Inferring and Assisting with Constraints in Shared Autonomy

Transcription

1 2016 IEEE 55h Conference on Decision and Conrol (CDC) ARIA Resor & Casino December 12-14, 2016, Las Vegas, USA Inferring and Assising wih Consrains in Shared Auonomy Negar Mehr, Robero Horowiz, Anca D. Dragan Absrac Our goal is o enable robos o beer assis people wih moor impairmens in day-o-day asks. Currenly, such robos are eleoperaed, which is edious. I requires carefully maneuvering he robo by providing inpu hrough some inerface. This is furher complicaed because mos asks are filled wih consrains, e.g. on how much he end effecor can il before he glass ha he robo is carrying spills. Saisfying hese consrains can be difficul or even impossible wih he laency, bandwidh, and resoluion of he inpu inerface. We seek o make operaing hese robos more efficien and reduce cogniive load on he operaor. Given ha manipulaion research is no advanced enough o make hese robos auonomous in he near erm, achieving his goal requires finding aspecs of hese asks ha are difficul for human operaors o achieve, bu easy o auomae wih curren capabiliies. We propose consrains are he key: mainaining ask consrains is he mos difficul par of he ask for operaors, ye i is easy o do auonomously. We inroduce a mehod for inferring consrains from operaor inpu, along wih a confidencebased way of assising he user in mainaining hem, and evaluae in a user sudy. I. Inroducion Decades ago, indusrial robos were developed o auomae diry, dull, and dangerous asks, and hey purposely eschewed human involvemen for reasons of speed and safey. In sark conras, a new generaion of medical and healh care robos is designed for direc ineracion wih human users in environmens such as he surgical heaer, he rehabiliaion cener, and he family room. Teleoperaed robos such as he da Vinci Surgical Sysem are used o perform minimally invasive surgery around he world, resuling in shorer recovery imes and more reliable oucomes in selec procedures [1] [3]. Physically assisive sysems are being developed for in-home use o help limied mobiliy users wih Aciviies of Daily Living (ADLs) [4] [7]. These robos have he poenial o help docors and paiens alike wih performing asks ha are difficul for hem o accomplish wih heir own body: robos have access o quaniaive daa abou asks and environmens, and can move accuraely wihou iring. Despie his, inegraing hem wih human users sill presens significan challenges in performance and user accepance, for wo reasons. On he one hand, eleoperaing and conrolling hese robos is edious and does no ake advanage of many of he poenial advanages of arificial inelligence and robo mechanisms. On he oher hand, curren manipulaion research is no advanced enough o make hese robos auonomous in medical and healh care environmens in he near erm. Our insigh is ha here are imporan aspecs of manipulaion asks ha are difficul for human operaors o achieve, bu relaively easy o auomae wih curren capabiliies. Raher han aemping full auomaion, we propose o auomae hese aspecs. We focus on ask consrains as he key, because mainaining ask consrains is he mos difficul par of many asks for human operaors, ye auonomous sysems can easily keep rack of and saisfy muliple consrains. Figure 4 shows examples of consrains encounered in ADLs, including orienaion and posiion consrains: in order o place a book in he book shelf, is orienaion needs o be aligned wih he oher books; o wipe a board, he end effecor is consrained o move along he plane of he board; or he end effecor has o raverse an arc when opening he door of a refrigeraor. Two challenges make assising human operaors wih mainaining asks consrains difficul: 1) inferring which consrain he operaor is rying o enforce, and 2) deciding how o provide assisance once a consrain is inferred. Our conribuions are in line wih hese challenges: Consrain Inference: Typically, consrain inference is done from muliple demonsraions of he same ask [8] [11]. In shared auonomy, however, he robo needs o infer he consrain from a single ongoing execuion of he ask. We inroduce a consrain inference algorihm, capable of online inference of ask consrains from he ongoing sream of user s conrol inpus and rajecory of he robo in he ask space. Our approach is based on he Mowing Window KPCA [12], a varian of Kernel Principle Componen Analysis (KPCA) [13]. This enables he robo o handle non-linear consrains online, inferring he consrain solely based on he mos recen conrol inpus in order o make he compuaion real-ime. Moving Window KPCA idenifies a consrain in feaure space. To enforce he consrain, he robo has o firs map he user inpu ino feaure space, and hen projec i ono he consrain. This gives he robo a direcion in feaure space, bu does no idenify he consrain in ask space. We conribue a preimage learning echnique ha learns o approximaely projec a feaure space direcion back in he robo s ask space, which he robo can hen follow (e.g. via Jacobian-based or IK-based conrollers). Assising wih (Changing) Consrains: Given a prediced consrain, he robo has o decide how and how much o assis he user. One opion is o enforce he /16/$ IEEE 6689

