Design and Control of Roller Grasper V2 for In-Hand Manipulation

Shenli Yuan1,2, Lin Shao2, Connor L. Yako1,2, Alex Gruebele1, and J. Kenneth Salisbury2

Abstract— The ability to perform in-hand manipulationstill remains an unsolved problem; having this capabilitywould allow robots to perform sophisticated tasks requiringrepositioning and reorienting of grasped objects. In this work,we present a novel non-anthropomorphic robot grasper withthe ability to manipulate objects by means of active surfaces atthe fingertips. Active surfaces are achieved by spherical rollingfinger tips with two degrees of freedom (DoF) – a pivotingmotion for surface reorientation – and a continuous rollingmotion for moving the object. A further DoF is in the base ofeach finger, allowing the fingers to grasp objects over a rangeof size and shapes. Instantaneous kinematics was derived andobjects were successfully manipulated both with a custom hard-coded control scheme as well as one learned through imitationlearning, in simulation and experimentally on the hardware.

I. INTRODUCTION

In an effort to bring robots from the laboratory into realworld environments, researchers have endeavored to developincreasingly dexterous robots that can interact deftly withobjects. In order for such robots to take on a wide rangeof everyday tasks, they need to be capable of sophisticatedobject manipulation. Many vital higher-level tasks will relyon a robot’s capability to perform in-hand manipulation byre-orienting objects while maintaining the grasp. Out of allthe grasping and manipulation tasks, in-hand manipulationis among the ones that require the most dexterity.

A background of in-hand manipulation literature is pre-sented in [1] and a more extensive review of robot hands andgraspers is given in [2]. Common approaches to designingrobotic grippers that can perform in-hand manipulation are:anthropomorphic hands which take advantage of intrinsichuman dexterity, but due to the high number of degreesof freedom are complex and expensive [3] [4] [5]; under-actuated hands which passively conform to objects, achievinggood grasp stability, but at the cost of the controllabilityneeded to perform many in-hand manipulation tasks [6] [7][8] [9]; grippers with active surfaces (such as conveyors)which allow for the object to be manipulated without chang-ing grasp pose, but with a fixed conveyor orientation limitingpossible motions [10] [11] [12]

We developed a novel grasper design using articulated,actively driven spherical rollers located at the finger tips,shown in Fig. 1. By incorporating continuous rotating mecha-nisms, it is possible to create graspers that are highly capablebut relatively simple by design. The active surface achieved

*This work has been funded, in part, by the Stanford InterdisciplinaryGraduate Fellowship.

1Department of Mechanical Engineering, Stanford University2Stanford Artificial Intelligence Lab (SAIL), Stanford University{shenliy, lins2, clyako, agruebe2}@stanford.edu,

jks@cs.stanford.edu

Fig. 1. The Roller Grasper V2 prototype mounted on a UR-5 robot arm.Three fingers, each with three degrees of freedom, can grasp and reorientan object using rolling contact with the rubber coated rollers

by rolling and re-orientation of the spherical rollers allowthe grasper to perform in-hand manipulation without theneed for finger gaiting. Rolling contact on the object canbe viewed as a motion that continuously breaks contactwith the object while simultaneously re-establishing contactat adjacent locations. The ability to re-orient an objectto any direction also lessens the need to use externallyactuated degrees of freedom (e.g. actuation of the roboticarm and wrist) which simplifies the control scheme. Moreimportantly, the spherical design of the finger tips allowsfor stable grasps independent from the roller orientations,eliminating the need to analyze grasping modes for differentcombinations of roller orientations.

Learning robust policies for in-hand manipulation has beena long-standing challenge in robotics due to the complexityof modelling the object and grasper contacts and the diffi-culty of controlling finger motion in long and complicatedmanipulation sequences. Deep Reinforcement Learning hasbeen used to learn dexterous manipulation [13] [14]. How-ever, learning to hold the object firmly and stably whiletransforming the object with deep reinforcement learningrequires a much more significant amount of training episodesand a carefully designed reward function. To overcome theseissues, we used an imitation learning based approach tolearn a control policy in order to arbitrarily transform anobject while holding it. We demonstrated the effectivenessof this learned policy both in simulation and in real world

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experiments.Our in-hand manipulation system consists of a 3-fingered

grasper with spherical rollers at the fingertips, an overheadRGBD camera, objects with QR-tags, a naive control policy,and an imitation learning policy. Current robotic grasperseither lack the mobility to execute complex in-hand manipu-lation tasks, such as parallel jaw graspers, are underactuatedand difficult control, or are incredibly complex and difficultto control. Our system aims to perform complex in-handobject transformations with a robust control policy.

