A New, Necessary and Sufficient Vertex Solution for Robust Stability Check of Unstructured Convex Combination Matrix Families

This paper revisits the problem of checking the robust stability of matrix families generated by ‘Unstructured Convex Combinations’ of user supplied or externally supplied Vertex Matrices. A previous solution given by the author for this problem involved complete dependence on the quantitative (eigenvalue information) of a set of special matrices labeled the Kronecker Nonsingularity (KN) matrices. In this solution, the ‘convexity’ property is not explicit and transparent, to the extent that, unfortunately, the accuracy of the solution itself is being questioned and not embraced by the peer community. To erase this unforunate and unwarranted image of this author (in this specific problem) in the minds of the peer community, in this paper, the author treads a new path to find a solution that brings out the convexity property in an explicit and understandable way. In the new solution presented in this paper, we combine the qualitative (sign) as well as quantitative (magnitude) information of these KN matrices and present a vertex solution in which the convexity property of the solution is transparent making it more elegant and accepatble to the peer community, than the previous solution. The new solution clearly underscores the importance of using the sign structure of a matrix in assessing the stability of a matrix. This new solution is made possible by the new insight provided by the qualitative (sign) stability/instability derived from ecological principles. Examples are given which clearly demonstrate effectiveness of the new, convexity based algorithm. It is hoped that this new solution will be embraced by the peer community.

Model Predictive Control-Based Probabilistic Search Method for Autonomous Ground Robot in a Dynamic Environment

Target search using autonomous robots is an important application for both civil and military scenarios. In this paper, a model predictive control (MPC)-based probabilistic search method is presented for a ground robot to localize a stationary target in a dynamic environment. The robot is equipped with a binary sensor for target detection, of which the uncertainties of binary observation are modeled as a Gaussian function. Under the model predictive control framework, the probability map of the target is updated via the recursive Bayesian estimation and the collision avoidance with obstacles is enforced using barrier functions. By approximating the updated probability map using a Gaussian Mixture Model, an analytical form of the objective function in the prediction horizon is derived, which is promising to reduce the computation complexity compared to numerical integration methods. The effectiveness of the proposed method is demonstrated by performing simulations in dynamic scenarios with both static and moving obstacles.

Inertia-Driven Controlled Passive Actuation

A serious problem with using electrical actuators in legged locomotion is the significant energy loss. For this reason, we propose and analyse an alternative means of actuation: Controlled Passive Actuation. Controlled Passive Actuation aims at reducing the energy flow through electric actuators by actuating with a combination of an energy storage element and a Continuously Variable Transmission. In this work, we present a method where we apply a Continuously Variable Transmission with a storage element in the form of a mass to change the state of another mass (“the load”). An abstraction layer is created to abstract the inertia-driven Controlled Passive Actuation to a source of effort, a force actuator. On this abstracted system, feedback control can be applied to achieve control goals such as path tracking. With simulations and experiments, we show that inertia-driven Controlled Passive Actuation can be used to control the state of an (inertial) load. The experimental results show that the performance of the system is affected by the internal dynamics and limited rate of change of the transmission ratio of the Continuously Variable Transmission.

An Adaptive Robust Control for Hard Rock Tunnel Boring Machine Cutterhead Driving System

The cutterhead driving system of tunnel boring machine is one of the key components for rock cutting and excavation. In this paper, a generalized nonlinear time-varying dynamic model is established for the hard rock TBM cutterhead driving system. Parametric uncertainties and nonlinearities and unknown disturbances exist in the dynamic model. An adaptive robust control strategy is proposed to compensate the uncertainties and nonlinearities to achieve precise cutterhead rotation speed control. In order to simulate the comprehensive performances of adaptive robust control controller, three different kinds of external force disturbances are added in this model. Compared to the traditional PID, ARC can effectively handle the different kinds of external force disturbances with sufficient small tracking errors.

Dynamic Modeling of Robotic Fish Caudal Fin With Electrorheological Fluid-Enabled Tunable Stiffness

In this study, we investigate the modeling framework for a robotic fish actuated by a flexible caudal fin, which is filled with electrorheological (ER) fluid and thus enables tunable stiffness. This feature can be used in optimizing the robotic fish speed or maneuverability in different operating regimes. The robotic fish is assumed to be anchored and the flexible tail undergoes undulation activated by a servomotor at the base. Lighthill’s large-amplitude elongated-body theory is used to calculate the hydrodynamic force on the caudal fin, and Hamilton’s principle is used to derive the dynamic equations of motion of the caudal fin. The dynamic equations are then discritized using the finite element method, to obtain an approximate numerical solution. In particular, simulation is conducted to understand the influence of the applied electric field on the stiffness and thrust performance of the caudal fin.

