Robert G. Langlois

Pareto Optimality and Multiobjective Trajectory Planning for a 7-DOF Redundant Manipulator

This paper presents a novel approach to solve multiobjective robotic trajectory planning problems. It proposes to find the Pareto optimal set, rather than a single solution usually obtained through scalarization, e.g., weighting the objective functions. Using the trajectory planning problem for a redundant manipulator as part of a captive trajectory simulation system, the general discrete dynamic programming (DDP) approximation method presented in our previous work is shown to be a promising approach to obtain a close representation of the Pareto optimal set. When compared with the set obtained by varying the weights, the results confirm that the DDP approximation method can find approximate Pareto objective vectors, where the weighting method fails, and can generally provide a closer representation of the actual Pareto optimal set.

Stability-Guaranteed Assist-as-Needed Controller for Powered Orthoses

This brief describes the assistance regulation controller (ARC), a nonlinear admittance controller for powered orthoses (POs) and wearable robotics that simultaneously facilitates task completion and encourages user effort. This brief also introduces a novel acceleration-limited proportional derivative controller (ALPDC) that guarantees the stability of the ARCs inner position control loop. The stability analysis of the ALPDC shows that this simple and robust position controller promotes safer human-robot interactions in a large class of admittance-controlled haptic devices. Both the ARC and ALPDC are implemented on a one-degree-of-freedom PO designed to assist forearm flexion and extension. Experiments performed by a healthy male subject confirm that the ALPDC guarantees stable user-device interactions and bounded tracking errors during highly dynamic forearm motions that lead to instability with a conventional controller.

Comparing continuous and intermittent assistance controllers for assistive devices

This paper introduces a novel assistive device (AD) control strategy that provides intermittent assistance and is capable of encouraging user effort during AD use. The assistance regulation controller (ARC) presented here is designed to regulate joint torque and can be used for arbitrary joint and limb motions without requiring any a priori information about the users intended motion. Data from eight healthy subjects who performed a forearm tracking experiment using a single degree-of-freedom powered orthosis demonstrate that the ARC is capable of encouraging user effort. On average, subjects generated 40% more joint torque when performing the tracking experiment with the ARC instead of a conventional torque-amplifying controller. The results also demonstrate that the ARC is safe to use for dynamic orthosis-assisted joint motions which require several transitions into and out of the assistance and no assistance states of the controller. As such, the results also confirm that the ARC is an effective assist-as-needed control strategy suitable for use with ADs.

A Dynamic Programming Approach to Redundancy Resolution with Multiple Criteria

This paper studies the problem of generating optimal joint trajectories for redundant manipulators when multiple criteria need to be considered and proposes a novel approach based on dynamic programming and the use of the Pareto optimality condition. The drawbacks of the traditional weighting method in optimization for generating the Pareto optimal set are discussed and an alternate approach using dynamic programming is proposed. The two approaches are implemented on the model of a 7-DOF redundant manipulator with the end-effector moving along a prescribed trajectory, while the joint trajectories are required to minimize two particular criteria. The results illustrate that the dynamic programming approach provides a better approximation of the Pareto optimal set and a more flexible and predictable framework to control the objective vectors.

Unified Treatment of the Kinematic Interface Between a Sphere and Omnidirectional Wheel Actuators

This paper presents a general approach to the kinematics of an orientation motion platform utilizing a sphere actuated by omnidirectional wheels. The number and type of the omnidirectional wheels, as well as their position and orientation relative to the sphere are arbitrary, provided they are distinct. In this paper, the general kinematics are presented and illustrated by sample configurations with a range of omnidirectional wheel types and quantities. Moreover, no-slip conditions are identified, and the resulting expressions and their implications on the design of such a mechanical system are demonstrated by means of several benchmark examples.

A Discrete Dynamic Programming Approximation to the Multiobjective Deterministic Finite Horizon Optimal Control Problem

This paper addresses the problem of finding an approximation to the minimal element set of the objective space for the class of multiobjective deterministic finite horizon optimal control problems. The objective space is assumed to be partially ordered by a pointed convex cone containing the origin. The approximation procedure consists of a two-step discretization in time and state space. Following the first-order time discretization, the dynamic programming principle is used to find the multiobjective discrete dynamic programming equation equivalent to the resulting discrete multiobjective optimal control problem. The multiobjective discrete dynamic programming equation is finally discretized in the state space. The convergence of the approximation for both discretization steps is discussed.

