prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: Who was Ralph Rokebye's brother?

Read the following text and answer briefly.

Context 1: Rokebye, Ralph of Yorks, arm  Gloucester Hall, matric  9 Nov , 1582, aged 15; student of Lincoln's Inn 1585  See Foster's Inns of Court Register 
Rokebye, Ralph of Herts (? Yorks), gent  Broadgates Hall, matric  entry 28 Feb , 1589-90, aged 14  See pedigree in Foster's Yorkshire Collection 
Rokeby, William (brother of Sir Richard, treasurer of Ireland, son of John, of Thundercliffe Grange, Yorks), fellow of King's Hall, Cambridge, D Can L ; rector of Sandal 1487, and of Halifax, Yorks, 1502, rector of Fakenham, Norfolk, 1496, chancellor of Ireland 1498, and 1515, bishop of Meath, and privy councillor 1507, archbishop of Dublin 1512, archdeacon of Surrey 1520, until his death 29 Nov , 1521  See Ath  ii  717; Cotton, i  25; & Lansdowne MS  979, ff  4, 6 
Rolfe, Augustine (Rolfus) M A  from Queen's Coll , Cambridge, 1595; incorporated 10 July, 1599 
Rolf, Richard B A  from Emanuel Coll , Cambridge, 1584-5 (incorporated 11 July, 1585); M A  1588  See Foster's Graduati Cantab 
Rolfe, William cler  fil  New Coll , matric  10 March, 1656-7, B A  1660, fellow, M A  14 Jan , 1663-4; rector of Brampton 1668, and of Stoke Bruern, Northants, 1676, until his death, buried (at Stoke Bruern) 6 Sept , 1693  See Baker's Northants, i  86 
Rolfe, William s  William, of Stoke-Bruern, Northants, cler  Brasenose Coll  7 July, 1688, aged 16; student of Inner Temple 1692, buried in the Temple church 1 March, 1692-3  See Foster's Inns of Court Reg 
Rolle, Denis youngest son John, of Steventon, Devon, equitis  Exeter Coll , matric  15 Feb , 1666-7, aged 17; brother of John same date 
Rolle, Denis s  D , of Heanton, Devon, arm  Exeter Coll  matric  24 Oct , 1687, aged 17; B A  1691, M A  1694 (as Denys), rector of Merton, Devon, 1696  See Samuel 1687, & Foster's Index Ecclesiasticus 
Rolle, (Sir) Henry of Devon, arm  fil  Broadgates Hall, matric  14 June, 1594, aged 18; student of Middle Temple 1597 (as son and heir of Henry, of Steventon, Devon, esq ), knighted 23 July, 1603, died in 1617  See Foster's Inns of Court Reg 
Rolle, Henry of Devon, arm  Exeter Coll , matric  20 March, 1606-7, aged 17; bar -at-law, Inner Temple, 1618, bencher 1633 (2s  Robert, of Heanton, Devon), M P  Callington 1621-2, 1624-5, Truro 1625-1626, 1628-9, serjeant-at-law 1640, recorder of Dorchester 1636, a judge of king's bench 1645, chief justice of upper bench 1648-55, died 30 July, 1656, buried in Shapwick church, Somerset; brother of Samuel 1605  See Ath  iii  416; & Foster's Judges and Barristers 
Rolle, Henry s  Alex , of Tavistock, Devon, gent  Christ Church, matric  23 March, 1696-7, aged 17 
Rolle, John of Devon, arm  Exeter Coll , matric  30 May, 1589, aged 15; B A  8 Feb , 1592-3, M A  25 May, 1596 
Rolle, John 1s  John, of Steventon, Devon, equitis  Exeter Coll , matric  15 Feb , 1666-7, aged 18; of Bicton, Devon; died in his father's lifetime, buried at Bicton 22 April, 1689; brother of Denis 1667, and father of Denis 1698 
