On Steady-State Solutions of a Wave Equation by Solving a Delay Differential Equation With an Incremental Harmonic Balance Method

For wave propagation in periodic media with strong nonlinearity, steady-state solutions can be obtained by solving a corresponding nonlinear delay differential equation (DDE). Based on the periodicity, the steady-state response of a repeated particle or segment in the media contains the complete information of solutions for the wave equation. Considering the motion of the selected particle or segment as a variable, motions of its adjacent particles or segments can be described by the same variable function with different phases, which are delayed variables. Thus, the governing equation for wave propagation can be converted to a nonlinear DDE with multiple delays. A modified incremental harmonic balance (IHB) method is presented here to solve the nonlinear DDE by introducing a delay matrix operator, where a direct approach is used to efficiently and automatically construct the Jacobian matrix for the nonlinear residual in the IHB method. This method is presented by solving an example of a one-dimensional monatomic chain under a nonlinear Hertzian contact law. Results are well matched with those in previous work, while calculation time and derivation effort are significantly reduced. Also there is no additional derivation required to solve new wave systems with different governing equations.

Multi-Objective Optimal Design of Passive Suspension System With Inerter Damper

This paper presents a many-objective optimal design of a four-degree-of-freedom passive suspension system with an inerter device. In the optimization process, four objectives are considered: passenger’s head acceleration (HA), crest factor (CF), suspension deflection (SD), and tire deflection (TD). The former two objectives are important for the health and comfort of the driver and the latter two quantify the suspension system performance. The spring ks and damping cs constants between the sprung mass and unsprung mass, the inertance coefficient B, and the tire spring constant ky are considered as design parameters. The non-dominated sorting genetic algorithm (NSGA-II) is used to solve this optimization problem. The results show that there are many optimal trade-offs among the design objectives that could be applicable to suspension design in the industry.

Could Chalk Hopping Be Caused by Reverse Chatter?

Anyone who has ever used a chalkboard is probably familiar with the phenomenon of “chalk hopping,” where the chalk unexpectedly skips across the chalkboard, leaving a dotted line in its wake. Such behavior is ubiquitous to mechanical systems with moving parts in contact, where it is almost always undesirable. It is widely believed that hopping behavior is a physical manifestation of either the classical Painlevé paradox or a related phenomenon called dynamical jam. The present paper poses the question of whether chalk hopping might be caused by a different, and much more recently discovered, instability called “reverse chatter,” in which two bodies initially in sustained contact can lose contact through a sequence of impacts with increasing amplitude. Previous simulations of reverse chatter have considered only constant external loads, which do not adequately model the forces exerted on a piece of chalk. The current work presents simulation results for a model system in the presence of a control algorithm that mimics the human hand by attempting to keep the chalk in contact with the chalkboard. The simulations reveal that there exist physically realistic parameter values for which a loss of contact occurs that cannot be attributed to either the classical Painlevé paradox or dynamical jam, but which can only be attributed to reverse chatter. Furthermore, the subsequent motion of the system after losing contact is found to be strikingly similar to that of chalk hopping on a chalkboard, to a hitherto unparalleled degree. These results show that neither the classical Painlevé paradox nor dynamical jam is necessary for hopping behavior, and suggest that reverse chatter may be the most plausible explanation for chalk hopping.

Proportional Navigation and Model Predictive Control of an Unmanned Autonomous Vehicle for Obstacle Avoidance

This paper presents a new approach for the guidance and control of a UGV (Unmanned Ground Vehicle). An obstacle avoidance algorithm was developed using an integrated system involving proportional navigation (PN) and a nonlinear model predictive controller (NMPC). An obstacle avoidance variant of the classical proportional navigation law generates command lateral accelerations to avoid obstacles, while the NMPC is used to track the reference trajectory given by the PN. The NMPC utilizes a lateral vehicle dynamic model. Obstacle avoidance has become a popular area of research for both unmanned aerial vehicles and unmanned ground vehicles. In this application an obstacle avoidance algorithm can take over the control of a vehicle until the obstacle is no longer a threat. The performance of the obstacle avoidance algorithm is evaluated through simulation. Simulation results show a promising approach to conditionally implemented obstacle avoidance.

Application of Mixed H2/H∞ Data Driven Control Design to Dual Stage Hard Disk Drives

A data driven control design approach in the frequency domain is used to design track following feedback controllers for dual-stage hard disk drives using multiple data measurements. The advantage of the data driven approach over model based approach is that, in the former approach the controllers are directly designed from frequency responses of the plant, hence avoiding any model mismatch. The feedback controller is considered to have a Sensitivity Decoupling Structure. The data driven approach utilizes H∞ and H2 norms as the control objectives. The H∞ norm is used to shape the closed loop transfer functions and ensure closed loop stability. The H2 norm is used to constrain and/or minimize the variance of the relevant signals in time domain. The control objectives are posed as a locally convex optimization problem. Two design strategies for the dual-stage hard disk drive are presented.

