the isokinetic and isoinertial modes of this simulator are delineated. Areas of technological improvement have been identified to close the gap between the simulated isoinertial condition and the free weight lifting task. >

A gas-phase electron-diffraction study of trvinylborane

Trivinylborane has been studied by standard electron-diffraction techniques. The best agreement with experiment is obtained with a planar dynamic model in which steric strain within the molecule is reduced by distortion of the vinyl groups, and shrinkages simulate considerable torsional motion about the B-C bonds. The following parameters ( r a basis) and e.s.d. were obtained: C-H = 1.092± 0.003 Å; C-C = 1.370 ± 0.006 Å; B-C = 1.558± 0.003 Å; ∠BCH = 116.5 ± 0.9 °; ∠BCC = 122.4 ± 0.9°; ∠CCH ( trans to B) = 124.0 ± 1.6°; ∠CCH ( cis to B) = 132.2 ± 2.3°. A static non-planar model has also been considered. The probable planarity of the molecule and the length of the C C bond are interpreted as evidence for π-electron delocalisation from carbon to boron.