Rolle, Richard s  Richard, of Cookeburye, Devon, gent  New Inn Hall, matric  26 Sept , 1634, aged 18; B A  from Jesus Coll , Cambridge, 1638, incorporated from Gloucester Hall 17 Dec , 1639, M A  2 July, 1642, rector of Sheviocke, Cornwall, 1656; father of the next-named  See Foster's Index Eccl 
Rolle, Richard s  R , of Sheviock, Cornwall, cler  St  Alban Hall, matric  3 July, 1674, aged 17; B A  1678 
Rolle, Robert (Rooles or Roales) fellow New Coll  1551-60 from Mark Lane, city of London, B A  26 June, 1555, M A  26 July, 1560, B D  22 Jan , 1572-3, D D  June, 1585, a teacher in Westminster school; perhaps canon of Combe (4) in Wells, 1574, and rector of Stoke Climsland, Devon, 1574  See O H S  i  345; & Foster's Index Eccl 
Rolle, Samuel s  Denis, of Great Torrington, Devon, arm  Exeter Coll , matric  16 July, 1687, aged 18, B A  1691; bar -at-law Middle Temple 1697; M P  Barnstaple 1705, died 1747; see Denis 1687  See Foster's Judges and Barristers 
Rolle, William B C L  14 July, 1528; perhaps vicar of Yarncombe, Devon, 1536  See Foster's Index Ecclesiasticus 
Rolles, Gabriel (Rooles) B A  from St  John's Coll , Cambridge, 1610-11, M A  1614; incorporated 13 July, 1619, rector of East Locking, Berks, 1620, as Rolle  See Foster's Graduati Cantab 
Rolles, Richard gent  Jesus Coll , matric  1 March, 1632-3, B A  next day, M A  15 Oct , 1635; perhaps created B D  20 Dec  1642, "ex regis gratia," rector of Wavendon, Bucks, and of Witham, Essex, 1646, by the Westminster assembly  See Add  MS  15,670, p  70 
Rolles, William s  Richard, of Lewknor, Oxon, gent  St  John's Coll , matrie  12 March, 1637-8, aged 17, B A  9 Nov , 1641, M A  6 July, 1644; B D  from Jesus Coll  12 Sept , 1661, rector of Wheatfield, Oxon, 1660, and of Chalfont St  Giles, Bucks, 1662  See Foster's Index Eccl 
Rolles, William created M A  from Exeter Coll  14 April, 1648 
Rolleston, Simon created M A  31 Aug , 1636 
Rolleston, Thomas of Devon, gent  Wadham Coll , matric  12 May, 1620, aged 16 
Rollinson, Francis 1584  See Rallinson 
Rollinson, William s  "Jose," of London, gent  St  John's Coll , matric  7 March, 1694-5, aged 15; perhaps brother of John Rawlinson, of New Coll  1692  See page 1236 
Rolt, Edward youngest son of Tho , of London, equitis  Merton Coll , matric  7 Nov , 1701, aged 15; of Sacomb, Herts, and Chippenham, Wilts, student of Lincoln's Inn, 1702, M P  St  Mawes 1713, Grantham 1715-22, Chippenham 1722; died 22 Dec , 1722; his father knighted 1 Oct , 1682, and died 9 Sept , 1710  See Foster's Parliamentary Dictionary 
Rolte, George s  Thomas, of St  Margarets par  Darenth, Kent, pleb  St  Alban Hall, matric  17 June, 1631, aged 18; B A  20 June, 1631, M A  29 April, 1634, incorporated at Cambridge 1639 
Romane, Edmund pleb  Balliol Coll , matric  20 Feb , 1627-8, aged 18; B A  next day, M A  3 June, 1630 
Romaine, Matthew pleb  Balliol Coll , matric  10 June, 1630, B A  same day, M A  14 May, 1633, vicar of Stoke Gaylard, Dorset, 1639; father of the next  See Foster's Index Eccl 
