Underactuated Manipulator Research Articles

Equations of Motion of Free-Floating Spacecraft-Manipulator Systems: An Engineer's Tutorial.

The paper provides a step-by-step tutorial on the Generalized Jacobian Matrix (GJM) approach for modeling and simulation of spacecraft-manipulator systems. The General Jacobian Matrix approach describes the motion of the end-effector of an underactuated manipulator system solely by the manipulator joint rotations, with the attitude and position of the base-spacecraft resulting from the manipulator motion. The coupling of the manipulator motion with the base-spacecraft are thus expressed in a generalized inertia matrix and a GJM. The focus of the paper lies on the complete analytic derivation of the generalized equations of motion of a free-floating spacecraft-manipulator system. This includes symbolic analytic expressions for all inertia property matrices of the system, including their time derivatives and joint-angle derivatives, as well as an expression for the generalized Jacobian of a generic point on any link of the spacecraft-manipulator system. The kinematics structure of the spacecraft-manipulator system is described both in terms of direction-cosine matrices and unit quaternions. An additional important contribution of this paper is to propose a new and more detailed definition for the modes of maneuvering of a spacecraft-manipulator. In particular, the two commonly used categories free-flying and free-floating are expanded by the introduction of five categories, namely floating, rotation-floating, rotation-flying, translation-flying, and flying. A fully-symbolic and a partially-symbolic option for the implementation of a numerical simulation model based on the proposed analytic approach are introduced and exemplary simulation results for a planar four-link spacecraft-manipulator system and a spatial six-link spacecraft manipulator system are presented.

Effects of Viscous Damping on Differential Flatness-Based Control for a Class of Under-Actuated Planar Manipulators

For under-actuated manipulators, not all joint trajectories are dynamically feasible and it is difficult to characterize feasible joint trajectories analytically. Differential flatness, if applicable, provides a systematic approach to plan and control feasible trajectories for such systems. Previously, Agrawal and Sangwan (2008) have formulated a methodology to design under-actuated planar manipulators to be differentially flat. This methodology assumed that the joints in the manipulator have no dissipation. In real systems, however, these joints have dissipative effects (viscous damping, coulomb friction etc.). This letter studies effects of viscous damping at unactuated joints on differential flatness-based control for the class of under-actuated manipulators presented by Agrawal and Sangwan in 2008. It is shown that in presence of viscous damping the original flat outputs lose relative degree and a stable internal dynamics is induced. Hence, the original outputs are no longer flat outputs. However, because of the stable internal dynamics induced they are still useful in applications where only output control is needed and full-state control is not desired. It is also shown that although the original set of outputs lose relative degree with viscous damping, the system remains differentially flat with another set of flat outputs. Hence, full-state control can still be performed with a new set of flat outputs in presence of viscous damping. Simulation results for controllers based on the two scenarios mentioned above are presented with a 3-DOF manipulator.

Reducing Actuator Requirements in Continuum Robots Through Optimized Cable Routing.

Continuum manipulators offer many advantages compared to their rigid-linked counterparts, such as increased degrees of freedom and workspace volume. Inspired by biological systems, such as elephant trunks and octopus tentacles, many continuum manipulators are made of multiple segments that allow large-scale deformations to be distributed throughout the body. Most continuum manipulators currently control each segment individually. For example, a planar cable-driven system is typically controlled by a pair of cables for each segment, which implies two actuators per segment. In this article, we demonstrate how highly coupled crossing cable configurations can reduce both actuator count and actuator torque requirements in a planar continuum manipulator, while maintaining workspace reachability and manipulability. We achieve highly coupled actuation by allowing cables to cross through the manipulator to create new cable configurations. We further derive an analytical model to predict the underactuated manipulator workspace and experimentally verify the model accuracy with a physical system. We use this model to compare crossing cable configurations to the traditional cable configuration using workspace performance metrics. Our work here focuses on a simplified planar robot, both in simulation and in hardware, with the goal of extending this to spiraling-cable configurations on full 3D continuum robots in future work.