To the best of our knowledge, this paper is the first attemptat developing a grasper with active surfaces at the fingertipsthat transforms grasped objects through an imitation learningpolicy. We first discuss our previous iteration of this roboticgrasper as well as other design and algorithmic approaches torobotic grasping/in-hand manipulation (Section II). SectionIII then briefly describes the hardware. Section IV discussesthe formulation of the handcrafted control policy as well asthe imitation learning approach. The paper then provides anoverview of the experimental setup in simulation and in reallife, and concludes by reporting and discussing the results(Section V and Section VI).

II. RELATED WORK

A. Previous Grasper Design

Our previous work [1] used articulated, actively drivencylindrical rollers at the fingertips of a grasper to exploreimparting motion within a grasp using active surfaces. Thegrasper used three modular 3-DoF fingers, and demonstratedfull 6-DoF spatial manipulation of objects including a sphere,cube, and cylinder, as well as various grasping modalities.One limitation of the previous roller grasper is the graspstability. Due to the cylindrical design of the finger tips,several grasping configurations are unstable, resulting inundetermined manipulation behaviors. The redundant com-binations of grasping configurations also complicates thecontrol scheme as the configuration used is dependent onspecific manipulation tasks and object being manipulated.

B. In-Hand Manipulation

In-hand manipulation is an age-old question in roboticswith a rich literature, from two-fingered grippers [15] [16],to dexterous hands [13]. We briefly review the relevant in-hand manipulation works in this subsection. To achieve in-hand manipulation, multi-fingered dexterous hands utilize theredundancy of the fingers to move the object while holdingit. Under-actuated hands are able to leverage model basedcontrol [17] for in-hand manipulation tasks. There are alsotask-specific designs of under-actuated hands which enablea limited set of re-positioning skills [18] [19].

Other approaches to in-hand manipulation have been ex-plored which rely on gravity with controlled slip [20] [21],induced accelerations [22] [23], or the environment [24][15] [25] to reduce dexterity required of the hand. Howeversuch approaches require complex controls or dependency onavailable geometry in the environment.

Contrary to modeling the complex dynamics involved ingrasping and object reorientation, some researchers haveopted to use reinforcement learning (RL) to search foroptimal policies. This is especially useful when using un-deractuated graspers or graspers with high DoF’s. In [26] anunderactuated grasper with tactile sensors on the fingertipswas used to horizontally slide a wooden cylinder back andforth by rolling it along each finger. The learned policy wasevaluated on cylinders of different masses, sizes, and frictioncoefficients. They found that the policy performed better thana hard-coded control policy, which was used as a baseline,but still struggled with cylinders with low-friction properties.RL has also been implemented successfully on the 24 DoFShadow Hand for dynamically moving a cylinder in-hand(model-based RL) and for arbitrarily re-orientating a cubeusing visual information [13] [14].

In our manipulation tasks, we aim to learn a robust controlpolicy in order to transform a given object that is heldsolely by friction at the roller contact. This means that atiny perturbation of the finger tip could possibly break thecontact and lead to a dropped object. Therefore, the spaceof successful policies is incredibly small relative to theentire policy space. Since exploration is necessary in anydeep reinforcement learning problem, it is difficult for thealgorithm to converge to the optimal policy. To overcome thisproblem, we instead adopted an imitation learning method,which will be discussed in the next section.

C. Imitation Learning Methods

Imitation learning aims to learn control policies by ob-serving expert demonstrations. There are in general twotypes of approaches to tackle an imitation learning problem.Behaviour cloning aims to train the agent to learn a mappingfrom observations to actions given demonstrations, in asupervised learning fashion [27] [28]. Another approach isInverse Reinforcement Learning [29], which attempts to learna reward function that describes the given demonstrations.Our method falls under the scope of Behavior Cloningwhich has led to many successes in robotics [30] [31]; ourapproach is based on one Behaviour Cloning method calledDAgger [28]. To tackle the problem of generating expertdemonstrations, we also develop a method to accumulatethe demonstration examples iteratively starting from a fewexpert demonstrations.