Asymptotically-Correct Structural Modelling Of Thin-Walled Anisotropic Closed Cross-Section Rotating Slender Beams

An application of a comprehensive and compact methodology to obtain the asymptotically-correct stiffness matrix of anisotropic, thin-walled, closed cross-section, and rotating slender beams is presented. The Variational Asymptotic Method (VAM), which utilizes small geometrical parameters inherent to thin-walled slender beams, is used to obtain the displacement and strain fields, and the cross-sectional stiffness matrix without any ad hoc assumptions. The advantage of this approach is that the asymptotically-correct and populated 4 × 4 cross-sectional stiffness matrix provides all the necessary information about the elastic behavior of the rotating beam, thereby nullifying the need for refined beam theories that incorporate higher order deformation modes, like the Vlasovs mode. The implementation of the theory usingMATLAB was validated against the Vartiational Asymptotic Beam Sectional Analysis (VABS) computer software, a two-dimensional finite element program that utilizes a more general approach to the VAM that is applicable to thick/thin-walled anisotropic crosssections with arbitrary geometry. Sample applications of the theory to rotor blades are presented. The paper concludes with a discussion of how the presented material would be used directly in the dynamic modelling of rotating helicopter blades.

Dynamics and vibration analysis of the interface between a non-rigid sphere and omnidirectional wheel actuators

This paper presents analysis of the dynamics and vibration of an orientation motion platform utilizing a sphere actuated by omnidirectional wheels. The purpose of the analysis is to serve as a design tool for the construction of a six-degree-of-freedom motion platform with unlimited rotational motion. The equations of motion are presented taking flexibility of the system into account. The behaviour of the system is illustrated by sample configurations with a range of omnidirectional wheel types and geometries. Vibration analysis follows, and sensitivity to various parameters is investigated. It is determined that the geometry of omnidirectional wheels has a significant effect on the behaviour of the system.

Actuation of Slender Thin-wall Anisotropic Open Cross-section Beams Based on Asymptotically Correct Vlasov theory

An asymptotically correct analysis of passive anisotropic thin-walled open cross-section beam-like structures using the variational asymptotic method (VAM) is extended to include embedded macro fiber composites. Application of the VAM to beam-like structures splits the problem into non-linear 1D theory along the selected beam reference line and linear 2D generalized 5 × 5 Vlasov theory augmented by a 5 × 1 actuation vector over the cross-section. The linear 2D cross-sectional theory is validated against the University of Michigan/variational beam sectional analysis 2D finite element software. The validation examples selected were based on practical cross-sectional geometry and material anisotropy under DC actuation voltage. Actuation-induced deformations predicted at the beam reference line are obtained using an intrinsic geometrically exact beam theory for open cross-sections. The predicted generalized deformations are compared with those obtained using the 3D finite element analysis software ANSYS Multiphysics, which further validates the extended theory. The analytical theory is shown to be straightforward to implement and efficient, yet sufficiently reliable to perform interdisciplinary studies and optimization of various engineering applications of such structures.

Analysis of active closed cross-section slender beams based on asymptotically correct thin-wall beam theory

An asymptotically correct theory for multi-cell thin-wall anisotropic slender beams that includes the shell bending strain measures is extended to include embedded active fibre composites (AFCs). A closed-form solution of the asymptotically correct cross-sectional actuation force and moments is obtained. Active thin-wall beam theories found in the literature neglect the shell bending strains, which lead to incorrect predictions for certain cross-sections, while the theory presented is shown to overcome this shortcoming. The theory is implemented and verified against single-cell examples that were solved using the University of Michigan/Variational Beam Sectional Analysis (UM/VABS) software. The stiffness constants and the actuation vector are obtained for two-cell and three-cell active cross-sections. The theory is argued to be reliable for efficient initial design analysis and interdisciplinary parametric or optimization studies of thin-wall closed cross-section slender beams with no initial twist or obliqueness.