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Two-arm mobile manipulators: (a) Justin (Courtesy of DLR); (b) ARMAR-III (courtesy of Karlsruhe Institute of Technology).
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This thesis is devoted to the study of robotic two-arm coordination/manipulation from a unified per- spective, and conceptually different bimanual tasks are thus described within the same formalism. In order to provide a consistent and compact theory, the techniques presented herein use dual quaternions to rep- resent every single aspect of robot k...
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... Figure 3 Two-arm mobile manipulators: PR2 and Twendy-one. 7 Figure 4 Justin and ARMAR-III. 8 Figure 5 Augmented object model. ...
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... Figure 39 Serially coupled kinematic chain for a two-arm mobile manipula- tor. 88 Figure 40 Sequence corresponding to the reaching phase in the task of pour- ing water. 92 Figure 41 Task of pouring water using the whole body motion. ...
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... Figure 43 Experimental setup for the human-robot collaboration. 98 Figure 44 Actuation of the human arm: positioning of the electrodes. 100 Figure 45 The human arm modeled as a one-link serial robot. ...
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... Figure 44 Actuation of the human arm: positioning of the electrodes. 100 Figure 45 The human arm modeled as a one-link serial robot. 100 Figure 46 Task of pouring water. ...
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... Figure 45 The human arm modeled as a one-link serial robot. 100 Figure 46 Task of pouring water. 102 Figure 47 Teleoperation with collaboration. ...
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... Figure 46 Task of pouring water. 102 Figure 47 Teleoperation with collaboration. 102 Figure 48 Sequence of human-robot collaboration (HRC) in mirror mode. ...
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... Figure 47 Teleoperation with collaboration. 102 Figure 48 Sequence of human-robot collaboration (HRC) in mirror mode. 104 Figure 49 Constrained movement in the ball in the hoop experiment. ...
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... Figure 48 Sequence of human-robot collaboration (HRC) in mirror mode. 104 Figure 49 Constrained movement in the ball in the hoop experiment. 105 Figure 50 Coordinate systems in the ball in the hoop experiment. ...
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... Figure 53 Number of trials versus individual performance. 110 Figure 54 Impact of the cooperation in the success of the task. 110 Figure 55 Comparison of the success rate. ...
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... Justin ( fig. 4a), currently one of the most popular two-arm mobile manipu- lators, "is designed for research on sophisticated control algorithms for complex kine- matic chains as well as mobile two-handed manipulation and navigation in typical hu- man environments" (Borst et al., 2009). This robot was developed by German Aerospace Center (DLR) and can ...
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... robot, ARMAR-III ( fig. 4b), is also capable of performing complex tasks in household environments. For instance, ARMAR-III can recognize cups, dishes, and boxes of any kind of food, and it can automously load and unload a dishwasher with different kind of objects-e.g., tetra packs, bottle with tags, etc (Asfour et al., 2006). The aforementioned robot systems ...
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... sequence for the reaching phase is shown, in top view, in figure 40. The robot must reach the person such that the absolute frame (the frame represented by x 0 a ) is inside the magenta circle 3 , while it must also bring one hand closer to the other with the purpose of saving time. ...
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... order to open the hand, the Extensor Digitorum Communis was activated. The placement of the electrodes is shown in figure 44. ...
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... to the restrictions imposed by the implementation of the FES controller, only the biceps was controlled in a continuous range, whereas the opening of the hand was controlled by an on/off controller. Hence, it was more appropriate to model the hu- man arm as a one-DOF serial robot with the rotation axis located at the elbow and the end-effector located at the wrist, as illustrated in figure 45. The corresponding Denavit- Hartenberg (D-H) parameters are shown in table 5, where the parameter a was loosely defined. ...
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... 100 ms, the device provides a good estimation of the marker's pose with respect to its reference frame, F M . In the first three experiments, the marker was placed on the subject's hand or wrist, as shown in figure 46 and figure 47, defining the frame F H . ...
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... the experiment, the cooperation happened when a second person, the collaborator, interacted with the robot. Figure 47 shows a sequence of teleoperation with cooperation. Using the robot, the teleoperator could grab the pipe and hand it to the collaborator. ...