III. DESIGN

A. Hardware Design

The gripper (Fig. 2A) consists of three fingers, eachhaving three degrees of freedom (DoF). The first DoF isat the base of each finger and consists of a revolute jointdirectly driven by a Robotis Dynamixel XM430-W350 smartactuator. The other two DoF are located at each fingertip,and are responsible for steering and rolling. The secondjoint shown in Fig. 2A is orthogonal to the first DoF, andis driven by a micro DC motor with built-in gearbox andquadrature encoder (Servocity Part 638099). For a compactform-factor, this actuator is located remotely from the axis

Fig. 2. A CAD model of the grasper: (a) the three degrees of freedom each finger has (b) an exploded view of each finger (c) an exploded view of theroller assembly that contacts the object being manipulated

of rotation through a timing belt (Fig. 2B), and allows theroller assembly to be pitched up to 180 deg. The finalDoF is actuated using the same type of geared motor buthoused inside the roller assembly (Fig. 2C), allowing it toperform continuous rotation of the spherical contact surfacewithout its cables winding. The roller is encased in a pairof 2 mm thick semi-spherical silicone covers (SmoothOnMoldStar 16) to provide a high-friction surface for graspingand manipulation. The reference frame and key dimensionsof the grasper is shown in Fig. 4. The whole grasper weighsapproximately 700g, and each finger is capable of outputtinga maximum 33.6 N of force at its fingertip.

B. System Architecture

The system architecture used to operate the gripper isshown in Fig. 3. A high-level API was developed to interfacethe low-level (hardware) information to the manipulationalgorithm or user input. Information transferred during thebidirectional communication includes positions for each jointof the fingers, the current limit of the base joint, as well asthe control parameters for controlling the motors. Current tothe Dynamixel motors is used to set the stiffness of the basejoints and measure force exerted by the object on each fingerduring manipulation.

A Teensy 3.6 microcontroller is used to handle communi-cation with the high-level API as well as low-level controlof the motors. The six micro gearmotors located at theintermediate joints and within the rollers are controlled byPD position controllers handled by the microcontroller. TheDynamixel motors each run local PD control and commu-nicate with the Teensy microcontroller through a TTL half-duplex asynchronous serial communication protocol.

IV. TECHNICAL APPROACH

In this section we begin by describing the analyticalapproach that led to development and implementation of ahandcrafted control policy. This control policy was then fine-tuned based on simulation results in order to act as an expert

Fig. 3. System architecture

trajectory generator for the imitation learning. The controlpolicy to rotate an object firmly and stably is usually within asmall region in the police function space. A tiny perturbationof the demonstrator’s control policy may lead to unstableand even unsuccessful within hand manipulation result. It’sbecomes a critical problem when exploration is necessaryfor deep reinforcement learning. We barely get stable graspsduring the training stages of deep reinforcement learningexperiments. Experiments demonstrates that it requires asignificant time and effort for deep reinforcement learningapproaches to explore and is extremely difficult to find theoptimal policies . Instead we adopt an imitation learningapproach and demonstrate that it is effective and efficient.

A. Analysis

Manipulating an object through rolling contact can beviewed as navigating the rollers on the object. Therefore,an object transformation can be achieved by navigating therollers from their initial contact locations to the desired finalcontact locations. While there is no unique solution for thepaths the rollers take during their navigation for given initialand final grasping poses, it is possible to solve, or thisnon-holonomic system, for the instantaneous joint velocities

Fig. 4. Reference frames of each of the three joints within eachfinger, relative to the base coordinate system. Dashed lines indicate neutralpositions from which joint angles are measured. (a = 48mm, b = 122mm,r = 21.5mm)

based on known (1) object geometry, (2) object pose, (3)object velocity, and (4) contact conditions (rolling withoutslipping).