2 (a) Orienaion Consrain (b) Posiion Consrain - Plane (c) Posiion Consrain - Disance Fig. 1: Example consrains for ADL-assisive roboics wih a Kinova arm ha will be mouned o a wheelchair. prediced consrain, bu his can be caasrophic if he robo has he wrong predicion. Building on [14], we propose o mediae assisance by he robo s confidence in he consrain. We inroduce a confidence measure capable of dealing wih he fac ha consrains may be changing over ime, or ha he user migh be going from no consrain o a consrain and vice-versa. User Sudy Evaluaion: We conduc wo user sudies wih novice users in which we measure he effeciveness of our algorihm in assising users wih mainaining ask consrains. When dealing wih a single consrain, our resuls suppor ha users prefer o be assised by he robo, and heir objecive measure of performance improves significanly by means of assisance. When dealing wih swiching consrains, our measure of confidence enables he robo o sop assising and make i easier for he user o perform he swich, improving subjecive and objecive measures. II. Relaed Work Shared Auonomy. The very firs insance of shared auonomy (or shared conrol) was in manipulaors uilized for ransporing radioacive maerial, where he low accuracy of user conrol inpu can lead o violaing safey crieria [15]. Since hen, various mehods have been inroduced [16] [21]. [14] characerized he problem of shared conrol in asks where here is coninuous user inpu as arbiraing beween he user inpu and a robo prediced policy, showing how many algorihms insaniae his characerizaion by using differen predicors and differen arbiraion funcions. This is he paradigm we adop as well. However, insead of predicing he operaor s desired goal and assuming ha he robo can achieve i as in [14], we predic desired consrains. This requires more limied robo capabiliy, ye sill capures a difficul aspec of he ask for he operaor. Virual Fixures. Virual fixures [22] are he mos relaed ype of shared auonomy o he opic of his work. Virual fixures assis he operaor wih mainaining consrains by consraining or guiding eiher he user s inpu or he robo iself [23], [24]. Implemenaions in absrac and surgical environmens have demonsraed he effeciveness of saic virual fixures, as well as he role of hapic feedback in wo-degree-of-freedom guidance [25] [27]. Thus far, he assumpion has been ha he robo knows he consrain (fixure) o mainain. In his work, we enable he robo o infer i from operaor daa and conrol inpus. This is no only an inference challenge, bu also an assisance challenge because he robo is no longer cerain of wha fixure or consrain he user wans. Consrain Inference. Alhough inferring consrains has no been acively sudied in eleoperaion, i has been a focus in Learning from Demonsraion [28]. There, consrains are idenified as he invarians among a se of demonsraed rajecories for he same ask [8] [11]. Unlike Learning from Demonsraion, our robo does no ge access o muliple raining rajecories for he same ask. Insead, in eleoperaion, he robo needs o infer he consrain being mainained along a rajecory online, as he rajecory is being observed. III. Problem Saemen In his secion, we formulae he problems of consrain inference and assisance. A. Online Consrain Inference Le s S denoe he sae, here he end-effecor ask space in SE(3) and u U be he conrol inpu ha he user provides (via some inerface, e.g. a joysick) a ime. We represen a consrain ha a user migh aemp o saisfy, e.g. keeping a bole of waer uprigh, as he zero se of some funcion h of he sae s. The se of saes saisfying a consrain c denoed by S c S is: S c = {s h(s) = 0}, h : S R + (1) Given he operaor s conrol inpu from he saring ime o he curren ime sep, u 0,, u, and he robo rajecory so far, s 0,, s, he consrain inference problem requires finding he funcion h ha characerizes he consrain he operaor currenly wans o mainain. 6690

