Optimal control of dual-mass system motion in a medium with a piecewise linear resistance

Linear motion of a mechanical system consisting of two bodies??a container and an inner body??is considered. The container is located in an external medium with resistance, and the inner body moves inside the container without the interaction with the external medium. Under certain conditions, the periodic motion of the inner body causes the system as a whole to move. The external medium acts on the container with a force that is proportional to its velocity with a resistance coefficient depending on the motion direction. Only the motions of the inner body with continuous relative velocity are studied. The optimal periodic motion of the inner body corresponding to the greatest period-averaged velocity of the system as a whole is constructed and analyzed.     

Control of a two-degree-of-freedom lightweight flexible arm with friction in the joints

This article describes the design and control of a two-joint, two-link flexible arm. This flexible arm was built with very light links, has most of its mass concentrated at the tip and uses a special mechanical configuration to approximately decouple radial tip motions from angular tip motions. The lightweight design and decoupling maximize the efficiency of power transmitted to the load. An important problem when controlling lightweight flexible arms is the large Coulomb friction of the motors. A two-nested-loop multivariable controller is used to control the lightweight flexible arm with friction in the joints. The inner loop controls the position of the motors while the outer loop controls the tip position. The resolved acceleration method is generalized to control this flexible arm. The compliance matrix is used to model the oscillations of the structure and is included in the decoupling/linearizing term of this controller. Experimental results are presented. © 1995 John Wiley & Sons, Inc.     

Capsule-type vibration-driven robot with an electromagnetic actuator and an opposing spring: Dynamics and control of motion

A model of a mobile capsule robot that consists of the housing and internal body is considered. The internal body can move relative to the housing along a straight line. The internal body is attached to the housing by a spring. The system motion is excited by a force that acts between the housing and the internal body. The force changes in a pulse-width periodic mode. The robot’s motion along a straight line on a rough horizontal plane is investigated. It is assumed that the dry Coulomb friction acts between the housing and the plane. The dependence of the average steady state robot velocity on excitation parameters is analyzed. It is established that it is possible to control the magnitude and direction of the robot motion by changing the period and the duty cycle of the pulse-width excitation signal. The effect of the variation in the direction of the robot motion due to changing the excitation period is observed. This effect is associated with the phenomenon of resonance.     

Modeling of controlled motions of an elastic rod by the method of integro-differential relations

The possibilities of controlling elastic systems with distributed parameters and constructing a solution corresponding to some given quality criteria are studied. The regular integro-differential approach to the construction of solutions for a wide class of boundary-value problems is developed and a quality criterion for the obtained solution is proposed. The case of the relay control, which induces substantial elastic oscillations in the system and results in significant computational difficulties when applying classic approaches, is considered for plane motions of the homogeneous straight rod. The problem parameters are chosen so that the period of the lower mode of oscillation is comparable with the interval on which the motions are studied. The results obtained by the variable separation method and the integro-differential approach are analyzed and compared.     

Decentralized navigation method for a robotic swarm with nonhomogeneous abilities

This paper addresses the navigation of a robotic swarm with nonhomogeneous abilities, including sensing range, maximum velocity, and acceleration. With this method, the robotic swarm moves in a two-dimensional plane, and each follower distributedly constructs and maintains local directed connection using only local information to achieve maintenance of global connectivity. We also ensure the swarm is stable when the leader moves at a constant velocity. Validity and effectiveness of the proposed control strategy are shown by theoretical analysis, experiments with real robots, and numerical simulations.     

LANDING AN UNMANNED AIR VEHICLE: VISION BASED MOTION ESTIMATION AND NONLINEAR CONTROL

In this paper, we use computer vision as a feedback sensor in a control loop for landing an unmanned air vehicle (UAV) on a landing pad. The vision problem we address here is then a special case of the classic ego-motion estimation problem since all feature points lie on a planar surface (the landing pad). We study together the discrete and differential versions of the ego-motion estimation, in order to obtain both position and velocity of the UAV relative to the landing pad. After briefly reviewing existing algorithm for the discrete case, we present, in a unified geometric framework, a new estimation scheme for solving the differential case. We further show how the obtained algorithms enable the vision sensor to be placed in the feedback loop as a state observer for landing control. These algorithms are linear, numerically robust, and computationally inexpensive hence suitable for real-time implementation. We present a thorough performance evaluation of the motion estimation algorithms under varying levels of image measurement noise, altitudes of the camera above the landing pad, and different camera motions relative to the landing pad. A landing controller is then designed for a full dynamic model of the UAV. Using geometric nonlinear control theory, the dynamics of the UAV are decoupled into an inner system and outer system. The proposed control scheme is then based on the differential flatness of the outer system. For the overall closed-loop system, conditions are provided under which exponential stability can be guaranteed. In the closed-loop system, the controller is tightly coupled with the vision based state estimation and the only auxiliary sensor are accelerometers for measuring acceleration of the UAV. Finally, we show through simulation results that the designed vision-in-the-loop controller generates stable landing maneuvers even for large levels of image measurement noise. Experiments on a real UAV will be presented in future work.     

