Steven A. Velinsky

Variable Structure Control of a Differentially Steered Wheeled Mobile Robot

This paper discusses dynamic modeling and robust control of a differentially steered mobile robot subject to wheel slip and external loads. Consideration of wheel slip and external loads is crucial for high load and/or high speed applications because they act as disturbances to the system. Furthermore, a tire model that adequately accounts for the tire/ground interaction is essential and Dugoffs pneumatic tire friction model is utilized herein in deriving the dynamic equations of motion of the mobile robot. It is shown that the dynamic equations satisfy the matching condition, and the variable structure control method is employed to design a tracking controller of the mobile robot. Numerical simulation shows the promise of the developed control algorithm.

Dynamic model based robust tracking control of a differentially steered wheeled mobile robot

The expansion of wheeled mobile robot usage to applications with high loads and speeds requires reliable tracking control that is robust to the disturbances emanating from external loads and the wheel-ground contact. The motion of such robots can be accurately described with a dynamic model that includes both the external forces and a complex tire model. However, control design from the full dynamic model is not practical due to its complexity and nonanalytic form. In this paper, we derive a simplified dynamic model which is adequate for control design and treat the remaining terms as model uncertainty. Then, the uncertainty is analyzed and a robust control algorithm is designed. The performance and robustness is proven through computer simulation.

Improved velocity estimation for low-speed and transient regimes using low-resolution encoders

This paper presents a new estimation method, entitled the asynchronous sampling pulse method (ASPM), for determining velocity in systems with low but variable speeds, and/or with low-resolution encoders. The ASPM forces the estimator procedure to synchronize with the actual encoder pulse input, thus eliminating encoder positioning error independent of target velocity variations. This method is based on using an auxiliary sampling period to measure the time interval between the moment of encoder input and the control sampling instant, and its precision is shown to be dependent only on this auxiliary sampling period. Thus, the ASPM improves over existing methods in which estimator performance is dependent on both target acceleration and encoder resolution. Simulation and experimental results are used to verify the method.

Kinematics and Efficiency Analysis of the Planetary Roller Screw Mechanism

This paper analyzes the kinematics and the efficiency of the planetary roller screw mechanism (RSM) to provide a fundamental basis to support its various applications. The mechanical structure and practical advantages are presented in comparison with the conventional ball screw mechanism (BSM). Kinematic analysis involves derivation of the angular and axial motions, as well as the development of the slip pattern between the contacting components. Results show that for any motion of the RSM slip always occurs. Kinematic analysis including elastic deformation is also presented. The load carrying capacity and efficiency of the RSM are derived based on geometric and equilibrium conditions, and the results are compared with the BSM.

Kinematics of Roller Migration in the Planetary Roller Screw Mechanism

This paper develops a kinematic model to predict the axial migration of the rollers relative to the nut in the planetary roller screw mechanism (PRSM). This axial migration is an undesirable phenomenon that can cause binding and eventually lead to the destruction of the mechanism. It is shown that this migration is due to slip at the nut–roller interface, which is caused by a pitch mismatch between the spur-ring gear and the effective nut– roller helical gear pairs. This pitch circle mismatch can be due to manufacturing errors, deformations of the mechanism due to loading, and uncertainty in the radii of contact between the components. This paper derives the angle through which slip occurs and the subsequent axial migration of the roller. It is shown that this roller migration does not affect the overall lead of the PRSM. In addition, the general orbital mechanics, in-plane slip velocity at the nut–roller interface, and the axial slip velocities at the nut–roller and the screw–roller interfaces are also derived. Finally, an example problem is developed using a range of pitch mismatch values for the given roller screw dimensions, and the axial migration and slip velocities are determined.

On the Tracking Control of Differentially Steered Wheeled Mobile Robots

Fundamental tracking control algorithms ofa differentially steered wheeled mobile robot with two conventional driven wheels are studied through analyzing the robots inherent kinematics. This includes the tracking variable assignment as well as the tracking singularity and position-orientation tracking decoupling problems. Globally convergent tracking control algorithms are proposed, which can exactly track any differentiable reference path. A fundamental motion orientation equation under the condition of exact position tracking is developed, and it is shown that it is not possible to exactly track both position and orientation concurrently for this kind of mobile robot configuration if the tracking point is not on the baseline. Examples are provided illustrating the tracking ability of the developed control algorithms.

Kinematically-Redundant Variations of the 3-RRR Mechanism and Local Optimization-Based Singularity Avoidance

Abstract To avoid the singular loci of the 3-RRR mechanism that exist within its workspace, this paper applies kinematic redundancy. First, three feasible kinematic redundancy configurations for the 3-RRR mechanism are presented and singularity analysis of the kinematically redundant mechanisms is described. Then, based on local optimization suitable for real-time control, a general, simple, and effective redundancy resolution algorithm for the mechanisms is developed. Here, the cost function in the optimization is designed to avoid the most problematic singularity configurations, where the end-effector can be locally moved even though all actuated joints are locked. The kinematically redundant mechanisms are shown to effectively avoid singularities and correspondingly increase the singularity-free workspace.

Stiffness of the Roller Screw Mechanism by the Direct Method

In this paper, the direct stiffness method is used to construct a stiffness model of the roller screw mechanism. This method models the entire roller screw mechanism as a large spring system composed of individual springs representing the various compliances. In addition to predicting the overall stiffness of the mechanism, the direct stiffness method can calculate the distribution of load across the threads of the individual bodies. With the load on the individual threads known, the contact stresses can be calculated. This allows for a better understanding of the sensitivities of stiffness and contact stresses in the mechanism with various design parameters and can ultimately be used to design roller screws that are stiffer and with lower contact stresses.

Integrating embedded PC and Internet technologies for real-time control and imaging

The use of embedded personal computing (PC) technology allows desktop computer applications to evolve into the real-time control world. Such systems will be compact, reliable and low in cost. However, the mainstream PC platforms such as Windows NT have shortcomings concerning their real-time capabilities. The integration of embedded PC and Internet technologies make distributed real-time control a reality and eliminate the limitations of PC operating systems (OS). This paper discusses the general hardware, OS and software development tools for distributed, Internet-enabled, PC-based embedded control systems. A specific application of the approach is discussed, the development of a long-reach manipulator system for highway maintenance operations, which verifies the approach and illustrates its potential applicability.

Verification of a Wheeled Mobile Robot Dynamic Model and Control Ramifications

For low speed, low acceleration, and lightly loaded applications, kinematic models of Wheeled Mobile Robots (WMRs) provide reasonably accurate results. However, as WMRs are designed to perform more demanding, practical applications with high speeds and/or high loads, kinematic models are no longer valid representations. This paper includes experimental results for a heavy, differentially steered WMR for both loaded and unloaded conditions. These results are used to verify a recently developed dynamic model which includes a complex tire representation to accurately account for the tire/ground interaction. The dynamic model is then exercised to clearly show the inadequacy of kinematic models for high load and/or high speed conditions. Furthermore, through simulation, the failure of kinematic model based control for such applications is also shown.