Romayne, Thomas s  Matth , of Stoke Gaylard, Dorset, minister  Wadham Coll , matric  17 July, 1669, aged 17; B A  from Hart Hall 1673, "the intruded" rector of Stoke Gaylard 1675  See Foster's Index Eccl 
Romayne, William (Ronayne) gent  Trinity Coll , matric  31 July, 1671, aged 16 
Rome, Harcourt s  William, of London, p p  Brasenose Coll , matric  13 Dec , 1672, aged 17 
Rome, William s  G  (? "Gul "), of Northampton (city), pleb  Brasenose Coll , matric  11 Dec , 1684, aged 16 
Romney, Joseph B A  from Emanuel Coll , Cambridge, 1610-11, M A  1614; incorporated 8 July, 1614, student of Inner Temple 1610, as of London, gent  See Foster's Inns of Court Reg 
Rone, John s  Randolph, of Hanmer, Flints, pleb  Brasenose Coll , matric  10 Oct , 1634, aged 18; D D  Trinity Coll , Dublin, 25 Jan , 1666 (as Roane), vicar of Hanmer, Flints, 1644, ejected same year, dean of Clogher 1667, bishop of Killaloe 1675, until his death 5 Sept , 1692  See Cotton's Fasti Ecc  Hib  i  467 
Rone, William of New Coll  1661  See Roane 
Roode, Edward (or Rode) B A  21 July, 1522, M A  26 Nov , 1534; perhaps canon of Southwell 1561-73 
Roode, Edward cler  fil  Merton Coll , matric  22 Nov , 1650; Eton postmaster 1649, fellow 1651, B A  2 March, 1651-2, M A  14 Dec , 1655; incorporated at Cambridge 1657, and LL D  1671; vicar of Gamlingay, co  Cambridge, rector of one moiety 1661, and of the other 1677; died at Cambridge 1689  See Burrows, 525; & O H S  iv  292 
Roode, Onesiphorus s  Edward, of Thame, Oxon, sacerd  New Inn Hall, matric  27 Oct , 1637, aged 16, B A  1 July, 1641; incorporated at Cambridge 1645; chaplain to the house of lords after the expulsion of the bishops; minister of New chapel, Tuttle-Fields, Westminster, 1648, until ejected in 1660  See Calamy, i  195 
Rood, Richard M A  from Pembroke Coll  5 Dec , 1634 
Rooke, John s  Tho , of Broadwell, co  Gloucester, pleb  Pembroke Coll , matric  1 March, 1683-4, aged 17; brother of Thomas 1693 
Rooke, John s  Tho , of Whitchurch, Wilts, gent  Balliol Coll , matric  14 Jan , 1713-14, aged 17 
Rooke, Nicholas s  Arthur, of Totnes, Devon, gent  Exeter Coll , matric  10 March, 1670-1, aged 16; B A  1674, M A  1677, rector of Dartington, Devon, 1679  See Foster's Index Eccl 
Rooke, Robert "ser " Oriel Coll , matric  1 April, 1656, B A  1659 
Rooke, Robert s  R , p p  St  Alban Hall, matric  30 March, 1677, aged 17 
Rooke, Thomas pleb  Christ Church, matric  3 May, 1659 
Rooke, William (Roock) of Dorset, pleb  Brasenose Coll , matric  entry under date 20 March, 1578-9, aged 19; B A  from St  Alban Hall 30 Jan , 1582-3, M A  9 May, 1586 
Rooke, William of Dorset, gent  New Coll , matric  12 July, 1605, aged 18; B A  21 Feb , 1608-9, chaplain, M A  16 Dec , 1611, rector of North Cheriton, Somerset, 1618  See Foster's Index Eccl 
Rooke, William s  J , of Workington, Cumberland, p p  Queen's Coll , matric  22 Oct , 1669, aged 17; B A  1674, M A  1677, B D  1690, vicar of Plumstead, Kent, 1691, and rector of Hadley, Hants, 1695  See Foster's Index Eccl 
