Design-Informed Kinematic Control for Improved Dexterous Teleoperation of a Bilateral Manipulator System
Lasitha Wijayarathne, Juan Vallejo, Anthony Barnum, Zachary Cloutier, Frank L. Hammond III
DDesign-Informed Kinematic Control for Improved DexterousTeleoperation of a Bilateral Manipulator System
Lasitha Wijayarathne, Juan Vallejo, Anthony Barnum, Zachary Cloutierand Frank L. Hammond III,
IEEE Member
Abstract — This paper explores the possibility of improv-ing bilateral robot manipulation task performance throughoptimizing the robot morphology and configuration of thesystem through motion. To optimize the design for differentscenarios, we select a set of tasks that represent the variabilityin small scale manipulation (e.g. pick and place, tasks involvingpositioning and orientation) and track the motion to obtain areproducible trajectory. Kinematic data is captured through anelectromagnetic (EM) tracker system while a human subjectperforms the tasks. Then, the data is pre-processed and usedto optimize the morphology of each symmetric robot arm of thebilateral system. Once optimized, a kinematic control schemeis used to generate a motion with dexterous configurations. Thedexterity is evaluated along the trajectories with standard dex-terity metrics. Results show a 10% improvement in dexterousmaneuverability with the optimized arm design and optimalbase configuration.
I. I
NTRODUCTION
Execution of manipulation tasks in the operational (ortask) space is commonplace nowadays. This strategy appliesto both kinematic and force-torque control systems. If therobotic system is kinematically redundant for the given task,it is possible to perform additional secondary tasks simulta-neously, as exemplified in Figure 1. A general approach is toexecute them in a prioritized or combined manner using nullspace projections. These secondary tasks could include ob-stacle avoidance, visibility improvement, and configurationoptimization using the current design morphology.Dexterous robotic manipulation has been long studied, andmany commercial serial and parallel manipulators are avail-able for specialized and general applications. Among those,redundant manipulators are more appealing since they have awell-connected work-space and improved dexterity. Multiplearm manipulator systems (kinematic trees) take a vital placein terms of redundancy since they can be utilized to enhancethe performance for a given task. The performance of arobot system inherently relies on its geometrical design andcontrol scheme. Underlying control schemes could be usedto improve the performance but are limited by the boundsof the design. Thus, improved design can help enhance theperformance of the overall robot system.
Lasitha Wijayarathne, Anthony Barnum, Zachary Cloutier, Juan Vallejoand Frank Hammond are with the Woodruff School of Mechanical Engi-neering, Georgia Institute of Technology, Atlanta, GA, USA.Frank L. Hammond III is with the Woodruff School of Mechanial Engi-neering and the Coulter Department of Biomedical Engineering at the Geor-gia Institute of Technology. [email protected].
Fig. 1: Illustration of proposed bilateral manipulator systemII. M
OTIVATION
Today’s robots are good at performing specialized tasks [1]but not on everyday tasks that involve shifting workspaces,require adaptation and dexterity. While bilateral manipulationdelivers more combined manipulability to coordinated tasksencountered on a daily basis [2], [3], we still do not leveragethe knowledge of the design domain in motion generation.In this paper, we layout a formulation to optimize thedesign morphology of a bilateral system and use it in themotion generation of the entire system at a kinematic level.Our main contributions are: • A method for a data driven optimization of abilateral robot system morphology • Design informed optimization of the global posi-tioning of the bilateral system to achieve improveddexterity
III. R
ELATED W ORK