3 B. Assisance wih Mainaining Consrains Once he robo has an inference of he consrain, he quesion is how o deploy his predicion in assising he user. Paricularly, given he curren sae s, he user inpu u, and he curren predicion h, he robo needs o decide wheher and how o modify u o assis he user. IV. Inferring and Assising wih Consrains A. Online Consrain Inference Given he saes, L = {s 0,, s }, ha noisily saisfy a consrain h, along wih he user inpu vecor {u 0,, u } he goal is o infer h. Because he zero se of h is a manifold in S, manifold learning is a naural choice for idenifying he consrain. Manifold learning algorihms aemp o find a lower dimensional represenaion of given poins such ha a cerain proximiy crieria is me in a lower dimensional subse of daa poins. There exiss a large number of manifold learning algorihms [29] [33] ha could possibly be uilized in inferring h. The disincion beween he exising manifold learning algorihms arises from he ype of proximiy crieria ha hey ry o opimize, or he class of funcions hey can learn for h. Consrain inference raises some requiremens for manifold learning ha narrow down which algorihms are applicable. Firs, manifolds migh be non-linear. Second, manifolds need o be learned online, in real ime, as he operaor s inpu daa is coming in. Kernel PCA The requiremens above poin o Kernel Principle Componen Analysis [13] (KPCA) as he basis of our work. In his mehod, principle componens can be found in a non linear feaure space defined by he choice of a kernel funcion. KPCA maps he daa poins o a non linear, possibly infinie dimensional feaure space F, hrough a non linear feaure mapping φ: s φ(s) F, and compues principle componens of he mapped daa poins, {φ(s 0 ),, φ(s )}, in he obained feaure space. Nominally, his would be achieved by compuing he eigenvecors of he covariance marix C of mapped daa poins in F: C = 1 φ(s i )φ(s i ) T (2) i=1 The main idea behind KPCA is o compue he principal componens wihou ever mapping he daa o feaure space, or even explicily defining φ. Insead, KPCA operaes by inroducing a kernel funcion k and implicily defining φ such ha k(s i, s j ) = φ(s i ), φ(s j ). I consrucs a kernel marix K via K ij = k(s i, s j ). Each principle componen, v l, can be wrien as a linear combinaion of φ(s i ) s: v l = αi l φ(s i). (3) i=1 The vecor of coefficiens α l i, denoed by αl, can be compued solely from K by solving: λα = Kα, (4) where λ is an eigenvalue of K, and α is is corresponding eigenvecor. Noe ha in he above, for he sake of simpliciy, we have assumed ha he daa is cenered in he feaure space, i.e. i=1 φ(s i) = 0. In general, his does no need o hold. In ha case, we need he eigendecomposiion of he Gram marix G insead of K: G = K 1 KE 1 E K E KE, (5) where E is he marix wih all enries equal o 1. See [12] for more deails. Noe ha he oupu of KPCA is he se of vecors α. As a resul, he projecion of a sae s on he l h kernel principle componen of daa poins can be compued from α l using he kernel funcion, wihou explicily compuing φ(s): v l, φ(s) = = i=1 α l i φ(s i), φ(s) (6) αi l k(s i, s), (7) i=1 where α l i is he ih enry in he vecor of αs corresponding o he l h kernel principle componen. Projecing s on h in feaure space means projecing φ(s) ono he firs D principle componens according o he larges D eigenvalues: Ps = D v l, φ(s) v l=1 l, v l v l (8) We discuss raising Ps back ino ask space in "Enforcing an Inferred Consrain" below. Online KPCA Running KPCA over he enire se of user provided saes and conrol inpus is compuaionally prohibiive. We make KPCA online by using a finie ime horizon: a moving window where he newes user inpu poin replaces he oldes one, and we reuse compuaion from he previous sep whenever he window moves. We perform KPCA for a rolling consan lengh horizon of M daa poins, L = {s M+1,, s }. This implies ha a ime + 1, a new daa poin, s +1 is received and he very firs elemen of he horizon of daa, s M+1, is removed from he hisory of daa poins. This updaes he marix K. Running KPCA over a ime horizon of M sill requires he eigendecomposiion of K a each sep, which 6691

4 s M+1 s s +1 s M Fig. 2: We do online consrain inference by leveraging previous compuaion (for {s M s }) o infer he consrain based on he curren horizon ({s M+1 s +1 }). is in O(M 3 ). To overcome his compuaional hindrance of KPCA, we need o reuse he compuaion performed in he previous ime seps. Liu e al. [12] show ha updaing he eigendecomposiion of he Gram marix G = K 1 M KE M 1 M E MK + 1 M 2 E MKE M, (9) a every sep can be done in O(M 2 ). Here, E M = 1 M 1 T M and 1 M is he M dimensional vecor of 1 s. Enforcing an Inferred Consrain KPCA learns he consrain as a manifold in is Reproducing Kernel Hilber Space F. The oupu of KPCA is he se of vecors α l, which enable projecing he user inpued nex sae s ono each principle componen, and in urn ha enables compuing he projecion of s ono h in F, denoed by Ps, via (8). To enforce he consrain, he robo needs o compue he sae corresponding o Ps, i.e. he preimage of he projecion. In general, finding preimages is compuaionally expensive. The approach we ake for finding preimages is an approximaion based on [34]: we learn a funcion Γ : F R d such ha Γ(φ(s)) s locally. Our insigh for learning a Γ is o use he robo s rajecory so far, along wih he projecions Ps on he currenly learned manifold, as raining daa: D = {(s i, Ps i ) i = { M + 1,, 1}}. A few aspecs combine o makes his work well: 1) Γ only needs o work well locally, in he space of ineres, i.e. along he robo s rajecory, where he raining daa is; 2) he saes visied so far, s i, like approximaely on he manifold: even hough φ(s i ) = Ps i in general, his is approximaely rue along he rajecory so far (in he curren ime horizon); and 3) we use a simple funcion class for Γ o preven overfiing o he noise in s i, and consruc a funcion ha maps poins in feaure space closer o he acual manifold in ask space. We hus use a linear model for each oupu dimension of Γ: Γ j (ψ) = w T j ψ. j = 1,, d (10) for ψ F. We learn he weighs w j by solving he following opimizaion problem: w j = argmin w j 1 i= M+1 ( ) L s i, w T j Pφ(s i) + λω(γ), (11) where L is loss funcion penalizing disance in ask space, Ω is a a regularizer, and λ is a pre seleced non negaive weigh. Applying he learned funcion Γ o he projeced sae s in feaure space, Ps, yields he projecion of he user s desired nex sae in ask space ono he consrain: B. Assisance projecion of s : Γ(Ps ) (12) Assisance for One Consrain If he robo were assising wih a known consrain, hen i is sufficien o go o Γ(Ps ). However, he robo does no acually know he consrain, and is inference migh be wrong. Key o successful assisance is knowing when o (or no o) assis. Therefore, besides inferring he consrain manifold, he robo should also compue is confidence in he inference. In he case ha he user is always following he same consrain, how far away he rajecory so far is from he manifold is a good indicaor of how accurae he manifold is. We hus measure he confidence in he inference as inversely proporional o he average disance beween previous saes and he preimages of heir projecs ono he manifold: d = s i Γ(Ps i ), (13) i= M+1 The bigger d is, he less confiden he robo mus be in is predicion. Le c 1 denoe he confidence in he inferred consrain a ime : c 1 = e γ 1d, (14) where γ 1 is a posiive seleced scalar. Equaion (14) ensures ha c 1 [0, 1], and c1 decreases as d increases. We propose o blend beween he user provided s and is projecion on he inferred consrain, Γ(Ps ), using: s R = (1 c 1 )s + c 1 Γ(Ps ) (15) wih s R being he blended sae o which he robo moves a ime. Once s R is reached, he user provides he nex inpu u +1, leading o he inpued sae s +1, and he process repeas for L +1 = s M+2,, s +1. Assisance for Swiching Consrains The confidence measure c 1 is designed for when here is a single consrain ha he user is always rying o mainain. Bu execuing a real ask may require eiher mainaining a sequence of dissimilar consrains, or swiching from mainaing a consrain o being unconsrained. The confidence measure c 1 does no capure such cases well: once he robo becomes confiden, i sars assising a lo and biasing he sae sequence. Confidence could also be compued based solely on he user inpus; however, we found ha once people realize ha he robo is inelligen enough o guide hem hrough he consrain, hey sop providing informaive inpus. For insance, hey consanly move he joysick along a single Caresian direcion even hey need he robo 6692

5 d=2 User Inpu Real Consrain Consrain Inferred Inferences Consrain Error d=3 γ a (a)polynomial Kernel Degree (b) Shor Horizon (c) Long Horizon Fig. 3: Effecs of kernel parameers (a) and inference horizon (b,c) on performance. On average across our asks, a degree 3 polynomial kernel was mos robus. Shor horizons lead o overfiing, wih vasly differen inferred consrains over ime. Longer horizons are more compuaionally demanding bu beer a recovering a consrains close o he desired one. On he oher hand, making he horizon oo long makes swiching consrains difficul, which is where our confidence measure helps. o move along a direcion differen from heir inpu, making inpu based confidence impracical. Thus, while c 1 works well in he one consrain case (as we will see in he firs user sudy), we need o augmen i o deec changing consrains. We leverage he naural difference in operaor inpu when following a consrain versus swiching consrains. When he operaor is conrolling he robo on an ongoing consrain, once a deviaion from he underlying consrains is observed, he