Rookes, Christopher (Rokys or Rokkis) B A  8 July, 1522, M A  1 July, 1527, B D  supd  Oct , 1540; principal of Magdalen Hall 1529-32, vicar of Stanstead Abbots, Herts, 1534  See Foster's Index Eccl 
Rookes, Jonas B A  from Magdalen Hall 24 April, 1599, M A  11 Feb , 1601-2 (2s  William, of Roydes Hall); vicar of Penistone, Yorks, 1619, see Foster's Index Eccl ; styled fellow and bursar of University Coll  in Foster's Yorkshire Collection, possibly brother of the next-named 
Rookes, Robert of Yorks, pleb  Magdalen Hall, matric  14 May, 1602, aged 19; possibly brother of the last-named 
Ro(o)kes, William demy Magdalen Coll  1544, B A  supd  1551, fellow 1552-71, M A  27 April, 1556, B Med  supd  24 April, 1561  See Bloxam, iv  99 
Rookes, William s  William, of Rhodes Hall, Yorks, gent  University Coll , matric  30 June, 1665, aged 16; died at Oxford in 1667 
Roope, Ambrose s  A , of Dartmouth Parva, Devon, arm  Exeter Coll , matric  15 March, 1671-2, aged 16 
Roope, George s  Ant , of Bradford, Wilts, gent  Hart Hall, matric  10 Oct , 1702, aged 15 
Roope, John s  Nicholas, of Dartmouth, Devon, gent  Exeter Coll , matric  17 Nov , 1637, aged 15; student of Lincoln's Inn 1638  See Foster's Inns of Court Reg 
Roope, Nicholas of Devon, gent  Broadgates Hall, matric  6 Feb , 1606-7, aged 18; B A  6 Nov , 1610; probably father of the last-named 
Rooper, Thomas s  T , of London, gent  Trinity Coll , matric  9 July, 1699, aged 16; B A  1703, M A  19 Feb , 1705-6, as Roper 
Rooper, William of St  Alban Hall 1667  See Roper 
Roos, Brian D Can L  or doctor of decrees of the university of Valentia; incorporated 3 Feb , 1510-11; died 1529, buried in the church of Chelray  See Fasti, i  31 
Root, Isaac pleb  St  John's Coll , matric  2 July, 1658, admitted to Merchant Taylors' school 1649 (only son of Isaac, merchant taylor); born in Trinity parish 20 Aug , 1641  See Robinson, i  193 
Roots, Richard s  Tho , of Tunbridge, Kent, gent  St  John's Coll , matric  26 Dec , 1689, aged 15; demy Magdalen Coll  1690-1702, B A  1693, M A  1696, rector of Chilmarck, Wilts, 1702-27, canon of Sarum 1722, rector and vicar of Bishopstone, Wilts, 1728; brother of William 1699  See Rawl  iii  447, and xix  90; Bloxam, vi  111; & Foster's Index Eccl 
Roots, Thomas of Sussex, pleb  Magdalen Hall, matric  entry 17 Nov , 1581, aged 13; B A  supd  1 July, 1584, bar -at-law, Lincoln's Inn, 1594  See Foster's Judges and Barristers 
Rootes, Thomas s  William, of Tunbridge, Kent, pleb  St  John's Coll , matric  31 Jan , 1628-9, aged 23; B A  12 Feb , 1628-9, vicar of Long Stanton All Saints, co  Cambridge, 1630  See Add  MSS  15,669-70; & Foster's Index Eccl 
Rootes, Thomas pleb  St  John's Coll , matric  2 July, 1658; B A  1661, M A  1666; possibly father of Richard 1689, and William 1699 
Roots, William s  Tho , of Tunbridge, Kent, gent  Christ Church, matric  16 March, 1698-9, aged 18; B A  1704; clerk Magdalen Coll  1705-11, M A  1707, rector of Little Berkhampstead, Herts, 1714; brother of Richard 1689  See Bloxam, ii  85; & Foster's Index Eccl 