In the literature, design optimization of serial/parallelrobot manipulators has been widely studied. These works a r X i v : . [ c s . R O ] M a y an be mainly categorized into two sub-categories: designoptimization for general and specific tasks. Studies of [4],[5], [6] can be recognized as attempts to optimize the designfor general-tasks. In these, non-redundant manipulators havebeen considered where analysis is primarily done analyti-cally. On the other hand, works of [7], [8], [9], [10] can beregarded as optimizations for specific tasks. Tasks in thesevary from medical applications to construction work tasksand non-redundant, redundant, and continuum manipulatorshave been considered. Moreover, [11] used RRT (rapidlyexploring random trees) to optimize a continuum robotdesign for motion optimality and visibility. Here, the designis optimized for motion and design.Design optimization is broad in scope and the formulationused for optimization is important to ensure the design isrobust and physically realizable. Since the robot’s kinematicmodel and desired cost function are non-linear, most ofthe cited work here use global optimization techniques.Simulation annealing (SA) and genetic algorithms (GA) arewidely used as global optimization techniques. While the useof stochastic methods inhibits the reproducibility of results,it could guarantee that the optimal parameters are found(in a sense of probabilistic completeness[11]. In additionto design, optimizing for motion simultaneously has gainedattention. [12] use a co-optimization framework to iterativelyoptimize for motion and design parameters simultaneously.This method is well suited for a design with good priormorphology (with a fewer DOFs) as this method is a localoptimization technique.Kinematic and dynamic metrics are considered as primaryor secondary metrics used for design candidate assessment.Studies of [13], [14], [15], [16] use kinematic and dynamicisotropic metrics for evaluation, and variants of isotropicmeasures (e.g., weighted isotrophy, dynamic isotrophy) arediscussed in detail. In contrast, designs for specific tasks areevaluated with cost functions built using desired kinematicprofiles [17].Moreover, all the above work except for [4], [17] use theDH convention to represent the manipulators. DH (Denavit-Hartenberg) representation is suited in cases where orien-tation is not taken into account. If the objective functionconsists of the full pose (position+orientation), a repre-sentation of orientation should be used (e.g. quaternion,euler) where distance metrics of position and orientations arenot matched. This would result in poor inverse differentialsolutions compared to the manifold approach used in theproduct of exponential (PoE) method.Existing bilateral systems similar to the proposed systemin this paper can be cited as [18], [19]. These systems arebuilt primarily for surgical tele-operation and are equippedwith a fixed base. Furthermore, the fundamentals of au-tonomous bi-manual tasks have been studied in these works[3], [9] [20]. The work presented in this paper could be ex-tended easily to autonomous tasks with a focus on dexterityand configuration optimization. Fig. 2: Illustration of the relation of work-space and theprojection of it on the base of the toolIV. F UNDAMENTALS AND P RELIMINARIES
A. Small Scale Bi-manual Tasks
Small scale bi-manual tasks are found in many applica-tion domains (e.g., medical domain, micro-assembly, andbiological tissue manipulation).
Compared to large scalemanipulation tasks ([21], [3], small scale manipula-tion tasks generally require additional dexterity overworkspace volume . Moreover, the capability to generateexternal wrenches in desired directions is essential in smallscale manipulation tasks[22].This paper focuses on using kinematic data from humansubject trials to optimize the kinematic morphology of abilateral system. A few tasks were carefully chosen to coverthe variability of small scale tasks. For example, the suturingtask needs more orientational dexterity compared to thesoldering task, which needs a larger workspace and morepositional dexterity. The chosen tasks along with their high-level characteristics are listed below (refer to Figure 3). Thechoices of task and their characteristics are listed below:1)
Pick and Place, Dynamic Bandwidth: e.g. Solder-ing. Soldering involves picking IC components, placingthem on the PCB and finally soldering them to theboard. The main characteristics of the task are precision,workspace, accuracy and stiffness control of the system.2)
Orientation Dexterity: e.g. Suturing. Suturing requiresa smaller work-space but regular modulation of theorientation over a broader range.3)
External Wrench Generation: e.g. Knife Cutting.Cutting along a surface path requires positional andwrench generation to overcome contact frictional forces.4)
Position Dexterity: e.g. Small scale path tracking,incision paths