A quick control strategy based on hybrid intelligent optimization algorithm for planar n-link underactuated manipulators

This paper presents a quick two-stage position control strategy based on a hybrid intelligent optimization algorithm for a planar n-link underactuated manipulator with a passive first joint. In stage 1, the system is directly reduced to a planar virtual Acrobot by controlling n-2 active links to their target angles. A hybrid intelligent optimization algorithm, which includes genetic algorithm (GA) and particle swarm optimization algorithm (PSO), is used to solve all link target angles according to the target position of the system. By coordinating GA and PSO, the hybrid intelligent optimization algorithm ensures that all link target angles, the angle of the passive link at the end of stage 1, and the initial angle of the active link of the planar virtual Acrobot meet the angle constraint of the planar virtual Acrobot. So, the position control objective of the planar n-link underactuated manipulator is realized by controlling the active link of the planar virtual Acrobot to its target angle in stage 2.

State Feedback Switching Control of an Underactuated Planar Manipulator with Partial Feedback Linearization

In this paper, position control problem of a two-degree-of-freedom underactuated manipulator is considered and a state feedback control structure with energy-based switching is proposed. The mechanism has two revolute joints that move the two links on horizontal plane. Difficulties in system control arise with the fact that the manipulator has less control input signals than system degrees of freedom, and has complex nonholonomic structure. Furthermore, in horizontal operational conditions, position control of the system is a challenging work since free joint is not affected by the gravity. The system has only one actuator at the shoulder joint and the elbow joint is completely free. Therefore, the system cannot be stabilized around any equilibrium point by a linear state feedback control method. In this study, a control system that utilizes two stabilizing state feedback controllers and an energy-based supervisory switching mechanism is proposed. Stabilizing controllers are obtained utilizing the partial feedback linearization method. Proposed control is tested by computer simulations. First the open-loop plant dynamic model is obtained by Euler-Lagrange formulation and state-space modeling approach. Then, a simulation model of the system in closed loop with proposed control scheme is developed using the dynamic model and control law. Simulation tests are performed with respect to three different initial conditions. Performance of the control system is observed and revealed via simulations.

Nonlinear stabilizing control for a class of underactuated mechanical systems with multi degree of freedoms

An underactuated mechanical system with $$n~(n\ge 3)$$ degree of freedoms (DOFs) is a complicated nonlinear system. This paper develops a new strategy to solve the nonlinear stabilizing control problem for this kind of mechanical systems. First, we introduce a coupled relationship between control torques. It changes the n-DOF underactuated system into a cascade-connected system, which has a 2-DOF driven subsystem and a $$(n-2)$$ -DOF stable driving subsystem. And then, we analyze the passivity of the driven subsystem and discuss how to design an passivity-based controller that stabilizes the driven subsystem at the origin. Finally, the stabilization of the n-DOF underactuated system is achieved by the triangle lemma. Our proposed strategy transforms the stabilization of the n-DOF underactuated system into that of the 2-DOF driven subsystem. This makes the structure of the control system simple and also makes the problem of stabilizing a multi-DOF underactuated system easy to handle. As an application of the strategy, we give detailed statements of using it to achieve the global stabilization of a 3-DOF underactuated mechanical system called spring-coupled horizontal three-link underactuated manipulator. Simulation results demonstrate its validity.

Position-Posture Control of a Planar Four-Link Underactuated Manipulator Based on Genetic Algorithm

This paper presents a position-posture control strategy based on genetic algorithm (GA) for a planar four-link passive-active-active-active (PAAA) underactuated manipulator. The control objective of the system is to move the end effector from any initial position to any target position with a specified posture. First, the integrability of the PAAA manipulator is analyzed based on its dynamic model. Then, the control process is divided into three stages based on the partial integrability of a PAAA system and the complete integrability of an Acrobot system. In each stage, the system is reduced to be an Acrobot-like system, and an angle constraint between an actuated joint and the unactuated one is derived based on the complete integrability of an Acrobot system. Next, a mathematical optimization model is constructed to solve the target angles based on multiconstraints and the control objective. And GA is applied to obtain the target angles. Finally, the controllers are designed for each stage to move one actuated joint to the target angle in turn. Simulation results demonstrate the effectiveness of the proposed control approach.