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... order to define the task, consider the initial pose of the human hand as shown in figure 48a; that is, ...
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... differently from the two previous tasks, the parameters of this one is variable. Figures 48a-c show the sequence obtained from a manipulation task using mirrored movements. First, the system was initialized in the face-to-face configuration. ...
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... human arm was controlled by means of FES and both arms had to be coordinated in order to drop the ball inside the hoop. To simplify the experimental setup and avoid the requirements of precise multi-joint FES control, the human arm was constrained to move only in one plane, as depicted in figure 49. ...
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... the other hand, the robot's performance would have been better if the ball's orientation- i.e., the orientation of the marker attached to the ball-had not been considered in the task, or if the robot had had more DOF. Figure 54 shows the impact of the effective cooperation in the accomplishment of the task. Whenever there is effective cooperation, the number of accomplished tasks tends to be close to the number of effective co-operations. ...
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... In recent years, the special Euclidean group SE(3) [17][18][19] and dual quaternions [20][21][22] have been the most popular methods to describe the coupling motion of rigid bodies. A 4 × 4 homogeneous transformation matrix is utilized when modeling rigid bodies on SE(3), while the model is described more compactly by dual quaternions, which have only 8 parameters, and the dual-quaternions multiplications have a lower computational cost than homogeneous transformation matrix multiplications [23]. Wang et al. [24] proposed a quaternion solution for attitude and position control of rigid-bodies' networks, which was the first attempt to apply the dual-quaternion representation to the study of formation-control problems. ...
In order to meet the position and attitude requirements of spacecrafts and test masses for gravitational-wave detection missions, the attitude-orbit coordination control of multiple spacecrafts and test masses is studied. A distributed coordination control law for spacecraft formation based on dual quaternion is proposed. By describing the relationship between spacecrafts and test masses in the desired states, the coordination control problem is converted into a consistent-tracking control problem in which each spacecraft or test mass tracks its desired states. An accurate attitude-orbit relative dynamics model of the spacecraft and the test masses is proposed based on dual quaternions. A cooperative feedback control law based on a consistency algorithm is designed to achieve the consistent attitude tracking of multiple rigid bodies (spacecraft and test mass) and maintain the specific formation configuration. Moreover, the communication delays of the system are taken into account. The distributed coordination control law ensures almost global asymptotic convergence of the relative position and attitude error in the presence of communication delays. The simulation results demonstrate the effectiveness of the proposed control method, which meets the formation-configuration requirements for gravitational-wave detection missions.
... In recent years, Lie group SE(3) [6][7][8] and dual quaternions [9][10][11] have been the most popular methods to describe the coupling motion of rigid bodies. A 4 × 4 homogeneous transformation matrix is utilized when modeling rigid bodies on SE(3), while the model is described more compactly by dual quaternions, which have only eight parameters, and the dual quaternions' multiplications have lower computational cost than homogeneous transformation matrix multiplications [12]. Therefore, this paper uses dual quaternion as a tool to design an attitude-orbit coupling coordination controller for space gravitational wave detection formation. ...
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... where J x i = ∂f i /∂q i is the analytical Jacobian, which can be easily derived using dual quaternion algebra as in [70]- [72]. The matrix + H and − H are Hamilton operators that can be used to commute terms when performing dual quaternions multiplications. ...
... 5 As far as cooperative manipulation tasks are concerned, our focus in this paper is limited to these introduced subsets which are utilized for flexible control of the dual-arm system. For further details regarding cooperative primitives, we refer readers to [63] and also to [70], [72]. For a general treatment of geometric feature extraction from dual quaternions, we allude to [61], [62], and [73]. ...
... The CoSTP controller, along with the lower level motion controller, runs at 1KHz dispensing effective torque commands for the dual-arm system. dual quaternion set S into R 8 , that is, vec : S → R 8 and the dual quaternion z=xy, the Hamilton operators, vec x,[70]-[72]. ...