operaor provides conrol inpus ha correc and cancel ou he observed deviaion. In oher words, moving along a consrain is formed by a se of deviaions and correcions ha are on average in he direcion of he consrain. On he oher hand, while leaving a consrain, he saes ensuing from he user s raw (un arbiraed) inpus are consanly along a direcion differen from h. We can deec his. This suggess ha augmening our measure of confidence requires compuing he alignmen beween he direcion suggesed by he average user inpu, and he direcion of he consrain. We denoe he direcion of average user inpu by δ u, and compue i as δ u = 1 1 M 1 f (s i, u i ) s i (16) i= M+1 where f is he ask space dynamics model his compues he average difference beween he user inpued sae and he curren sae. The consrain manifold is feaure space, so we approximae i via δ s, he average direcion of he robo s rajecory: δ s = 1 1 M 1 s i+1 s i (17) i= M+1 Le θ be he alignmen beween hese wo measures: ( δ θ = cos 1 u, δ s ) δ u δs (18) We compue c 2 by: c 2 = e γ 2θ. (19) We measure he overall confidence in robo s inference, c 3, by combining he wo measures: c 3 replaces c 1 in 15. c 3 = c 1 c 2 (20) = e (γ 1d +γ 2 θ ) V. Experimens (21) Our experimens are wo-fold: we are ineresed in he performance of he consrain inference algorihm, as well as is impac on real user eleoperaion scenarios. A. Consrain Inference Analysis In order o evaluae he accuracy of our inference algorihm, we colleced direc eleoperaion daa (wihou assisance). We asked paricipans o eleoperae he 7-DOF arm from Figure 4 hrough a joysick inerface for moving a grasped objec along a predefined pah, demonsraed o he users in a simulaion environmen. We asked paricipans o raverse he pah in he shores possible ime while keeping he grasped objec as close as possible o he pah. We designed hree differen scenarios: racking a line, an arc wih a large radius and low curvaure as a resul and finally moving he grasped objec along a semicircle of low radius and high curvaure. Analysis A key elemen in he performance of any kernel based algorihm is he choice of kernel made for he algorihm. In our problem in paricular, he kernel funcion resrics he inferred consrain, h, o a subse of all possible consrains, i.e. i implicily makes assumpions abou real-world asks. We esed our mehod s performance across differen kernel parameer choices, manipulaing kernel ype 6693

6 60! 0.60! 6! No Assisance! Assisance! Task Time! 40! 20! Deviaion! 0.30! Inelligence! 4! 2! 0! Line! Arc! Circle! 0.00! Line! Arc! Circle! 0! Line! Arc! Circle! Fig. 4: Dependen measures in user sudy 1 (polynomial of differen degrees d) and kernel parameers (coefficiens γ and he free coefficien a). Across our asks, we found he 3 rd order o perform he bes and be more robus o parameers (Fig. 3(a)). We also analyzed he effec of he ime horizon on performance. Unsurprisingly, shor ime horizons produce inferred consrains ha overfi o he user s noisy inpu (Fig. 3(b)), while longer horizons more easily recover a consrain close o he ground ruh (Fig. 3(c)), canceling ou he deviaions in user inpu. B. User Sudy 1: Assisance wih A Single Consrain In his firs sudy, we assess he effeciveness of online assisance in mainaining a single consrain. Manipulaed Variables We asked paricipans o conrol an arm in he hree scenarios described previously: racking a line, an arc, and a semicircle. In each scenario, he operaor conrols he robo in wo condiions: direc eleoperaion (no assisance is provided), or he user is assised wih he inferred ask consrain via our (15). We hus manipulae wo facors in a facorial design: 1) Assisance: Wheher or no he robo provides assisance. 2) Task Difficuly: he consrain he user needs o mainain. This seup leads o 6 differen condiions experienced by each paricipan. Task difficuly ranges from simple, in he line case, o hard, in he semicircle scenario. We used he confidence measure c 1 in his sudy. Dependen Measures We have boh objecive and subjecive measures: 1) Task Execuion Time. 2) Average deviaions from he underlying consrain. Any componen of moion normal o he insananeous direcion of consrain is defined as deviaion. 