[机械模具数控自动化专业毕业设计外文文献及翻译]【期刊】新兴的运动特性：学习铰接式移动机器人中关节的协调性-外文文献

andasrolfreedomfinal states of the unactuated DOFs are viewed as an indirect consequence of the profile of the policies.Dynamical systems are used as acceleration policies, providing the actuated system with convenient1. Introductionaretasks.verse petball.aviorsestposture transitions. Moreover, cyclic and composed tasks may beProcedures that synthesize behaviors rely on the availability ofARTICLE IN PRESSContents lists available at ScienceDirectjournal homepage: www.elsevierNeurocomputin15630-C02-01).Neurocomputing 72 (2009) 36243630offering kinematic solutions to the problem of achieving theupc15838 (C. Angulo).specifications in terms of the workspace, which may include acomplete path or simply the initial and final positions of thecontrolled element. These specifications may be derived from adirect human imposition or by path-planning methods, often0925-2312/$-see front matter & 2009 Elsevier B.V. All rights reserved.doi:10.1016/j.neucom.2009.01.015C3Corresponding author.E-mail addresses: (D. Pardo), (C. Angulo), (S. del Moral), (A. CatalC18a).URLS: http:/www.upcnet.es/upc26174 (D. Pardo), http:/www.upcnet.es/decomposed into sequences of motions of this type 1.$This work was partly supported by the Spanish MEC project ADA (DPI2006-the factory-specified limit? Challenging questions arise about theoptimization of default motor behaviors, the design of new motorbehaviors and the overcoming of body constraints and limitations.motions, i.e. motions defined by an initial and a final state withvelocity equal to zero. Nevertheless, many of the motor behaof AMRs can be understood as a consequence of rest-to-rmotions 3, for example reaching 5, throwing 10 and simplemaximize the benefits provided by the kinematics and dynamics ofthe structure in order to perform motor behaviors better, such asrunning, kicking, heading the ball and goalkeeping. Hence, improvingand generating motor behavior capacities is a research challenge.Some questions are: (i) Is the default gait of the robot efficient or fastenough? (ii) Is it able to jump? (iii) Can it lift a weight heavier thanmethodology to synthesize motor behaviors in AMRs in this paper,where we understand motor behavior as a human interpretation ofthe motions of a robot and their consequences (e.g. sitting,throwing an object or walking).In order to restrict the problem, we shall focus on motorbehaviors that may be encoded by the realization of rest-to-restArticulated mobile robots (AMRs)constructed to accomplish genericfeatures that allow the generation of dibut also place restrictions on these behathis scenario is provided by the RoboCupstandard robot is used to play fooattractor properties. The control policies, parameterized around imposed simple primitives, aredeformed by means of changes in the parameters. This modulation is optimized, by means of astochastic algorithm, in order to control the unactuated DOFs and thus carry out the desired motorbehavior.& 2009 Elsevier B.V. All rights reserved.autonomous systemsThese platforms offerof motor behaviors,An initial example oftition 8,whereaResearch teams try toAMRs are often underactuated systems, i.e. not all of thedegrees of freedom (DOFs) are actuated, and therefore the globaldynamic balance of the system is constantly compromised.Additionally, they also are redundant, i.e. they have more DOFsthan those needed for representing the position and orientation ofthe controlled element of the robot (the workspace). It is notevident how to control this kind of mechanism, and this is still anopen area of research. Motivated by this challenge, we address aEmerging motor behaviors: Learning joinmobile robots$Diego PardoC3, Cecilio Angulo, Sergi del Moral, AndreuCETpD, Technical Research Center for Dependency Care and Autonomous Living, ESAII-UPC,Technical University of Catalonia, Vilanova i la Geltru, Barcelona, Spainarticle infoAvailable online 23 June 2009Keywords:Articulated mobile robotsMotor behaviorsRobot learningabstractIn this paper, we analyze thebehaviors in articulated mobapproach to this problemrest-to-rest motions. As wellabout the solution to the task,free of restrictions. Our contattracts actuated degrees oft coordination in articulatedCatalC18aAutomatic Control Department,insights behind the common approach to the assessment of robot motorile structures with compromised dynamic balance. We present