Distributed optimal consensus of multiple double integrators under bounded velocity and acceleration

This paper studies a distributed optimal consensus problem for multiple double integrators under bounded velocity and acceleration. Assigned with an individual and private convex cost which is dependent on the position, each agent needs to achieve consensus at the optimum of the aggregate cost under bounded velocity and acceleration. Based on relative positions and velocities to neighbor agents, we design a distributed control law by including the integration feedback of position and velocity errors. By employing quadratic Lyapunov functions, we solve the optimal consensus problem of double-integrators when the fixed topology is strongly connected and weight-balanced. Furthermore, if an initial estimate of the optimum can be known, then control gains can be properly selected to achieve an exponentially fast convergence under bounded velocity and acceleration. The result still holds when the relative velocity is not available, and we also discuss an extension for heterogeneous Euler-Lagrange systems by inverse dynamics control. A numeric example is provided to illustrate the result.     

Disc-type Underwater Glider Modeling and Analysis for Omnidirectional and Steering Motion Characteristics

A disc-type underwater glider (DTUG) has a highly symmetrical full-wing shape that allows it to move omnidirectionally and have the same hydrodynamic characteristics in all directions in the horizontal plane. These characteristics make the viscous hydrodynamic coefficients measured by conventional methods unsuitable for simulating the omnidirectional and steering motions of the DTUG. To further reveal the omnidirectional and steering motion characteristics of the DTUG, this paper proposes a new theoretical method for calculating the DTUG motion control equations in the velocity frame rather than the body frame. Based on the structural characteristics of the DTUG, the motion control equations are derived and then solved using the fourth-order Runge-Kutta method. The omnidirectional and steering motions of the DTUG are simulated in the velocity frame and compared with the results calculated in the body frame. The results show that the viscous hydrodynamic coefficients obtained by conventional methods are not suitable for analyzing the omnidirectional motion of the DTUG, and the method of calculating the motion control equations in the body frame has limitations in studying the steering motion. The new method proposed in this paper solves these limitations well and can more accurately reveal the motion characteristics of the DTUG without recalculating the hydrodynamic coefficients. The results also show that the DTUG can change the heading angle more easily than a torpedo-type underwater glider (TTUG), and the steering radius is much smaller, which means that the DTUG has greater flexibility in a small body of water. The DTUG can remain stable when the control variables are within the control range and the new method is adopted.

     

Estimating the Domain of Admissible Parameters of a Control System of a Vibratory Robot

We consider the rectilinear motion of a vibratory robot on a plane; the robot is presented by a rigid body and a pendulum inside it. The motion is carried out in the gravity field; the force of dry friction acts between the body and the plane. The robot is controlled by choosing the angular acceleration of the pendulum. Two modes of the robot’s control that correspond to various constraints on the choice of the control are investigated. Each of the studied control laws ensures a periodic displacement of the robot; here, the robot moves only in one direction (the motion is irreversible). We discuss the problem of finding the boundaries of the dry friction parameter and the control parameter; we find the boundaries with which the proposed control modes are feasible.     

Moving observer trajectory control by angular measurements in tracking problem

An optimal path synthesis problem for a moving observer that performs angular observations over a target moving uniformly along a straight line on a plane is solved. It is supposed that elevation and azimuth angles can be observed when the observer moves in space and only the azimuth angle can be observed when the observer moves on a plane. Observer’s trajectories are obtained with the help of Pontryagin’smaximum principle as numerical solutions of an optimal control problem. As a performance criterion the trace of covariance matrix of the target motion elements estimate is used. A possibility of solving the problem in real time on board for unmanned aerial vehicle is investigated. A comparison with the scenario of two unmanned aerial vehicles using is given.     