B. Kinematic Data Collection and Abstraction
Raw kinematic data was collected through an EM motion-tracking setup that is based on a fixed reference frame. In thecollection phase, human expertise on each above individualtask was given two manual tools (e.g. forceps with a needle).The base motion of each tool (shown in Figure 2) wastracked using an EM tracker probe. The motion of the tipwas obtained using a projection matrix as described in [22].ig. 3: Task kinematic profiles. Motion primitives of small tasks. Characteristics include High Dynamic Bandwidth, Positionaland Orientation Dexterity. Red: Left Arm, Black: Right ArmIn performing small scale manipulation tasks, we pay at-tention to continuous local variations of the motion envelope.This is due to prior global positioning of the body pose.Thus, data was post-processed to extract local variationsin motion as shown in Figure 4. Normalized data (withlocal variation) is clustered and re-sampled to generate auniform distribution. This is important since the kinematicdata collected tends to be non-uniform. (e.g., data tends toconcentrate in some spatial domains).Fig. 4: Flow of the data pre-processing. Raw data is pro-cessed to generate uniformly distributed dataFig. 5: Serial Chain Manipulator with revolute joints withproduct of exponential notation
C. Preliminaries of Multibody Kinematics1) Product of Exponential:
The methodology used inthis paper uses the basic product of exponential methodsfor robot kinematic analysis. Compared to the
Denavit-Hartenberg ( DH ) parameters, product of exponentials ( PoE ) provides a robust way to compute differential inversekinematic solutions (e.g. positions and orientations). Productof exponentials defines twist axes in the spatial frame ratherthan relative to the prior frame as seen in the Denavit-Hartenberg convention. As a result, it offers more intuitivesolutions in the design morphology optimization that will beshown in the subsequent sections.
2) Forward Kinematics:
Given the joint positions, for-ward kinematics are defined in the product of exponentialformulation as below[23]. T st = e ˆ ξ θ e ˆ ξ θ . . . e ˆ ξ i θ i . . . e ˆ ξ n θ n M ∈ SE (3) (1) ˆ ξ i is the twist and represented by ˆ ξ i = (cid:20) ˆ ω i v i (cid:21) ∈ se (3) . M ∈ SE (3) is home configuration and θ i ’s are thegeneralized coordinates of the joint positions.
3) Differential Inverse Kinematics:
In general, for a welldefined serial manipulator, workspace volume and reachabil-ity are known a priori. However, for a manipulator wherethe morphology is iteratively optimized through a globaloptimizer (e.g. simulated annealing), inverse solver shouldbe capable of being robust to ill-posed manipulator mor-phologies throughout the optimization routine. Furthermore,an appropriate IK solver would generate optimized solutionsfor each iteration where the cost is evaluated. Algorithm 1shows the modified first order differential IK solver adaptedfrom [24], [23]. V. D
ESIGN OPTIMIZATION
A. Robot Morphology Optimization
In Section IV, the fundamentals needed for the formulationof the optimization is given. In this section, we use thefundamentals to formulate the design problem. ˆ ω ∈ so (3) is the skew symmetric matrix formed by angular twistcoordinates lgorithm 1 Robust Differential Kinematic Solutions procedure D IFFERENTIAL I NVERSE S OLUTION2:
Initial configuration ← random seed Desired pose ← given by data e = 1 (cid:46) initialize error α = 0 (cid:46) step size while norm ( V ) (cid:54) = (cid:15) or k ≤ max do T sb ← FK ( θ ) (cid:46) current pose V ← [ Ad T sb ] log( T − T ) ∨ (cid:46) error in twistcoordinates J ← Spatial Jacobian ( θ ) if rcond [ JJ T ] < . then (cid:46) checksingularities J † ← JW − J T ( JW − J T ) + 0 . I n else J † ← JW − J T ( JW − J T ) end if θ ← θ + α J † V end while return θ end procedure
1) Geometric optimization for Morphology:
The model ofa robot is dependant on its geometrical parameters as well theinertial parameters. For fabrication and physical feasibility,optimization of geometrical parameters is easier to achieve,whereas inertial parameters are dependent on actuator vari-ants (e.g., brushed, brush-less DC, gearing, stiffness, etc.),fabrication material, and transmission mechanisms. In thispaper, we consider a task-driven manipulator optimizationwhere local variations of kinematic data from the tasksare used to optimize each of the symmetric manipulatorsof the system.