Future robots operating in fast-changing anthropomorphic environments need to be reactive, safe, flexible, and intuitively use both arms (comparable to humans) to handle task-space constrained manipulation scenarios. Furthermore, dynamic environments pose additional challenges for motion planning due to a continual requirement for validation and refinement of plans. This work addresses the issues with vector-field-based motion generation strategies, which are often prone to local-minima problems. We aim to bridge the gap between reactive solutions, global planning, and constrained cooperative (two-arm) manipulation in partially known surroundings. To this end, we introduce novel planning and real-time control strategies leveraging the geometry of the task-space that are inherently coupled for seamless operation in dynamic scenarios. Our integrated multi-agent global planning and control scheme explores controllable sets in the previously introduced
Cooperative Dual Task-Space
and flexibly controls them by exploiting the redundancy of the high Degree-of-Freedom (DoF) system. The planning and control framework is extensively validated in complex, cluttered, non-stationary simulation scenarios where our framework is able to complete constrained tasks in a reliable manner while existing solutions fail. We also perform additional real-world experiments with a two-armed 14 DoF torque-controlled KoBo robot. Our rigorous simulation studies and real-world experiments reinforce the claim that the framework is able to run robustly within the inner loop of modern collaborative robots with vision feedback.
... Successive rigid body transformations in robot kinematic chains can also be defined using dual quaternions [11][12][13][14]. Dual quaternions are the most compact mathematical construct for defining the screw motion [10,15]. ...
... They represent, however, a more general concept of transformations that is valid in any dimension. Furthermore, due to their similarities with dual quaternions the same advantages over transformation matrices apply to motors as well, i.e. they require less memory and operations for multiplication compared to transformation matrices [49]. The motor manifold being a Lie group consequently makes the bivector algebra its Lie algebra. ...
... Finally, we find the manipulator inverse dynamics equation in geometric algebra to be τ (q,q,q) = τ ext + I(q)q +İ(q,q) + V (q)m V(q)q +V(q,q)q + G , (49) and consequently the forward dynamics of a serial manipulator can be expressed as ...
... where the torque vector τ is computed as presented in Equation (49). K p and K d are the stiffness and damping gains, respectively. ...
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... In order to make the best use of the visualization tools available with ROS in tasks that include forward kinematic calculation for a robot model that has been developed according to rules of the DH convention, an elegant solution based on the application of unit dual quaternions and the use of third-party graphic modeler is proposed herein. The solution is founded on the fact that the representation of the DH parameters in unit dual quaternion space is straightforward [3]. Consequently, a rigid transformation between adjacent joints is defined by dual quaternion multiplication of the four unit dual quaternions corresponding to four defined DH parameters. ...
... Consequently, a rigid transformation between adjacent joints is defined by dual quaternion multiplication of the four unit dual quaternions corresponding to four defined DH parameters. Furthermore, complete rigid transformation is described by a single mathematical object, which has advantages in developing various robotic algorithms [3]. ...
This paper presents a method for the
implementation of a robot forward kinematics algorithm that
complies with the Denavit-Hartenberg (DH) convention in Robot
Operating System (ROS). The integration of the algorithm in
ROS is based on the representation of DH parameters in dual
quaternion space. The main motivation for the presented
research is to make use of ROS powerful visualization tools
available in tasks that require robot forward kinematics
calculation while keeping the principles of DH robot modeling
convention. Implementation of the dual quaternion-based robot
forward kinematics algorithm in ROS is demonstrated using a
serial 6DoFs robot as an example.
... The differential forward kinematics, which describes the mapping between the joints velocities and the end-effector (generalized) velocity is given by (Adorno, 2011) ...
This paper proposes a robust dual-quaternion based H∞ task-space kinematic controller for robot manipulators. To address the manipulator liability to modeling errors, uncertainties, exogenous disturbances, and their influence upon the kinematics of the end-effector pose, we adapt H∞ techniques – suitable only for additive noises – to unit dual quaternions. The noise to error attenuation within the H∞ framework has the additional advantage of casting aside requirements concerning noise distributions, which are significantly hard to characterize within the group of rigid body transformations. Using dual quaternion algebra, we provide a connection between performance effects over the end-effector trajectory and different sources of uncertainties and disturbances while satisfying attenuation requirements with minimum instantaneous control effort. The result is an easy-to-implement closed form H∞ control design criterion. The performance of the proposed strategy is evaluated within different realistic simulated scenarios and validated through real experiments.