3) User s subjecive measure of robo s inelligence for assisance vs. no assisance in each scenario (on a 7 poin Liker scale) Hypohesis: H1. Assisance improves he performance of he human robo eam, boh objecively and subjecively. Subjec Allocaion: We chose a wihin-subjec design for 9 paricipans (4 females and 5 males, 27 years old on average) o enable hem o compare he assisance vs. no assisance condiions in each scenario. We counerbalanced he order of he condiions o avoid any biases resuling from ordering effecs. In order o conrol for he prior skill in playing wih joysicks, we asked each paricipan o ake par in a raining phase o eleoperae he arm hrough joysick wih no assisance. Analysis: Figure 4 shows he resuls. We ran a facorial repeaed measures ANOVA wih assisance and ask as facors for each of our dependen measures. For ime, we found boh facors had significan effecs and here was a significan ineracion effec F(2, 56) = 6.1, p <.01. The pos-hoc analysis wih Tukey HSD correcions showed ha assisance improved he iming performance for he line ask, p <.01. As he graph shows, he iming for he oher wo asks were almos idenical. The resuls for deviaions suppored our hypohesis: here was a significan effec for assisance, F(1, 57) = 13.56, p <.01. There was no significan effec for ask and no ineracion effec: assisance improved deviaions across he board. The resuls for raing also suppor our hypohesis: here was a significan effec for assisance, F(1, 57) = 17.29, p <.001, and no oher effecs were significan. Raings for he assisance robo were higher across he board. Overall, he resuls sugges ha assisance does improve subjecive and objecive performance. Even for 6694

7 80" 1.20" 6.0! c3 = c1! c3 = c1 c2! Task Time! 60" 40" 20" Deviaions! 0.80" 0.40" Inelligence! 4.0! 2.0! 0" line-line! line-sine! 0.00" line-line! line-sine! 0.0! line-line! line-sine! Fig. 5: Dependen measures in user sudy 2 simple asks in 2D, assisance can significanly improve user s comfor. We expec ha common ADL s will include 3D consrains which are much harder o saisfy hrough eleoperaion. Furhermore, mainaining ask consrains becomes much harder for people wih physical impairmens. C. User Sudy 2: Assisance wih Changing Consrains Our firs sudy indicaed ha assisance is good when dealing wih a single consrain. Nex, we invesigaed wha happens when he user needs o swich from a consrain. We conduced a second sudy o evaluae he effec of our proposed confidence measure, c 3, on he performance of assisance. Manipulaed Variables We considered wo scenarios: swiching from one consrain o a a new consrain, or leaving a consrain and enering free space, hus requiring no assisance for he res of he ask execuion. 1) Wheher or no he confidence measure c 2 is aken ino accoun (c 3 = c1 c2 vs. c 3 = c1 ). 2) Wheher o swich o a new consrain, or o a no consrain scenario. We mimicked he scenario of swiching o a new consrain by designing he racking pah o be wo line segmens perpendicular o each oher (called line o line scenario). We imiaed requiring no assisance from he swiching poin onward, by designing he pah o be a line segmen followed by a sequence of high curvaure semicircles depicing a sinewave like shape (line o sine scenario). Dependen Measures: We used he same objecive and subjecive measures as before: ime, deviaions, and raing. Hypohesis: H2: Incorporaing he c 2 measure of confidence improves he performance boh subjecively and objecively. Subjec Allocaion: Analogous o user sudy 1. Analysis: Figure 5 shows he resuls. We ran a facorial repeaed measures ANOVA wih confidence measure and ask as facors for each of our dependen measures. For ime, supporing our hypohesis, we found a significan effec for confidence measure, F(1, 27) = 6.39, p =.0210: using he augmened confidence mean o handle changing consrains lead o lower ask ime. The ask facor was also significan, wih changing from one consrain o he oher aking longer han changing from a consrain o no consrain. There was no significan ineracion effec. For deviaions, also supporing he hypohesis, we found a significan improvemen for he augmened confidence F(1, 27) = 19.01, p <.001. Task again had a significan effec. For raing, also supporing our hypohesis, we found ha users raed he robo using he augmened confidence more highly, F(1, 27) = 10.47, p <.01. There was no oher significan effec. Overall, he resuls suppor ha our confidence meric ha augmens manifold-based confidence wih user inpu direcion-based confidence leads o beer assisance when dealing wih changing consrains. VI. Discussion Summary. We inroduced and evaluaed a mehod for inferring and assising wih ask consrains. Consrain inference happens online, in real-ime, and assisance is mediaed by confidence and capable of handling changing consrains. This improved eleoperaion boh objecively and subjecively. Limiaions and Fuure Work. Albei useful, consrains are complex and difficul o idenify, and much work remains in his area: being able o resric he space of possible consrains based on possible real-world asks, incorporaing prior knowledge abou 6695

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