Convergence properties of a class of pointwise control strategies

In recent years, a number of nonlinear power system stabilization problems have been approached using techniques termed "velocity-matching" or "optimal-aiming" strategies. At each instant of time, these strategies require that the velocity of the system be adjusted through instantaneous control action such that the state moves in some "preferred" direction subject to constraints imposed by an admissible input set, the choice of a preferred direction producing the different control strategies. In this paper, we show that for any such control strategy σ and independent of preferred direction choices, there will be a controllable linear time-invariant system which is rendered unstable under σ, even if arbitrarily large inputs and nonlinear dependence of σ on its arguments is permitted.     

Analysis of factors related to vertical vibration of continuous alternate wheels for omnidirectional mobile robots

Omnidirectional mobile robots (OMRs) are capable of arbitrary motions in arbitrary directions without changing the direction of wheels since they perform 3-DOF (degree of freedoms) motions on a plane. Various omnidirectional wheels including the continuous alternate wheel (CAW) with passive rollers for OMRs have been researched. The CAW has been developed for the purpose of minimizing vibration. The CAW has alternating inner and outer rollers around the wheel which makes nearly continuous contact with the ground. The ideal CAW reduce vibration for certain; however, the real CAW fail to do so due to various errors. In this regard, more research is needed to bring vibration under acceptable tolerance. In this paper, vertical vibration characteristics of the real CAW with tolerance are researched. Simulation models of CAWs are implemented using flexible body dynamics of Recurdyn. To verify vibration characteristics of the model, simulation results are compared with experimental results from the improved CAW with five rollers set (CAW5). Vertical vibration is affected by various factors: geometry errors, the gap, the thickness of flexible body, the angular velocity, the alignment angle, the load and the elasticity of flexible body, etc. To efficiently analyze the effects of various factors, dynamic simulations are conducted using Taguchi method. As a result, it is found that the main factors which affect vibration are the angular velocity and the alignment angle followed by the geometry errors, the load, the elasticity of flexible body, the thickness of flexible body and the gap. This process can be applied to the analysis of the other omnidirectional wheels with passive rollers.     

Dynamics of controlled motion of vibration-driven systems

The rectilinear motion on a horizontal rough plane of a vibration-driven system consisting of a carrying body, which interacts with the plane directly, and of internal masses that perform harmonic oscillations relative to the carrying body is considered. The vertical and horizontal oscillations of the internal masses have the same frequency, but are shifted in phase. It is shown that by controlling the phase shift of the horizontal and vertical oscillations and their frequencies, it is possible to change the direction and magnitude of the average velocity of the steady motion of the carrying body. A similar system may provide a model of a vibration-driven robot that does not require special limbs (wheels, legs, or chain tracks)     

Control and optimization in a collision avoidance problem in oscillating systems

The development of control algorithms, including optimal control ones, in the collision avoidance problem for a system of two pendulums with a controllable common base is considered. Two problems are solved. The first one searches for the law of variation of the bounded control force that makes the system move from its initial state of rest to the given final state of rest during a finite time and ensures the pendulums do not collide in the process of oscillatory motions. The second problem searches for the performance-optimal law of variation of acceleration of the base and the bounded force that generates the acceleration. The algorithms for constructing the sought controls that use Kalman controllability conditions and Pontryagin’s maximum principle method are presented. The dynamics of the system involved is simulated for the constructed control laws. The numerical results of both problems are compared to find that implementation of the developed performance-optimal control algorithm can help significantly decrease the releasing time of the pendulums while preventing a possible collision.     

An insectomorphic robot climbing over a freely rolling ball

An algorithm for the control of an insectomorphic robot climbing over a ball that rolls freely on a horizontal plane is developed and tested using computer simulation. The proposed motion involves three maneuvers. First, the robot climbs the ball at rest from the horizontal surface. At the end of this maneuver, the ball gains an angular velocity due to errors in the execution of the programmed motion. The further motion of the robot is designed so as to reduce the velocity gained in the course of climbing to an acceptable level. The motion is completed by the maneuver of getting down to the supporting horizontal plane from the almost motionless ball. The robot motion is implemented using the Coulomb friction without any special devices. The asymptotic stability of the programmed motion of the system as a whole is ensured by a PD controller that implements the step cycles of the leg motions and the planned motion of the body. Results of 3D computer simulation of the robot motion are discussed. The model of the mechanical robot-ball system is formed using the Universal Mechanism program package; this model is described by an automatically derived system of differential equations that take into account the dynamics of all solid elements.     