... The interpolated poses are also independent of the choice of the coordinate frames. For a more detailed discussion on dual quaternions and their interpolation we refer readers to [24,25]. ...
Despite the increasing number of collaborative robots in human-centered manufacturing, currently, industrial robots are still largely preprogrammed with very little autonomous features. In this context, it is paramount that the robot planning and motion generation strategies are able to account for changes in production line in a timely and easy-to-implement fashion. The same requirements are also valid for service robotics in unstructured environments where an explicit definition of a task and the underlying path and constraints are often hard to characterize. In this regard, this paper presents a real-time point-to-point kinematic task-space planner based on screw interpolation that implicitly follows the underlying geometric constraints from a user demonstration. We demonstrate through example scenarios that implicit task constraints in a single user demonstration can be captured in our approach. It is important to highlight that the proposed planner does not learn a trajectory or intends to imitate a human trajectory, but rather explores the geometric features throughout a one-time guidance and extend such features as constraints in a generalized path generator. In this sense, the framework allows for generalization of initial and final configurations, it accommodates path disturbances, and it is agnostic to the robot being used. We evaluate our approach on the 7 DOF Baxter robot on a multitude of common tasks and also show generalization ability of our method with respect to different conditions.
... where q = [q T 1 q T 2 ] T ∈ R n is the augmented joint vector, and J x i = ∂f i /∂q i is the analytical Jacobian, which can be easily derived using dual quaternion algebra as in [2], [28], [31]. The matrix J x 2ext is defined by [0 J x 2 ], and J x r/2 is given by 2 The absolute pose is located between end-effectors w.r.t. to a common coordinate system yet, without loss of generality, it can be shifted by means of a constant transformation. ...
... where q = [q T 1 q T 2 ] T ∈ R n is the augmented joint vector, and J x i = ∂f i /∂q i is the analytical Jacobian, which can be easily derived using dual quaternion algebra as in [2], [28], [31]. The matrix J x 2ext is defined by [0 J x 2 ], and J x r/2 is given by 2 The absolute pose is located between end-effectors w.r.t. to a common coordinate system yet, without loss of generality, it can be shifted by means of a constant transformation. 3 Similar to SE (3), unit dual quaternion multiplication is not commutative. ...
... see [2], [28], [31] for further details. ...
Similar to human work, robotic tasks sometimes require two hands to be fulfilled. This requires coordinated planning and motion. While fulfilling the task in a coordinated manner is already a big challenge, the task at hand becomes even harder, when obstacles in the environment are introduced that need to be avoided. Furthermore, in the case of dynamic environments, contacts cannot be avoided all the time, even with very good planning. Thus also bimanual systems need to be able to detect and react to contacts during task execution. We, therefore, integrate a circular field-based planning scheme based on dual quaternions that is able to avoid obstacles with contact detection and reactive control methods based on contact wrench estimation such as admittance control. We even integrate the real contact forces into the planner directly together with the circular force fields. The resulting planner-controller combination is capable of obstacle-avoiding planning as well as reaction control in case of unforeseen contacts that can also be used in situations where the manipulation needs to be guided by the environment such as landing control in only roughly known environments. We evaluate our approach on the Kobo bimanual setup and also perform rigorous simulation studies.
... where J x i = ∂f i /∂q i is the analytical Jacobian, which can be derived using dual quaternion algebra as in [37]- [39]. [39]. ...
... Among the vast number of geometric task primitives we can seek within a multi-arm system, we shall focus on the ones in Table I which are often required in most interactions, and particularly useful for cooperative manipulation. Further details about the above cooperative primitives can be found in the pivotal work [36] and within [37], [39]. For general geometric features that can be extracted from dual quaternions, we refer to [21], [40], [48]. ...