2) Gradient-free optimization for the above data metrics:
Since the cost function for the manipulator optimization isnon-linear, gradient-based optimization techniques are notwell suited. Hence we used simulated annealing to retrievethe optimal parameters. With an appropriate number ofiterations and uniform sampling over the design parametersspace, it can be assumed to converge to the optimal parameterset. Algorithm 2 shows the procedural pseudo-code of thesteps used.
3) Design Parameters:
In the optimization framework, weassume both the arms are symmetric . Thus, optimizationis done with symmetric arms on bi-manual tasks. Figure 6visualizes the design parameters that were used. Here, ¯ c i is the distance to each joint frame from the base frame { XY Z } B and ξ i is the twist at ¯ c i . ¯ d is the distance vectorto the first joint from the base frame. Moreover, we impose adesign structural constraint ( ¯ c = ¯ c = ¯ c ) for the wrist suchthat last three axes intersect ( ξ , ξ , ξ ). This is to ensurefabrication feasibility and prior morphological initialization.For certain bilateral tasks, the center distance ¯ d is impor- This is to facilitate, especially in teleoperation, right and left handdominancy
Fig. 6: Illustration of the Design parameters in the dualmanipulator systemtant. For instance, in tasks with a small work-space volume(e.g. soldering), the center distance between two manipula-tors could be small. This will allow inter-crossing betweentwo arms which is preferable in some tasks. However, thewider the center distance, the more convenient it becomes todo bilateral manipulation of larger objects.
4) Cost Function for Design Optimization:
Since theapplication focus of this work is to get a design candidatethat can achieve pose variations, we design the cost functionto achieve the desired poses and have a well-connectedworkspace. We define the cost function for design as: C = N (cid:88) i =1 δ p T W δ p + W (¯ q c [ i ] − ¯ q c [ i − (2)where, δ p = [ Ad T sb ] log( T − T ) ∨ , W and W areweighting matrices. To ensure a well-connected workspace,the error term (¯ q c [ i ] − ¯ q c [ i − between last and currentjoint vectors needs to be minimized. B. Design Optimization
We used simulated annealing (SA) for the optimizationof the post-processed data. SA was run with uniform re-sampling to select new candidates. At each iteration, themotion data set with the local cloud was added to the currentwrist pose ( ¯ c ) [Line 9 of Algorithm 1]. This is because thedata is normalized and the optimal dexterous pose of thewrist from the is not known beforehand. The optimizationprocess yields an optimal set of design parameters afteran appropriate number of iterations with no further notableimprovement. Data processing and optimization were donewith the aid of MATLAB c (cid:13) c (cid:13) was used in this work.VI. D ESIGN I NFORMED M OTION O PTIMIZATION
In Section V, the optimal pose (the distance vector andorientation from the base, ¯ c ) in which the robot is most T sb is the current pose and T is the desired pose lgorithm 2 Kinematic Optimization Routine procedure M ORPHOLOGY O PTIMIZATION2:
Robot Morphology ← twist and distance to axis err = 1 (cid:46) initialize error i = 0 (cid:46) iteration R = Robot Morphology (cid:46) initial robot D [ i ] ← post-processed local pose data, normalized while e (cid:54) = (cid:15) or i ≤ max i do D [ i ] ← D [ i ] + [¯ c , R ] (cid:46) adds current wrist poseto point data cloud C [ i ] ← IK Cost ( D [ i ]) Temp. = F [ i ] (cid:46) temp. exponential decay R i +1 ← G ( P [ R [ i ]] , Temp. ) (cid:46) new candidate(constrained) Update P [ R [ i ] , C [ i ]] (cid:46) update the distribution end while return R n (cid:46) Optimized Robot end procedure dexterous is calculated . Since this information is known apriori, it is possible to infuse this information to robot motiongeneration. A. Spatial Jacobian of the Manipulator Tree