Object geometry and pose are necessary to calculate thecontact locations, which determine the relationship betweenjoint motions and given contact motions on the rollers (thecontact jacobian matrix). Knowledge of object geometry,pose, and roller contact locations can be used to map thedesired object motion to the motions at the contact point onthe object. Applying the contact condition of rolling withoutslipping means that the contact velocity on the object andthe contact velocity on the roller are equal. Thus, inversekinematics can be used to calculate the joint velocitiesrequired for a desired object motion, a process similar tothe calculation of geometric stiffness for grasping presentedin [32].

The problem is formulated as follows: given the object’sinitial and target position and orientation, compute the con-tact location and contact motion on the roller, and thencompute the pivot joint orientation and motions of the base

Fig. 5. Contact motion breaks down to two components

and roller joints.Given the desired motion of the object and known contact

locations, we can obtain the contact motion by

δxcontact = Jobjδxobj (1)

where Jobj is the jacobian matrix mapping object motion tothe motion at the contact frame.

On the other hand, with the contact motion δxcontact, theobject position xobj , and roller position xroller all known,the contact motion can be interpreted as the motion at thecontact location due to the movement of the 3 joints:

δxcontact = Jθδθ (2)

Where Jθ is the contact jacobian matrix for mapping fingerjoint motions to motions in the contact coordinates, andδθ is a vector of joint motions of the finger. In manyrobotics applications δθ is determined directly by solving(2). However, this method is not particularly applicable tothis gripper design for the following reasons:

1) The contact locations are very close to the pivot jointso the finger is always close to a singularity.

2) The pivot joint has a joint limit of [−π2 ,π2 ] meaning

that in many cases the instantaneous velocity requiredfrom the pivot joint to achieve the desired contactvelocity cannot be reached.

Therefore, instead of carrying out the full inverse kine-matics, we divide the contact motion into two components:the component resulting from the motion of the base joint,δxcb, and the component resulting from the rolling, δxcr.The pivot joint is used to reorient the roller so that therolling direction at the contact point is aligned with δxcr.This approximation is sufficient because (1) when the contactlocations are close to the pivot axis, the pivot motion doesnot move the object much, and (2) the object being grasped isover constrained by the three fingers, so using the soft fingermodel [33] to approximate roller contacts, the torque exertedby pivoting is compensated by the lateral frictions from thetwo other fingers. Thus, the singularity is advantageous inthat it enables sole use of the pivot joint to align the rollerin order to achieve δxcr.

We developed a naive control strategy based on the aboveformulation with some modifications that fit the gripperdesign. The handcrafted control policy tested in simulationand on the hardware assumes that the object geometry isspherical with radius R. Specifically, the below calculationsare for a single finger, but can be applied to the twoother fingers as well. For the simplicity of notation, we usesubscript 1, 2, and 3 to represent the base joint, pivot joint,and roller joint, respectively, and leave out the subscript A,B or C because the following derivation would be identicalfor each finger.

In order to obtain δxcb and δxcr, we need to projectδxcontact onto Z2 and the contact plane (Fig. 5). The contactplane can be described by its normal vector ~ncon:

n̂con =xobj − xroller||xobj − xroller||2

(3)

Using the fact that δxcr is orthogonal to n̂con and is alsoin the plane formed by δxcb and δxcontact, we can computethe direction of δxcr as:

δ̂xcr =(δxcb × δxcontact)× n̂con||(δxcb × δxcontact)× n̂con||2

(4)

It is also easy to find that the direction of δxcb aligns withZ2:

δ̂xcb = Z2 (5)

Projecting δxcontact onto δ̂xcb and δ̂xcr gives δxcb and δxcr.It is equivalent to solving α and β in equation:

δxcontact = αδ̂xcb + βδ̂xcr (6)

By cross multiplying δ̂xcb and δ̂xcr to (6), respectively, wecan solve for α and β, and the resulting δxcb and δxcrare shown below. Note that n̂z is only used to extract themagnitude from the cross products.

n̂z =δ̂xcr × δ̂xcb||δ̂xcr × δ̂xcb||2

(7)

δxcb =n̂z · (δ̂xcr × vcontact)n̂z · (δ̂xcr × δ̂xcb)

δ̂xcb (8)

δxcr =n̂z(·δ̂xcb × vcontact)n̂z · (δ̂xcb × δ̂xcr)

δ̂xcr (9)

The joint velocity of base joint (ω1) and roller joint (ω3) canbe calculated using inverse kinematics.