Roper, Francis s  Robert, of Trimdon, co  Durham, gent  Corpus Christi Coll , matric  16 Dec , 1661, aged 18; probably identical with Francis, son of Robert, of Kelloe, co  Durham, farmer, was admitted sizar of St  John's Coll , Cambridge, 21 Sept , 1658, aged 16; fellow, B A  1662-3, M A  1666, B D  1673, vicar of Waterbeach, co  Cambridge, 1678, canon of Ely 1686-90, rector of Northwold, Norfolk, 1687, died 13 April, 1719  See Mayor, 138; Surtees' Durham, i  107; & Foster's Index Eccl 
Roper, John (or Rooper) demy Magdalen Coll , from Berks, M A  fellow, 1483, D D  disp  27 June, 1506, (first) Margaret professor of divinity, 1500, vice-chancellor of the university 1505, and 1511, principal of Salesurry and George Hall, rector of Witney, Oxon, 1493, vicar of St  Mary's church, Oxford, canon of Cardinal Coll  1532; died May, 1534  See Ath  i  76; & Landsowne MS  979, f  118 
Roper, John B A  disp  4 July, 1512 
Roper, Thomas of Trinity Coll  1699  See Rooper 
Roper, Philip of Kent, arm  Gloucester Hall, matric  7 Sept , 1588, aged 15 (subscribes Rooper) 
Roper, William (subscribes Rooper) of co  Hereford, militis fil  St  Alban Hall, matric  entry dated 5 June, 1607, aged 13; probably of Malmains, Kent, 2nd son of Sir Christopher Roper, afterwards 2nd baron Teynham  See Foster's Peerage 
Roscarrock, Henry of Cornwall, arm  Hart Hall, matric  entry under date 17 Dec , 1576, aged 21; probably son of Thomas, of Roscarrock, and brother of the next, and of Richard 1581 
Roscarrock, John B A  11 Feb , 1576-7; perhaps from Exeter Coll  (and 1s  Thomas, of Roscarrock, Cornwall); died 24 Nov , 1608; brother of Henry and Richard  See O H S  xii  65 
Roscarrock, Nicolas (Roiscariot) B A  supd  3 May, 1568, student Inner Temple 1571, as of Roscarrock, Cornwall  See Foster's Inns of Court Reg 
Roscarrock, Richard of Cornwall, arm  Broadgates Hall, matric  entry under date circa 1581, aged 19; student of Middle Temple 1583 (as 3s  Thomas, of Roscarrock, Cornwall, esq ), brother of Henry and John  See Foster's Inns of Court Reg 
Rosdell, Christopher of Yorks, pleb  St  Edmund Hall, matric  entry under date 22 Dec , 1576, aged 22, B A  4 July, 1576; rector of St  Bennet Sherehog, London, 1579, and vicar of Somerton, Somerset, 1582  See Foster's Index Eccl 
Rose, Christopher s  John, of Marlow, Bucks, gent  Christ Church, matric  13 Feb , 1622-3, aged 21, B A  same day; rector of Hutton, Essex, 1642  See Foster's Index Ecclesiasticus 
Rose, Christopher s  Giles, of Lynn Regis, Norfolk, gent  Lincoln Coll , matric  8 July, 1670, aged 15; student of Gray's Inn, 1673  See Foster's Gray's Inn Register 
Rose, Gilbert Augustinian Canon, B D  supd  22 May, 1512, and supd  12 Dec , 1519, for incorporation as D D 
Rose, Henry "ser " Lincoln Coll , matric  22 July, 1658, B A  16 Jan , 1660-1, fellow 1662 from Pirton, Oxon, M A  1663 (incorporated at Cambridge 1688), B D  1672; minister of All Saints, Oxford, but running much into debt, and marrying beneath himself, left his fellowship and church about 1674, retired to London, and at length to Ireland  See Ath  iv  561 