a newa methodology that implements it for motor behaviors encapsulated incommon methods, we assume the availability of kinematic informationbut reference is not made to the workspace, allowing the workspace to beframework, based on local control policies at the joint acceleration level,(DOFs) to the desired final configuration; meanwhile, the /locate/neucomgARTICLE IN PRESSdesired motor behavior. Subsequently, robot control methods arerequired to compute torque-level actions that drive the mechan-ism according to the given specifications. As an inheritance fromexperience in the control of robot manipulators, where theelement that defines the workspace is the end-effector of a jointchain with a limited motion domain, most of the approaches torobot control consider a workspace reference as input data,computed off-line or generated within the methodology of therelevant approach, starting from pure kinematic informationabout the solution to the task. When workspace references arefollowed, the torque control actions are computed with theThe key attribute in both approaches was the direct connectionbetween the desired behavior and the torque commands, i.e. theworkspace requirements were almost null, leaving the system freeto be modulated in order to fulfill the behavior, i.e. lift a definedweight. Both approaches use optimization as the main route;nevertheless, the analytical solution in 19 implies a detailedformulation of the problem and its restrictions, which is perfectlyviable for manipulators in structured environments, but this is notthe case for AMRs. On the other hand, the solution given in 15 isnot analytical but numerical; it searches in the solution spaceusing a learning algorithm, i.e. a numerical optimization of policyD. Pardo et al. / Neurocomputing 72 (2009) 36243630 3625purpose of achieving desired joint accelerations, which impliescompensation of rigid-body dynamics, canceling the effects ofgravity, and other nonlinearities.Some of the approaches described in 9 consider thekinematics and rigid-body dynamics of the robot in the genera-tion of the workspace reference, but this is usually done toestablish sufficient conditions for the accomplishment of thebehavior, rather than to take advantage of the kinematics andrigid-body dynamics. An example of this is evidenced in the gaitcontrol system used in the ASIMO humanoid (which has one ofthe best humanoid gaits developed so far), where control forcesare computed to maintain balance stability during gait execution,i.e. the effects of gravity are canceled while suitable accelerationsare imposed to accomplish the motion; consequently, the energyconsumption is more than 15 times (scaled) the amount requiredduring human gait 18. However, it has been demonstrated thatduring human gait, not only are the dynamic effects of gravity notalways canceled but also they are actually employed 14. It seemsthat the current strategies to carry out a given motor behavior arewell-suited to obtaining a particular solution of the problem.Thus, the space of behavior solutions is narrowed by the approachused rather than by the capacities of the robot.However, some results using new perspectives showevidence ofalternative solutions, ones that favor the execution of the motionand expand the capacities of the robot. For instance, results in 19show that the given factory-maximum payload of an industrialmanipulator (a 6-DOF PUMA-762) can be greatly increased byexploring new zones of the solution space with suitable controlpolicies. The approach used was the formulation of a parameter-ized optimal control problem, where body dynamics and timeranges were stated as restrictions. Torque-level actions were foundsuch that the payload lifted by the manipulator was much more(six times) than the load reachable by the default aggregation ofpath planning, workspace reference and torque control. Surpris-ingly, contrary to standard procedures, the resulting trajectoriesincluded singularities, letting the robot rest the payload against itsstructure on its way to the goal. Along the same lines, a similarresult was later presented in 15, where a simple manipulator (2D,3-DOF) accomplished a weightlifting behavior, avoiding workspacerestrictions in the formulation. Besides maximizing the payloadlifted, the results included quite different workspace trajectoriesthat accomplished the same behavior.Fig. 1. (a) Initial state of the robot for the