Negative Obstacle Detection Using LiDAR Sensors for a Robotic Wheelchair

The objective of this work is to develop a negative obstacle detection algorithm for a robotic wheelchair. Negative obstacles — depressions in the surrounding terrain including descending stairwells, and curb drop-offs — present highly dangerous navigation scenarios because they exhibit wide characteristic variability, are perceptible only at close distances, and are difficult to detect at normal operating speeds. Negative obstacle detection on robotic wheelchairs could greatly increase the safety of the devices. The approach presented in this paper uses measurements from a single-scan laser range-finder and a microprocessor to detect negative obstacles. A real-time algorithm was developed that monitors time-varying changes in the measured distances and functions through the assumption that sharp increases in this monitored value represented a detected negative obstacle. It was found that LiDAR sensors with slight beam divergence and significant error produced impressive obstacle detection accuracy, detecting controlled examples of negative obstacles with 88% accuracy for 6 cm obstacles and above on a robotic development platform and 90% accuracy for 7.5 cm obstacles and above on a robotic wheelchair. The implementation of this algorithm could prevent life-changing injuries to robotic wheelchair users caused by negative obstacles.

Planar Motion Control, Coordination and Dynamic Entrainment in Chaplygin Beanies

The Chaplygin beanie is a single-input robotic vehicle for which partial planar motion control can be achieved by exploiting a simple nonholonomic constraint. A previous paper suggested a strategy for such motion control. In the present paper, this strategy is validated experimentally and extended to the context of multi-vehicle coordination. It is then shown that when the plane on which two such vehicles operate is translationally compliant, energy transfer between the two can enable a mechanism whereby one (operating under control) may entrain the other (operating passively), partly coordinating their motion. As an extension to this result, it is further demonstrated that a pair of passive vehicles operating on a translationally compliant platform can eventually attain the same heading when released from their deformed configurations.

Integration of Multibody System Dynamics With Sliding Mode Control Using FPGA Technique for Trajectory Tracking Problems

Trajectory tracking robotic systems require complex control procedures that occupy less space and need less energy. For these reasons, the development of computerized and integrated control systems is crucial. Recently, developing reconfigurable Field Programmable Gate Arrays (FPGAs) give a prominence of the complete robotic control systems. Furthermore, it has been found in the literature that the model-based control methods are most efficient and cost-effective. This model must interpret how multiple moving parts interact with each other and with their environment. On the other hand, MultiBody Dynamic (MBD) approach is considered to solve these difficulties to attain the models accurately. However, the obtained equations of motion do not match the well-developed forms of control theory. In this paper, the MBD model of a mobile robot is established; and the equations of motion are reshaped into their control canonical form. Additionally, the Sliding Mode Control (SMC) theory is used to design the control law. The constraints’ manifold, which is available in the equations of the MBD system, are imposed systematically as the switching surface. SMC is applied because of its ability to address multiple-input/multiple-output nonlinear systems without resorting any approximations. Eventually, the experimental verification of the proposed algorithm is carried out using DaNI mobile robot in which, a Reconfigurable Input/Output (RIO) board is used to reorient the control design, so that can fit the required trajectory. The control law is implemented using LabVIEW software and NI-sbRIO-9631 with acceptable performance. It is obvious that the integration of MBD/SMC/FPGA can be used successfully to develop embedded systems for the applications of trajectory tracking robotics.

Robust UAV Attitude Estimation Using a Cascade of Nonlinear Observer and Linearized Kalman Filter

This paper presents a new approach for Unmanned Aerial Vehicle (UAV) attitude estimation using a cascade of nonlinear observer and linearized Kalman filter. The nonlinear observer is globally asymptotically stable and is designed using linear matrix inequalities (LMI). The exogenous signal from the nonlinear observer is used to generate a linearized model for the Kalman filter. The method is implemented for attitude estimation of a quadcopter. The nonlinear model is derived from the Newton-Euler equations. The nonlinear model is locally Lipschitz due to the cross and dot products between the angular and linear velocity vectors. The attitude estimation from the dynamical system presented in this paper can be used as a module for fault detection. Simulations in Gazebo on a PX4 using Software In The Loop (SITL) shows the proposed method is able to estimate the attitude of a quadcopter accurately.

Reconfigurable Fault-Tolerant Tilt-Rotor Quadcopter System

In this paper, fault-tolerance characteristics of a reconfigurable tilt-rotor quadcopter upon a propeller failure are presented. Traditional quadcopters experience instability and asymmetry about yaw-axis upon a propeller failure but the design and control strategy presented here can handle a complete propeller failure during flight. Fault-tolerance is achieved by means of structural and flight controller reconfiguration. The concept involves conversion of a tilt-rotor UAV into a T-copter. The dynamics and control of the tilt-rotor quadcopter are presented for ideal flight condition and for the reconfigured system in case of propeller failure. Analytical solution for trim flight conditions yielding zero angular rates for the UAV is derived. It has been shown that the structurally reconfigured UAV is controllable and completes the flight mission without much compromise in flight performance. The controllability and observability analysis of the reconfigured system is shown by state space formulation. The flight controllers for both dynamic models are analyzed and the applicability of the proposed concept is presented by propeller failure simulation during the way-point navigation.