The final step is to calculate the pivot angle θ̂2 to alignthe rolling direction with δ̂xcr:

Z3 = ± Z2 × δ̂xcr||Z2 × δ̂xcr||2

(10)

Note that because there is a joint limit at the pivot, weare limiting Z3 to always have a component along the Z0

direction. The pivot angle θ2 can be calculated by

θ2 = arccos(Z1 · Z3

||Z1||2||Z3||2) (11)

The above process only describes how each joint shouldmove given the instantaneous desired velocity of the object;no path planning is used for navigating the rollers giventhe initial and target poses of the object. In our case, wesimply compute the difference between the initial and targetpose, and set the desired velocity equal to a scaling factormultiplied by this computed difference: δxobj = λ∆xobj .This method works very well for convex objects whoseradii of curvature do not change drastically. Experimentalvalidation of manipulating a sphere will be shown in SectionV.

B. Handcrafted Control Policy

The handcrafted control policy is formulated accordingto the results from the previous section. Given the currentobject position and orientation, the target object positionand orientation, and the current joint values, the positionsof all nine joints are calculated for the following timestep.One difference between the implemented policy and thetheoretical policy is that the base joint velocities are notcontrolled based on the derivation above. Instead, they areposition controlled to a setpoint located inside of the objectin order to maintain contact with the object. This is becausewe are focusing on the rotation of the object instead oftranslation. The main purpose of the base joint in our caseis to keep the rollers in contact with the object.

C. Imitation Learning Algorithms

We adopted imitation learning in order to learn how totransform an object. Imitation learning aims to learn controlpolicies by observing demonstrations. Within imitation learn-ing our method mostly resembled Behavior Cloning, whereour model learned the optimal policy through given expertdemonstrations. This method is particularly useful when itis difficult to explicitly specify the reward function or thedesired policy.

In our case, the state space is defined as |S| ∈ R35, andconsists of the following: the current state of the grasper(s1 → s9), current object position (s10 → s12), currentobject orientation quaternion (s13 → s16), previous objectposition (s17 → s19), previous object orientation quaternion(s20 → s23), object initial position (s24 → s26), object initialorientation in angle-axis representation (s27 → s29), objecttermination position (s30 → s32), and object terminationorientation in angle-axis representation (s33 → s35). Theaction space is defined as |A| ∈ R9 and contains the ninejoint positions (a1 → a9).

We constructed a deep neural network to determine theactions for each of the nine gripper joints. The networkconsisted of three fully connected hidden layers with leakyReLU activations, execpt at the output layer, and 256 nodesin each hidden layer.

The handcrafted control policy from the previous sectionwas used to generate N expert trajectories, which are simplyseries of state-action pairs. The ith trajectory is defined as:

T (i) = [(s(i)0 , a

(i)0 ), (s

(i)1 , a

(i)1 ), . . . ] (12)

We first trained our policy π0(si) to predict the expertaction by minimizing the loss L between π0(sij) and aij ina supervised approach:

Lij = ‖π0(sij)− aij‖2, ∀ sj ∈ |T i|, i ∈ N (13)

Subsequent policy updates are computed according to DAg-ger [28], however, our case is formulated as a regressionproblem instead of a classification problem.

We also implemented a method to increase the numberof expert demonstrations iteratively. For a given object,

every object transformation trajectory is specified by a 12-dimensional vector containing the object starting and tar-get position and orientation: (xiobj,s, q

iobj,s, x

iobj,t, q

iobj,t). By

imitating the expert demonstration examples, we learn apolicy supported by these expert demonstrations. This controlembedding is able to interpolate between known trajectoriesusing a nearest neighbor policy in order to generate trajec-tories for previously unseen transformations.

Based on the learned policy, we accumulate nearby trans-formations. Let D = (xiobj,s, q

iobj,s, x

iobj,t, q

iobj,t) represent

the transformations which our policy already knows. If aninterpolated trajectory transformation is nearby to one of thetransformations in D, we add the transformation to D, andthen continue to train our policy based on the transformationdemonstrations in D. Through this fashion, we kept growingand maintaining a traversable graph of transforming theobject between various poses, similar to [34]. The learnedcontrol policy could also be treated as an efficient initializa-tion for a deep reinforcement learning approach or motionplanning for in hand manipulations.