Rose, Hugh s  "Dav  Ni " (Nigg 4to ), of Ross, Scotland, p p  (subs  pleb )  Balliol Coll , matric  3 April, 1707, aged 20; B A  1709 
Rose, John B A  8 June, 1519, fellow Merton Coll  1523, M A  31 March, 1525; one of these names vicar of Shoreham, Kent, 1536  See Foster's Index Ecclesiasticus 
Rose, John of co  Leicester, pleb  Merton Coll , matric  24 Nov , 1581, aged 21 
Rose, John s  Jeremy, of Swell, co  Gloucester, pleb  Corpus Christi Coll , matric  12 Dec , 1623, aged 15; B A  4 July, 1626 
Rose, John s  Rich , of Halberton, Devon, gent  Exeter Coll , matric  14 May, 1688, aged 17 
Rose, John s  J , of West Derby, co  Lancaster, pleb  University Coll , matric  7 March, 1712-13, aged 18, B A  1716; rector of Bilborough, Notts, 1722  See Foster's Index Eccl 
Rose, Jonathan s  Th , of Mickleton, co  Gloucester, pleb  St  Alban Hall, matric  16 May, 1677, aged 18; B A  9 Feb , 1680-1 
Rose, Joseph s  Thomas, of Sturminster Newton, Dorset, pleb  Oriel Coll , matric  12 Dec , 1623, aged 19 
Rose, Richard B A  from Exeter Coll  14 June, 1621; perhaps student of Middle Temple 1622 (as son and heir of John, of Lyme, Dorset, gent ), and M P  Lyme Regis April-May, 1640, 1640 (l p ), till his death after 1648  See Foster's Inns of Court Reg  & Foster's Parliamentary Dictionary 
Rose, Richard arm  Exeter Coll , matric  29 March, 1656; student of Lincoln's Inn 1659, as 4s  Richard, of Wootton Fitzwarren, Dorset, esq  See Foster's Inns of Court Reg 
Rose, Richard s  Richard, of Monks Kirby, co  Warwick, pleb  Magdalen Coll , matric  3 May, 1672, aged 16 (as Rosse); chorister 1670-6  See Bloxam, i  95 
Rose, Richard s  R(ichard), of Wyng, Bucks, gent  Trinity Coll , matric  7 May, 1680, aged 16; bar -at-law, Inner Temple, 1699  See Foster's Judges and Barristers 
Rose, Stephen of co  Gloucester, pleb  Corpus Christi Coll , matric  21 Jan , 1619-20, aged 16; B A  13 Nov , 1621, M A  2 July, 1625, vicar of Aldermaston 1627, and rector of Barkham 1633, and of Arborfield, Berks, 1640, and perhaps of Hartley Mawditt, Hants, 1652  See Foster's Index Ecclesiasticus 
Rose, Stephen "ser " Lincoln Coll , matric  19 Nov , 1650 
Rose, Stephen "servi  fil " Magdalen Coll , matric  19 Nov , 1650 (subscribes "serv ") 
Rose, Stephen "ser " Magdalen Coll , subscribed 23 Nov , 1655; B A  from Wadham Coll  1659, vicar of Cold Overton, co  Leicester, 1662-3, and rector of Woolhampton, Berks, 1667-95, father of Temple  See Foster's Index Eccl 
Rose, Temple s  Step , of Woolhampton, Berks, cler  Trinity Coll , matric  29 March, 1693, aged 17, B A  1696 
Rose, Thomas Minorite, B D  22 June, 1509 
Rose, Thomas of Herts, pleb  Magdalen Hall, matric  10 Oct , 1589, aged 15 
Rose, Thomas s  Seth, of Telscombe, Sussex, sacerd  Oriel Coll , matric  5 June, 1640, aged 18; his father rector of Telscombe 1604, etc  See Foster's Index Eccl 
Rose, Thomas s  Edw , 
Context 2: 'Quectel_QuecPython_BC25 开发板使用说明 版本：Quectel_QuecPython_BC25 开发板使用说明_V1 1日期：2021-11-30 状态：临时文件