standing-up behavior. (b) Desired final configurparameters by means of iterative evaluation of experiences.Nevertheless, its control framework, based on the coordinationof lower-level PID controllers, cannot be directly extrapolated tomore complex problems.Recently, the attention given to the use of learning as aparadigm to exploit the capacity of robots has being growing. Thelatest publications on learning of motions by robots 7 revolvearound early results on imitation 6, where the initial solution inthe workspace is directly guided by a human, and afterwards therobot joints are controlled by parameterized policies that areintended to accomplish the behavior. The type of the functionsused as control policies is that of dynamical systems (DSs). Theoptimal parameters of the policy are found using reinforcementlearning (RL) 17 algorithms. Extensive work on RL algorithmssuitable for computing robot control policies has been presentedin 13.In the methodology presented in this paper, we assume theavailability of kinematic information equivalent to the initial andfinal states of the desired behavior. In contrast to the imitationapproach, a reference in the workspace is not specified. Ourcontrol framework, based on local control policies at the jointacceleration level, attracts actuated DOFs to the desired finalconfiguration; meanwhile, the resulting final states of theunactuated DOFs are viewed as a consequence of the actuatedacceleration profiles. DSs are used as acceleration controllers,providing the systemwith these attractor properties. Additionally,the control policies are parameterized around imposed simpleprimitives, which may by deformed by means of changes in theparameters in order to obtain complex accelerations.Subsequently, we present an example that provides a qualita-tive description of the type of problems that this paper addresses.The standing-up behavior illustrates those motor behaviors ofunderactuated systems in which dynamic balance is compro-mised. Fig. 1 shows the initial and final states for this behavior.Note that the behavior is enclosed by a motion where the initialand final velocities are equal to zero. The robot starts in a lying-down posture and should stand up, ending up as shown in Fig.1b.However, gravity and other nonlinearities can influence thebehavior in such a way that the robot ends up in a differentstate (see Fig. 1c). The achievement of desired values for theactuated DOFs is not enough for the desired behavior to be theresult.ation. (c) Undesired final configuration, where motor behavior has failed.ARTICLE IN PRESSu Mqq N_q;q4D. Pardo et al. / Neurocomputing 72 (2009) 362436303626where u 2 Rnrepresents the vector of joint torques, M 2 RnC2nisthe mass matrix that describes the inertial properties of the robot,and N 2 Rncontains nonlinear terms such as Coriolis forces andgravity.The accelerations of the actuated DOFsqb2 Rband theunactuated DOFsqc2 Rc, may be considered separately withoutWe present the basic definitions and a formal formulation ofthe problem in Section 2, and then the methodology forcomputing controllers is described in Section 3. A demonstrationmotor behavior in a simulated humanoid is synthesized byapplying this methodology in Section 4. Finally, the conclusionsare gathered together in Section 5.2. Controlling robot motor behaviorsThe configuration of a robot specifies the location of all parts ofthe mechanismwith respect to a reference frame, and is given byavector of independent position variables (generalized coordinates)q 2 Rn; the number of generalized coordinates defines thenumber of degrees of freedom of the mechanism. The joint spaceis the set of possible values for the joints of the robotH2 Rb; brn.The state of the robot is given by the set formed by the positionsand velocities of the generalized coordinates, i.e. z q_qC1382R2n.An element controlled by a robot also has a configuration thatdetermines its position and orientation. This configuration definesthe workspace, denoted by x 2 Rm. The geometrical relation thatmaps the generalized coordinates to the configuration of thecontrolled element is known as the forward kinematicsx fkinemq1In those cases where the number of DOFs of a robot is greater thanthat of the controlled element, i.e. n4m, the system is calledredundant owing to the existence of more DOFs than are requiredfor the control of the operational space.The relation between the