We leverage the redundancy of the system in motiongeneration along with the design limitations and prior infor-mation (e.g., where the most dexterous location is relativeto the base). We propose a kinematic differential solver thatwill use the known information to optimize the configurationof the overall system. ¯ J = (cid:20)(cid:2) J K Ad T sk J L (cid:3) (cid:2) J K Ad T sk J R (cid:3)(cid:21) (3) ¯ J is the overall spatial jacobian of the system where, J K indicates the spatial jacobian of the global positioner system(industrial manipulator), J L and J R are the left and rightmini manipulators. In solving the differential motion, inverseof the ¯ J should be defined. B. Generalized Inverse
In comparison to single-arm serial manipulators, dual-armsystems have a higher order of redundancy. Thus, in orderto get inverse kinematic solutions[25], differential kinematicsolutions are often used. Kinematic redundancy of the systemcould be used to satisfy a secondary objective function inaddition to satisfying the desired pose ( ∈ SE (3) ). Theinverse of the Jacobian matrix for a redundant system is notunique and subject to satisfy a user-defined cost function. Acommonly used inverse is the MoorePenrose inverse where Data is local variations around a pose relative to the base || ˙ θ || = (cid:112) ˙ θ T ˙ θ is minimized. In general, the formulationcould be written as:min θ
12 ˙ θ T M ( θ ) ˙ θ + ∇H ( θ ) T ˙ θ subject to V d = ¯ J ( θ ) ˙ θ , θ ≤ θ ≤ ¯ θ where, H is a user defined artificial potential field (describedin Section VI-C). M ( θ ) is the inertial matrix of the overallsystem and V d is the desired spatial velocity. The solutionto this optimization could be written as : ˙ θ = G V d + ( I − G ¯ J ) M − ∇H (4) G = M − ¯ J T (¯ JM − ¯ J T ) − (5)where, ∇H is the partial derivative with respect to each jointcoordinate. C. Null Space Cost Function
We define a secondary cost function where we canleverage the redundancy and use the prior knowledge aboutmanipulator dexterity in the motion planner as shown in theFigure 6. The function can be expressed as: H = (cid:88) i = L,R ( ¯ w i − (¯ r i + ¯ t i )) T Q i ( ¯ w i − (¯ r i + ¯ t i )) (6)where, Q i is the weighting matrix, ¯ r i is the distance tothe current end-effector location of each arm, ¯ w i is thedesired pose of the desired workspace pose and ¯ t i is thetool geometry of the left and right arms respectively. Allvectors are defined relative to the { XY Z } B in the globalworld frame.Fig. 7: Bilateral system with desired workspace poses andcurrent pose of the manipulator system full derivation could be found on Appendix D of [24] Primary function is to get to the pose commanded by the user ig. 8: Motion of the global to maintain the dexterity throughtask transitions ( W → W ). D. Adaptation to Task through Inertial Matrix M ( θ ) In general, M ( θ ) is defined to be the mass matrix ofthe entire manipulator tree. We use the mass matrix witha scaling parameter to be adaptive to the task in hand. Forinstance, if the desired and predetermined dexterous work-space of the system is at a far distance, the cost of H ismade dominant. In such case, motion to the new work-spaceis achieved by the movement of the base. We modulate thescaling of the mass matrix of each segment via: M ( θ ) = diag (cid:0) ¯ M K ( θ K ) ¯ M L ( θ L ) ¯ M R ( θ R ) (cid:1) (7)where, M K ( θ K ) , M L ( θ L ) , and M R ( θ R ) are the massmatrices of the base manipulator, left and right arms re-spectively. Each of the mass matrices were scaled as desiredby the user and the task in hand. We used the followingcontinuous switching law where β i is the threshold of theactivation of each manipulator segment based on the left andright end-effector poses relative to the workspace. This canbe defined as a binary switching law if desired. ¯ M i ( θ i ) = (cid:0) tanh ( | w i − r i | − β i ) + 1 . (cid:1) M i ( θ i ) (8)Intuitively, the reasoning for the above-chosen scaling pa-rameters is as follows. The joint configuration is optimizedcontinuously while following the desired Cartesian trajectoryas commanded by the user. Secondary function for nullspace optimization is given by Eq. 6 and Eq. 8 updatesthe weighting matrices of each manipulator segment ofthe kinematic tree. This facilitates the user to manipulatethe relative motion of kinematic segments while leveragingdifferent bandwidth capabilities needed for the task (forexample, certain tasks need high bandwidths and manipulatorsegments with low inertia are better suited for actuation). E. Kinematic Differential Motion Control