Quectel_QuecPython_BC25 开发板使用说明一、基本概述BC25_QuecPython_EVB_V1 1 开发板（本文简称“V1 1 开发板”）是专门针对 BC25 制造，是一款小巧便携的“口袋型”开发板。体型虽小，但是功能丰富，拥 有 SIM 卡座、板载天线、磁开关、LED 等元件。开发者仅需一条 USB Type-C 数据线即可轻松玩转开发板。二、开发板资源Quectel 移远 BC25 通信模组NANO SIM 自弹卡座USB Type-C 数据接口开机按键，唤醒按键磁开关单色灯GPIO 排针上海市闵行区田林路 1016 号科技绿洲 3 期（B 区）5 号楼 200233 邮箱: info@quectel com 网址: www quectel com 1 / 6
三、开发板介绍Quectel_QuecPython_BC25 开发板使用说明开发板是为方便开发者使用 QuecPython，而设计的一款基于 BC25 通信模块 的开发板，其上集成了开发常用的配置，可以满足开发者的开发需求。V1 1 开发板正面接口V1 1 开发板配置开发板配备了多种外设。明细如下：序 号名称型号是否支持接口类 型1磁开关KTH1601SL-ST3是GPIO2LED 灯S3528UG6W9TLC2G- 是GPIOTJ- 34微动按键GPIOA5--------是是---------上海市闵行区田林路 1016 号科技绿洲 3 期（B 区）5 号楼 200233 邮箱: info@quectel com 网址: www quectel com 2 / 6
Quectel_QuecPython_BC25 开发板使用说明四、功能详解4 1 磁开关开发板集成了一个磁开关。使用磁铁靠近，可使磁开关输出引脚变为低电平， 默认为高电平。4 2 LED 灯开发板集成了一颗高亮度灯珠，可以用来做显著指示灯。上海市闵行区田林路 1016 号科技绿洲 3 期（B 区）5 号楼 200233 邮箱: info@quectel com 网址: www quectel com 3 / 6
4 3 按键开发板集成了 2 个微动按键，其功能是 S1 为开机键，S2 为睡眠唤醒按键。Quectel_QuecPython_BC25 开发板使用说明五、调试步骤1 拿到开发板 V1 1 先插上 USB 安装串口驱动，在官方 QQ 群文件搜 CP210 或者自 行百度下载 CP210x 的串口芯片驱动进行安装。2 使用串口工具（例如 QCOM_V1 6）连接 BC25 的主串口（硬件 17、18 脚）。V1 1 选择 Enhanced COM 口，波特率选择 9600,打开串口，按下 PWK 键约一秒松开进 行开机，串口工具收到消息则代表开机成 功，然后按下 EINT 键串口显示 +QATWAKEUP 表示模组唤醒了。3 从 https://python quectel com/download 下载 BC25QuecPython 版本固件， 使用 Qflash（群文件下载）选择 BC25 的调试串口（硬件 38、39 脚），波特率选 择 921600，选择 lod 后缀的固件，按下 EINT 键串口工具显示模组已经唤醒串口 工具发 AT+QSCLK=0 可关闭睡眠（不会发 AT 则多按几次 EINT 键），点击 Start 开 始下载固件,下载进度条开始下载，等待下载完成。关闭以上所有工具，并给板 子断电重新上电。4 从 https://python quectel com/download 下载 QPYCOM 工具，直接解压运行 工具，选择主串口（同第 2 步），选择 57600 波特率，打开串口。再按 PWK 按键 进行开机，会看到 QPYCOM 有打印 mount Type "help()" for more information 然后就可以进行 QuecPython 的交互调 试了。上海市闵行区田林路 1016 号科技绿洲 3 期（B 区）5 号楼 200233 邮箱: info@quectel com 网址: www quectel com 4 / 6
六、常见问题解决Quectel_QuecPython_BC25 开发板使用说明Q：模块的固件在哪？A：请登录 QuecPython 网站下载：http://python quectel com/downloadQ：哪里有开发板和其他常用资料？A：请登录 QuecPython 网站下载：http://python quectel com/downloadP S  如果您遇到任何问题，请参照本官网在线文档进行解决或访问 QuecPython 社区进行搜索、交流、提问：QuecPython 社区或者联系我们的在线支持：QQ 群 445121768获取 QuecPython 开发固件及加入官方交流群官网主页：https://python quectel com官网文件下载（各类资料、工具）：https://python quectel com/download官网 wiki（常用于视频教程、手把手教程下载、API 库）：https://python quectel com/wiki/#/官网文档中心(拥有从入门到精通的各种文档介绍、必看)：https://python quectel com/doc/工单系统：https://workorder quectel com/QuecPython 社区：https://forumschinese quectel com/c/function-subjects/quectpython/43QuecPython 官方 QQ 开发交流群：445121768微信公众号：QuecPython移远 OTA 升级平台： https://cloudota quectel com/移远 IoT 管理平台：https://python quectel com/doc/doc/Advanced_development/zh/QuecPython Cloud/QuecCloud html上海市闵行区田林路 1016 号科技绿洲 3 期（B 区）5 号楼 200233 邮箱: info@quectel com 网址: www quectel com 5 / 6
附录 1 V1 1 开发板丝印图Quectel_QuecPython_BC25 开发板使用说明附录 2 V1 1 开发板原理图上海市闵行区田林路 1016 号科技绿洲 3 期（B 区）5 号楼 200233 邮箱: info@quectel com 网址: www quectel com 6 / 6
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ground_truth: Sir Richard.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: Where can users go for troubleshooting and support?

Read the following text and answer briefly.