V. EXPERIMENTS

A. Simulation Experiments

Mujoco 2.0 was used to simulate both the hand craftedcontrol policy and the learned policy before transferringthem to the physical setup (see Fig. 6). By default, Mujocoassumes a soft-contact model which leads to tendencies toslip at the contacts, but the solver parameters (solref andsolimp) were changed to better model the friction betweenthe object and the spherical rollers. An elliptical friction conewas used along with the Newton solver to evaluate theseconstraints.

The gripper was modeled in the software, and the follow-ing parameters specified. The base joints had a gear ratioN = 3, were position controlled, and had their force outputclamped; these settings allowed the fingers to act compliantlyand conform to an object’s shape as it was reoriented, andstabilized the grasp. A higher gear ratio of N = 10 was usedfor the pivot joints to prevent them from being backdrivenby the object. The pivots also had a rotation range from[−π2 ,

π2 ] (with the zero position corresponding with the pivot

aligned along the length of the finger) in order to representthe limited range in the physical setup due to motor wires.A pivot rotation threshold of 3◦ per timestep was used to

Fig. 6. A visualization of our simulation in Mujoco. In simulation thegripper maintains the same physical design as the real gripper.

Fig. 7. Top row: the cube being manipulated from a starting positionshown on the left. Bottom row: the novel object, a rectangular prism beingsimilarly manipulated

prohibit quick jumps between the two rotation limits in favorof smoother motion that stabilized the simulation.

Sensors were placed at all nine joints to read joint posi-tions and two sensors were placed on the object to obtainits orientation (quaternion) and 3D position relative to theglobal frame. The learned policy outputs values for all ninejoints. The handcrafted control policy only used the latter twosensors and the base joint positions to calculate the outputvelocities for the pivots and rollers at every timestep.

Experiments were run by specifying a desired orientationin angle-axis representation

([x, y, z]T , θ

). Most experi-

ments were carried out with a 6 cm cube with a mass of32.4 grams that had a starting quaternion of q0 = [1, 0, 0, 0].Rotation angles were specified as 90◦ in the majority ofexperiments to ensure that the rollers had to traverse acrossthe edges of the cube. Rotation axes ranged from morevertical axes – which were generally easier for the simulationto realize – to purely horizontal axes which were moredifficult.

B. Experimental Setup

The experimental setup included the grasper, an overheadIntel Realsense D400series RGBD camera, and various 3Dprinted objects including a cube, a cube with filleted edges,and spheres of various masses and sizes. The handcraftedcontrol policy was able to be run both open-loop and closed-loop. Since object orientation and position were used as inputto the control policy, only the cube was run in the closed-loopoperation with QR-tags on all 6 faces. Open-loop runs withthe spheres were used to qualitatively verify the handcraftedcontrol policy on the hardware.

At the start of each experiment the fingers would spreadout, allowing a human operator to hold the cube at approx-imately the initial position specified for that particular trial.The fingers would then move inwards and grasp the object.At every timestep the joint positions, object orientation, andposition would be read-in, from which the correspondingjoint output would be calculated and sent to the actuators.

Fig. 8. Orientation error for real world experiment results. The vertical axesrepresents the orientation error defined in V-C. The horizontal lines repre-sents various experiments. S D and N denote simple manipulations tasks,difficult manipulation tasks and novel object transformations,respectively.

C. Evaluation Metric

We adopted the orientation error metric suggested in [35]which can be computed by using the sum of quaternions andnormalizing. Given the desired object orientation, qobj,d, andthe current object orientation, qobj,c, the error is calculatedas the following:

eω = 100min(||qobj,d − qobj,c||2, ||qobj,d + qobj,c||2)√

2(14)

VI. RESULTS AND ANALYSIS

The results of the experiments carried out on the hard-ware are presented in Fig. 8. All reported percent averageerrors were calculated according to (14). The experimentswere divided up as follows: simple transformations, whichhad axes of rotations with strong ZG components, difficulttransformations, which had axes of rotations with strong xand y components, and novel object transformations, whichconsisted of transforming an elongated rectangular prismwith filleted edges (6 cm × 6 cm × 8 cm) (Fig. 7). Thereason transformation with strong ZG component rotation iseasier is due to the three-finger design of the grasper, leadingto a much better force closure around XG−YG direction thanthe ZG direction. All experiments specified the target as anaxis and a 90◦ rotation about that axis. This choice of arotation angle is described in Simulation Experiments.