Once the optimum design morphology was achieved, theoptimal distance vector to the dexterous location is known( ¯r = ¯ c ). It is to be noted that the obtained dexterity is only We used only the base manipulator with a activation function here valid when ¯r is maintained throughout the task completion.This objective is achieved through the continuous motion ofthe base using a weighting matrix M ( θ ) .Moreover, this motion can undesirable in cases wherethe system is teleoperated due to the change of the viewperspective. In such a scenario, the weights correspondingto the base could be made larger. On the other hand, in au-tonomous tasks, continuous optimization of the configurationcan improve task safety, performance, and dexterity. F. Conversion of PoE to DH
Once the optimum morphology of the system is found,we use the method used by [26] to convert obtained PoEparameters to DH (Denavit-Hartenberg). This conversion wasused as there isn’t a visualization tool for robot simulationwith PoE parameters. The visualization was done with theaid of Peter Corke’s robotics toolbox [27] with standard DHparameters (converted).VII. K
INEMATIC P ERFORMANCE E VALUATION
In order to evaluate the performance of the optimizeddesign and kinematic control scheme, standard performancemetrics were used. The global metric to asses the perfor-mance is can be written as: E = N (cid:88) i =1 (cid:16) max λ [ J i J Ti ]min λ [ J i J Ti ] − (cid:17) + det J i J Ti (cid:124) (cid:123)(cid:122) (cid:125) A + ( q − ¯ q ) + ( q − q ) (cid:124) (cid:123)(cid:122) (cid:125) B (9)where J i is the spatial jacobian and ¯ q and q are the jointlimits. A and B are the terms that corresponds to dexteritymeasure and joint limit constraint respectively.VIII. A NALYSIS
We explored the possibility of optimizing the manipulatorgeometry and then using the optimal design parameters in thekinematic motion generation. To evaluate the performancegain, we used two methods. 1) Kinematic dexterity compari-son over optimizing each individual task vs all tasks (shownin Figure 11). 2) Kinematic dexterity throughout the taskwith and without design informed motion (Figure 10)We used a data-driven approach to optimize morphologicaldesign parameters for a manipulator arm with seven DOFs(one of the symmetric arms). As discussed in Section V, wehad imposed morphological constraints to facilitate physi-cal feasibility. We show that the optimal design obtainedby utilizing pose data throughout all tasks would resultin a more versatile design morphology. Figure 11 showsthe performance comparison over three different tasks thatrepresent the motion characteristics. The performance metric(from Section VII) is normalized such that orientational andpositional metrics could be represented on the same axis.To show the successful incorporation of design infor-mation to motion, we chose two work-spaces adjacent toig. 9: Evolution of the design parameters over iterations. A few intermediate states.each other (as shown in Figure 8). We chose target posi-tions in work-space regions W and W . The goal was toswitch between these workspaces with and without designinformed motion optimization. Figure 10 shows dexterityevaluation during the transition. It can be observed thatdexterity throughout the duration is more uniform whendesigned informed motion generation is used. This is due tomotion compensation of the base throughout the task to keepthe dexterity of the bilateral system optimal. However, themotion of the base is not desired in cases where manipulationtasks require high bandwidth and precise performance. Insuch scenario, motion of each segment can be modulated bydefining custom thresholds in Eq. 8. This approach wouldfacilitate smooth transitioning and near uniform dexterityFig. 10: Performance comparison with and without designinformed motion optimization throughout task manipulation.IX. C ONCLUSION AND F UTURE W ORK
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