Gait motion for naturally curving variously shaped corners

Modeling the curving motion of humans in actual environment is rarely done because of the complexity and variability of the turning motion. In this study, various gait motions, including straight, round corner, and circular walks, were recorded and analyzed using factor analysis. As a result, we successfully extracted several factors that represent turning motions, such as long stride motion, turning motion led by the inner leg, and turning motion led by the outer leg. In particular, we found that the natural curving motion, which is a motion that results when turning around a round corner, is widely and continuously distributed on the factor space. Although several typical stepping strategies were reported by related studies, we found that the stepping motion changes between straight and turning gaits in the factor space during natural curving motions. Thus, the classification of curving motion into several typical distinct stepping patterns is probably insufficient to understand the natural curving motion. Furthermore, natural curving motions that comprise circular curving motions that were believed to represent typical curving motions was not validated. On the other hand, this result also suggests the possibility of generating curving motions for a physical assistant robot by combining straight gait and circler curving motion.     

Analytical Solution of the Minimum Time Slew Maneuver Problem for an Axially Symmetric Spacecraft in the Class of Conical Motions

The conventional problem of the time-optimal slew of a spacecraft considered as a solid body with a single symmetry axis subject to arbitrary boundary conditions for the attitude and angular velocity is considered in the quaternion statement. By making certain changes of variables, the original dynamic Euler equations are simplified, and the problem turns into the optimal slew problem for a solid body with a spherical distribution of mass containing one additional scalar differential equation. For this problem, a new analytical solution in the class of conical motions is found; in this solution, the initial and terminal attitudes of the space vehicle belong to the same cone realized under a bounded control. A modification of the optimal slew problem in the class of generalized conical motions is made that makes it possible to obtain its analytical solution under arbitrary boundary conditions for the attitude and angular velocity of the spacecraft. A numerical example of a spacecraft’s conical motion and examples demonstrating the proximity of the solutions of the conventional and modified optimal slew problems of an axially symmetric spacecraft are discussed.     

Optimal shock isolation of a two-component viscoelastic object

A limiting performance of shock isolation is studied for an object modeled by two rigid bodies connected by a viscoelastic element with a linear characteristic. The object is attached to a movable base by means of a shock isolator, which is regarded as a device that produces a control force between the base and the object. The base and the object move along the same straight line. The base is subject to an external shock excitation that is characterized by the time history of the acceleration of the base. A control law is defined for the shock isolator to minimize the maximum magnitude of the displacement of the object relative to the base, provided that the force of interaction between the components of the object does not exceed a prescribed value. An algorithm for constructing the exact solution of the problem under certain assumptions is presented. A technique for constructing an approximate solution for an object having high stiffness is described. The optimal control is shown to have impulse components. Examples are given. The two-component model considered in the paper is known to have been utilized to describe the mechanical response of a human body to a shock load along the spine or from thorax to back. Therefore, the problem under consideration can be regarded as a benchmark optimal control problem for a system that protects from injuries cased by shock loads. Solution of such problems is highly topical for development of safety systems for vehicles.     

Analytical solution of the optimal slew problem for an axisymmetric spacecraft in the class of conical motions

The traditional problem is discussed of an optimal spacecraft slew in terms of minimum energy costs. The spacecraft is considered as a rigid body with one symmetry axis under arbitrary boundary conditions for the angular position and angular velocity of the spacecraft in the quaternion formulation. Using substitutions of variables, the original problem is simplified (in terms of dynamic Euler equations) to the optimal slew problem for a rigid body with a spherical mass distribution. The simplified problem contains one additional scalar differential equation. A new analytical solution is presented for this problem in the class of conical motions, leading to constraints on the initial and final values of the angular velocity vector. In addition, the optimal slew problem is modified in the class of conical motions to derive an analytical solution under arbitrary boundary conditions for the angular position and angular velocity of the spacecraft. A numerical example is given for the conical motion of the spacecraft, as well as examples showing the closeness of the solutions of the traditional and modified optimal slew problems for an axisymmetric spacecraft.     

Three-axis pneumatic tactile display with integrated capacitive sensors for feedback control

In this paper, we propose a three-axis pneumatic tactile display that is precisely controlled by using integrated capacitive displacement sensors. The proposed tactile display consists of a core body with a 3 × 3 balloon array on its top surface, four lateral balloons made of latex rubber, and inner and outer frames that include capacitive displacement sensors based on a flexible printed circuit board. The 3 × 3 balloon array on the core body is designed to apply normal haptic stimulation to a human fingertip. In addition, the lateral motions of the core body and each frame produce haptic stimulation in a tangential direction. Precise control of lateral motion was achieved by feedback control using the capacitive displacement sensors. The size of the fabricated tactile display was 26 × 26 × 18 mm³. We experimentally performed manipulation of the proposed device with a custom control system, thereby demonstrating accurate control of displacement.