A. Simple Test Cases & Simulation to Real Transfer

The imitation learning method performed better for 3 outof the 5 simple transformation cases (S1 → S5). The averageorientation error across these 5 trials shows that the imitationlearning method (15.3%±2.2%) and the handcrafted controlpolicy (13.6% ± 7.2%) are comparable when performingobject rotations about more vertical axes. However, thehandcrafted control policy has more than 3 times the standarddeviation of the imitation learning.

As with any physical system there is a performance dif-ference when compared to the simulation setup. Fortunately,this difference was small with the imitation learning’s resultsin simulation reporting an average error of 12.7%. We believe

this is due to inclusion of sensor noise in the simulation, aswell as fine tuning of the contact model to more closely alignwith observations of the physical system performance.

B. Untrained Target Pose Test Cases

For the difficult transformations (D1 → D6), the imitationlearning outperformed the handcrafted policy across all 6trials by an average percent average error of 16.0%. Threeof these trials, D1 → D3, including target poses not trainedon in simulation. Overall, the imitation learning achieved apercent average error of 25.3%±4.2%, while the handcraftedcontrol policy achieved 41.3%± 5.8%. Again, the imitationlearning was able to demonstrate more stable trajectoriesdespite the sensor noise.

C. Novel Object Test Cases

Tests with the novel object (N1 → N2), a rectangularprism, demonstrated similar results to the simple transforma-tion case. The percent average errors were comparable be-tween imitation learning (17.1%±3.9%) and the handcraftedcontrol policy (20.3% ± 10.3%). However, the handcraftedcontrol policy had a much higher standard deviation.

D. Discussion

Imitation learning was successful for a couple of reasons:(1) the policy was learned from noisy sensor data whichincreased its robustness, and (2) the discovery of safe andrepeatable trajectories. The handcrafted control policy alwaysgenerated linear trajectories from the current position to thetarget. However, in many cases, especially for rotation axeswith dominating horizontal components, taking a linear pathcan lead to the gripper dropping the object. As the object isrotated closer to the desired axis of rotation, one or more ofthe rollers can roll onto a surface where the contact normalhas a −ZG component; the contact normal can overcomethe frictional support provided by another roller and resultin dropping the object. This problem can be mitigated byincreasing the positional compensation in order to moreactively control the object height. Unfortunately, placinga greater emphasis on controlling the object position wasseen to cause previously successful trajectories to fail. Nocombination of gains was seen to work across all observedsuccesses. This suggests that the gain space is of too low di-mensionality to define all of the successful linear trajectories,and that non-linear trajectories may provide an advantageousalternative. While the former statement was not explored inthis work, our results demonstrate the latter to be true.

VII. CONCLUSION AND FUTURE WORK

This paper presents Roller Grasper V2, a new design fora grasper based on steerable spherical rollers located at thefinger tips. The hardware design choices and engineeringdetails were provided. A naive control policy was constructedthat utilized the active surfaces of the rollers to transforman object to an arbitrary target pose. This control policywas used to generate expert trajectories in order to developan imitation learning based policy. This learned policy was

able to interpolate between learned trajectories in orderto successfully reach new targets; these new trajectorieswere placed in a buffer of known trajectories in order todevelop a traversable graph. Experiments for the handcraftedpolicy and the learned policy demonstrated the utility of thisgraph for generating safe trajectories, as the learned policyoutperformed the handcrafted policy for all difficult targetposes. For simple cases, the two policies performed com-parably, except the learned policy had much lower variancein the trajectory. Future work includes developing a novelmechanism that solves the non-holonomic constraints andincorporating tactile sensing on the rollers to provide high-fidelity feedback.

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