velocities and accelerations in theoperational space and those in the configuration space is obtainedfrom the derivative and second derivative of (1), leading to_x Jq_qx Jqq _Jq_q 2where Jq is the Jacobian matrix of fkinemq.Now that the elements that describe the motion of a robothave been established, we now focus on the forces that generatethe motion. The relation between the control vector (the appliedforces) u 2 Rband the resulting accelerationsq 2 Rnis given bythe robot dynamics, and may be written in the constrained formq f1q;_q; tf2q;_q;tu 3The system is called underactuated when the configuration is notable to command an instantaneous acceleration in an arbitrarydirection of q. In the case of an AMR, the assumption that all jointsare actuated is coherent, but, because they are not secured to theground, the AMR can move in directions other than those allowedby its actuators, and therefore it has more DOFs than joints, i.e.rankf2C138bon. The nonactuated DOF may be represented asvirtual joints that correspond to the motion of a reference frame atthe robot base with respect to the inertial frame 16, here thisvirtual joints are denoted asqc2 Rc, where c n C0 b.Provided that articulated robots are rigid bodies, theirdynamics can be described as second-order systems where torquecommands (control actions) interact with the rest of the forcesacting on the mechanism. A well-known model describing thisinteraction is given byloss of generality 2. We can expand the dynamics of the systemin (4) asub0C20C21MbbMcbMbcMcc#qbqc#NbNc#5where ub2 Rbis the vector of actuation torques, and Nb;NcC138Tgather together the projections of other forces (gravitationalforces, Coriolis forces and ground reactions) in the correspondingsubspace. The inertia matrix M is divided into four matrices(Mbb;Mcb;Mbc;Mcc), consequently relating causes and effects foractuated and unactuated accelerations.We denote an element of the given robot posture set byP, i.e.P2fsitting; standing; arm raised; etc:g. Let us assume that acertain function P maps robot configurations q 2 Rnto thecorresponding robot postures, i.e. P : q-P. Let us denote by QPthe set of all configurations that represent the posture P, i.e.QPfqjPqPg. We define as motor behavior the process oftaking the robot from an initial robot posture Q0 to a finalposture QF within a delimited amount of time 0ototf.Itisassumed that representative elements of the initial and finalposture sets are known, i.e. q02Q0;qf2QF, including actuatedand unactuated DOFs, i.e. q0q0b;q0c, qfqfb;qfc.Itisassumed that all joints are actuated, i.e. qbH.We control actuated joints at the acceleration level usingdynamical systems as policies, which allows on-line modificationof acceleration commands. Provided the DSs have attractorproperties, the policies are designed to attract each joint to itscorresponding final state qfbHg, while it follows a smoothtrajectory. In order to select an appropriate policy, we first definethe following term as a local primitive:pitaiC0_yitbiygiC0yitC138; i 2f1; .; bg6This represents the state of the velocity and position error of jointi at instant t. The parameters ai;bi locally encode the propertiesof the primitive. We define as a local control policy thecombination of the local primitives involvedqdb;itXbj1oijC1 pjt7where the oijare scaling factors for the influence of the primitivesj on the desired accelerationsqdb;iof individual joints. In this paper,we assume that there exists a lower-level controller that convertsthe desired accelerations into suitable torque commands (e.g. bythe computed torque method). Therefore we assume that theactual accelerations of the actuated DOFs are given by (7).Before continuing, and for clarificationpurposes, we define as abasic policy the case where the scaling factors are given byoi;j0; iaj1; i j(8When a basic policy is used, the position and velocity errors of thejoints behave as a simple damped harmonic system with anattractor in (ygi;0). The dynamics of this system are modulatedwhen the nondiagonal weighting factors are not zero. This allowsthe generation of complex forms in the actual profiles followed bythe joints.The whole-body policy, generically denoted byqb hq;_q,may be explicitly presented, dropping the time dependencynotation, in a single expressionqb WC1 A_qbqb#9where the matrix A 2 RbC22bis formed by the set of a;b-factorsfrom the local primitives represented in (6), and the matr