UMan: A Low-Impedance Manipulator for Human–Robot Cooperation Based on Underactuated Redundancy

This paper revisits the concept of underactuated manipulator in order to significantly improve physical human–robot cooperation for the assembly industry. The main focus is to achieve intuitive and minimum effort fine manipulation, regardless of the payload's shape and weight. An underactuated manipulator—referred to as uMan—based on a macro–mini architecture is designed with a novel passive mini mechanism, which aims at minimizing the impedance, eliminating the nonlinear impedance, and decoupling the human and robot dynamics. A specific control strategy is developed to achieve these objectives, while handling the underactuated nature of the robot for cooperative and autonomous assistance. Experimental validations are provided to assess the ease of fine manipulation using a peg-in-hole task to demonstrate the safety of the device using an effective collision detection and to establish the viability of the concept for practical industrial assembly tasks.

Underactuated Manipulatorの非ホロノミック制御 (高機能化を目指した非線形システム制御総合特集号-I)

Underactuated Manipulatorの非ホロノミック制御 (高機能化を目指した非線形システム制御総合特集号-I)

Fuzzy MTEJ controller with integrator for control of underactuated manipulators

Abstract This paper presents control of underactuated robot manipulators in task space utilizing novel algorithm called fuzzy modified transpose effective Jacobian (MTEJ) with integrator term which ensures tracking trajectory in task space with high-quality performance. Although non-model base MTEJ have been introduced before and evaluated for underactuated robots, this method has poor operation against non-linear factors in actuators and joints observed in practical tests like deadband, backlash or Coulomb damping. The contributions of this paper are in twofold. First, to introduce improved MTEJ algorithm with additional integrator term that is efficient to eliminate effects of mentioned factors or other source of steady state error (SSE). Second, using new fuzzy rules to manage its terms to stabilize system with better control properties, the controller is used to make the endeffector to both track a predefined trajectory or set on an exact point. Global stabilization of this control method is proved. Simulation and experimental results are offered which compared tracking performance of the improved fuzzy MTEJ with integrator to other methods for both tracking and point to point (P.T.P) control. Outcomes of these experiments reveal privileges of using fuzzy improved MTEJ in various areas like removing SSE with better control characteristics and low computational efforts.

Master-slave teleoperation of underactuated mechanical systems with communication delays

This paper addresses the control problem of master-slave teleoperation of a class of underactuated mechanical systems with communication delays. The core of the proposed solution introduces a suitable coupling matrix, so the complete error dynamics is written in a linear part, and a nonlinear one, for which the matching condition is satisfied. Then, from this representation, discontinuous causal controllers are designed to achieve bilateral coordination in force and position. The proposal is valid for underactuated manipulators with second-order non-holonomic constraints, and represents, to our best knowledge, a contribution in teleoperation systems where these mechanisms have been barely considered. Numerical simulations and real-time experiments developed over the Internet are provided to show the effectiveness of the proposed control scheme.

Analysis of stable model inversion methods for constrained underactuated mechanical systems

Inverse dynamics methods are presented and analyzed in detail for the feedforward control of underactuated manipulators. Thereby, two different exact strategies are discussed: the standard stable inversion method, which relies on the formulation of a two-point boundary value problem, and an alternative optimization problem formulation, which does not require any boundary conditions. This paper proves that the solution of the optimization problem converges to the solution of the boundary value problem in the limit case where the lengths of the pre- and post-actuation phases tend to infinity. It is also shown that both strategies can be directly based on the DAE form of the equations of motion, so that there is no need to explicitly derive the input-output normal form, and standard multibody modeling codes can be used. The developments are illustrated using examples of manipulators with passive and compliant joints.

Nonlinear controllability of an underactuated two-link manipulator

In this contribution, we show the global controllability of an underactuated two-link manipulator model using the characteristic of the system's drift vector field and weak Poisson stability. The main idea is to proof the general possibility to let the system return to its starting equilibrium point even though the state space is not compact. After this analysis, a control method based on the controllability property of the system is suggested. More precisely, we concatenate flows of vector field of the system to generate appropriate constant input values. This method is especially useful for underactuated systems which fail to meet the so-called Brockett condition.