Indoor Mapping and Localization for a Smart Wheelchair Using Measurements of Ambient Magnetic Fields

Freedom of mobility is a crucial aspect of our daily lives. Consequently, engineering solutions for mobility, including smart wheelchairs, are becoming increasingly important for those with disabilities. However, the lack of a reliable solution for indoor localization has affected the pace of research in this direction. GPS signals cannot be measured indoors and environment modifications for wheelchair localization can be expensive and intrusive. This research explores the feasibility of using ambient magnetic fields for indoor localization by exploiting the spatial non-uniformity due to ferromagnetic objects in ordinary working environments. A non-parametric density estimation technique was developed to build magnetic field maps. This approach is compared to an existing regression technique. Two different approximate kinematic models for the wheelchair are presented and implemented in a particle-filtering framework. Finally, the efficacy of these mapping techniques and motion models, including and excluding odometry information, are compared via tracking experiments conducted with a smart wheelchair.

Active Wide-Band Vibration Rejection for Semiconductor Manufacturing Robots

Currently, the semiconductor manufacturing industries over the world are upgrading from processing 300mm wafers to processing 450mm wafers. In order to satisfy the requirements of producing and processing 450mm wafers, vibration control of wafer handling tools has to make new breakthroughs. This paper introduces an active wide-band vibration rejection method with a vibrotactile actuator and applies it to a wafer transfer robot. Compared to conventional methods based on motor control of the robot, active vibration cancellation with a separate actuator does not risk compromising the tracking accuracy of wafer transfer motions. A three-step controller synthesis scheme is developed by analyzing and combining the strengths of several control strategies. Experimental validation shows a vibration reduction of more than 40% in energy and 30% in amplitude.

Hybrid System Based Analytical Approach for Optimal Gear Shifting Schedule Design

In this paper, we present a systematic design for gear shifting using a hybrid system approach. The longitudinal motion of the vehicle is regulated by a PI-controller that determines the required axle torque. The gear scheduling problem is modeled as a hybrid system and an optimization-based gear shifting strategy is introduced, which guarantees that the propulsion requirements are delivered while minimizing fuel consumption. The resulting dynamics is proved to be stable theoretically. In a case study, we compare our strategy with a standard approach used in the industry and demonstrate the advantages of our design for class 8 trucks.

Continuous Structures With Viscoelastic Supports: Tuning of Material Parameters and Support Location

Polymeric smart materials exhibit viscoelastic behavior and their dynamic characteristics are dependent on both frequency and temperature. This allows the tuning of material properties (stiffness and loss factor) to manipulate the vibration behavior for a wide range of engineering applications. In this research, the effects of viscoelastic supports on the vibration of continuous structures such as axially vibrating rods and transversely vibrating beams are investigated. The governing equations of motion for harmonically excited rods with end supports, and the free vibration of beams with intermediate viscoelastic support are developed. The analytical response equation for a harmonically excited rod with viscoelastic ends is obtained. The resulting frequency response equations are then used to design the modification of the stiffness and loss factor of the viscoelastic materials in order to achieve the desired vibration response of the rod. By solving the resulting transcendental eigenvalue problems, the natural frequencies and damping ratios as a function of viscoelastic support parameters are computed for beams. The performance of structures with viscoelastic support is demonstrated with various numerical examples. The formulation and results can be utilized for estimating the optimal material tuning parameters as well as support locations for controlling and manipulating the vibration response of the structures.

Instrumented Walkway for Estimation of the Ankle Impedance in Dorsiflexion-Plantarflexion and Inversion-Eversion During Standing and Walking

This paper describes in detail the fabrication of an instrumented walkway for estimation of the ankle mechanical impedance in both dorsiflexion-plantarflexion (DP) and in inversion-eversion (IE) directions during walking in arbitrary directions and standing. The platform consists of two linear actuators, each capable of generating ±351.3 N peak force that are mechanically coupled to a force plate using Bowden cables. The applied forces cause the force plate to rotate in two degrees of freedom (DOF) and transfer torques to the human ankle to generate DP and IE rotations. The relative rotational motion of the foot with respect to the shin is recorded using a motion capture camera system while the forces applied to the foot are measured with the force plate, from which the torques applied to the ankle are calculated. The analytical methods required for the estimation of the ankle torques, rotations, and impedances are presented. To validate the system, a mockup with known stiffness was used, and it was shown that the developed system was capable of properly estimating the stiffness of the mockup in two DOF with less than 5% error. Also, a preliminary experiment with a human subject in standing position was performed, and the estimated quasi-static impedance of the ankle was estimated at 319 Nm/rad in DP and 119 Nm/rad in IE.