Nonlinear controllability of an underactuated two-link manipulator

Nonlinear controllability of an underactuated two-link manipulator

Measurement and Control System for Underactuated Manipulator Based on LabVIEW

The paper describes the method which is used to develop measurement and control system for manipulator based on LabVIEW since motion control of servo motors and data acquirement of joints are operating in different programming environment, respectively. The motion control system makes up of two parts: the upper computer for human-computer interface and the lower computer for explanation of program command and analysis and transmission of data. UMAC (Universal Motion and Automation Controller), the lower computer, is programmed to control velocity of servo motors by calling dynamic link library in upper computer. Simultaneously, the real-time data, which includes velocity and position of servo motors and those of joints, can be acquired from UMAC and DAQ and compared with the theory data to achieve the error that can offer some reference for improvement of measuring and controllable precision and mechanism accuracy of manipulator. The experimental result indicates that it is effective and feasible to achieve pickup operation of the five joint manipulator and decrease development threshold of motion control system.

Fault Detection for Underactuated Manipulators Modeled by Markovian Jump Systems

This paper is concerned with the fault detection problem for underactuated manipulators based on the Markovian jump model. The purpose is to design a fault detection filter such that the filter error system is stochastically stable and the prescribed probability constraint performance can be guaranteed. The existence conditions for a fault detection filter are proposed through the stochastic analysis technique, and a new fault detection filter algorithm is employed to design the desired filter gains. In addition, the cone complementarity linearization procedure is employed to cast the filter design into a sequential minimization problem, which can be solved efficiently using existing optimization techniques. A numerical example is exploited to illustrate the effectiveness of the proposed method.

直動３自由度劣駆動マニピュレータのGAによる切換え制御器パラメータ決定法

直動３自由度劣駆動マニピュレータのGAによる切換え制御器パラメータ決定法

Design Parameter Setting by GA with Switching Method for Three-DOF Underactuated Manipulators

Underactuated manipulators have some passive joints in general, where the number of inputs is less than the degrees of freedom. These systems have complex properties in structure and they have to control a lot of generalized coordinates by few inputs. In this paper, we propose a switching control method for tree-DOF underactuated manipulators. Then, we convert a system of underactuated manipulator to one applied extend nonholonomic double integrator form. We try to control this system using switching control method. Here, we need to decide gain parameters using this switching control method. And we optimaze such gain parameters by a genetic algorithm (GA). The effectiveness of the propose method is illustrated through simulations with a tree-DOF under actuated manipulator.

3RD PASSIVE JOINT POSITION ANGLE VALIDATIONON 3R UNDER-ACTUATED ROBOT ARM

Position angle analysis by learning algorithm on robotics is extremely important as a tool for predictive maintenance to detect faults and mechanical problems. This paper presents position angle analysis on passive joint using three rotations (3R) under-actuated robot manipulator. Experiment was conducted to predict the position angle which were applied to three joint; Active 1, Active 2 and Passive respectively. Experiment by SIMULINK software was carried out to validate the value of position angle obtained during real-time experiment. As a conclusion, the 3rd position angle of passive joint followed the position angle for Active 1 and Active 2.

Development of Efficient Nonlinear Benchmark Bicycle Dynamics for Control Applications

We present a symbolic method for modeling a nonlinear multibody bicycle with holonomic and nonholonomic constraints. The method, developed for robotic multibody dynamics, is applied to a benchmark bicycle, in which all six ground contact constraint equations are eliminated, leaving analytic coupled ordinary differential equations corresponding to the bicycle rear body roll, steer angle, and rear wheel rotation degrees of freedom without any approximation. We have shown that the nonlinear dynamics of the bicycle satisfies an underactuated manipulator equation and demonstrated an analytic method to solve the vehicle pitch angle from a quartic equation. This reduced analytic model offers insights in understanding complex nonlinear bicycle dynamic behaviors and enables the development of an efficient model suitable for real-time control outside of the linear regime.