Context 3: Paper Info

Title: Incorporating Human Path Preferences in Robot Navigation with Minimal Interventions
Publish Date: 16 Mar 2023
Author List: Oriana Peltzer, Dylan Asmar, Mac Schwager, Mykel Kochenderfer

Figure

Hyperplane arrangement of a twodimensional space containing two obstacles (colored in gray) The robot is located inside the pink polytope, surrounded by three adjacent obstacle-free polytopes Each hyperplane on the boundary of the robot's polytope corresponds to one of the nonredundant constraints in eq (4) (b)Graph derived from the hyperplane arrangement The nodes on the graph designate polytopes, and edges designate transitions to adjacent polytopes To estimate the human's preference, the robot updates a posterior over the goal and over which of the graph transitions φ 1 , φ 2 and φ 3 is preferred by the human (c)Example preference defined over the graph The location of the goal is indicated in yellow in the lower right polytope For each node, the outgoing pink arrow designates the edge on the graph corresponding to the preferred transition between polytopes 
Simple, 10 × 10, 8 polytopes (b) Map 2: Office, 10 × 10, 56 polytopes (c) Map 3: Classroom, 20 × 20, 73 polytopes (d) Sampled observations and robot's executed trajectories 
Fig 5: Maps used for simulating the robot navigation problem with path preferences In (d), the heading angles observed are indicated with arrows The goal is indicated with a pink circle, and the orange robot corresponds to the starting location The blue robot follows a policy that accounts for path preference, while the green robot does not The opacity of the robots increases with time 
Map 1 problem setup and example realizations for goal-only (green) and path preference (blue) solution methods The robot starts at the lower left corner of the environment, and the goal of the task (pink circle) is in the upper left area The robot does not know which goal, among 10 options (shown in light blue squares), is the correct goal The human provides noisy observations, indicated by arrows, at each iteration The green robot selects actions according to the goal-only baseline, and the blue robot uses our proposed method to infer path preferences The polytopes composing G are drawn in blue Probability of correct goal WLPHVWHS +J (c) Entropy of goal distribution g 
Fig  6: Probability of the correct goal, fig 6b, and entropy of the goal belief distribution P (g), fig 6c, for the same problem setup, fig 6a In this problem instance, the human's preference is to go to the goal by passing on the right side of the obstacle Results are averaged over 50 runs and the area filled represents one standard deviation above and below the mean value The goal-only baseline shows an over-confident prediction (shown by the strong reduction in belief entropy) that the correct goal is less likely, making it more difficult to reach the correct goal compared to a method that accounts for path preference 
Success rates in the simple environment (Map 1) The results are averaged over 6 randomly sampled problem instances (start location, goal location, and goal possibilities), and over 50 runs per problem instance ∆T is the number of time steps separating two consecutive human inputs The robot's mission time is Tmax = 30 time steps We selected γ h = 1 5, corresponding to relatively noisy human inputs and making the problem more difficult to solve for the robot 
Computation times for Goal Only and Path Preference methods on Map 1 (fig 5a),Map 2 (fig 5b), and Map 3 (fig 5c),averaged over 100 runs with randomly sampled problem instances The 95 % confidence interval is provided with the mean We evaluate computation time at the first iteration of each run (where the search depth takes on its highest value Tmax) 

abstract

Robots that can effectively understand human intentions from actions are crucial for successful human-robot collaboration  In this work, we address the challenge of a robot navigating towards an unknown goal while also accounting for a human's preference for a particular path in the presence of obstacles 
This problem is particularly challenging when both the goal and path preference are unknown a priori  To overcome this challenge, we propose a method for encoding and inferring path preference online using a partitioning of the space into polytopes  Our approach enables joint inference over the goal and path preference using a stochastic observation model for the human 
We evaluate our method on an unknown-goal navigation problem with sparse human interventions, and find that it outperforms baseline approaches as the human's inputs become increasingly sparse  We find that the time required to update the robot's belief does not increase with the complexity of the environment, which makes our method suitable for online applications 

INTRODUCTION

Collaboration between humans and robots has become increasingly important and one key aspect of this collaboration is the ability for robots to adapt to human decisions  In many scenarios, such as a robot navigating through a busy room to deliver an item, it is important for the robot to take into account human preferences 
For instance, humans may prefer a specific path that would allow their colleagues to notice the item being delivered, but this preference may change dynamically based on various factors such as changes in the environment or unforeseen circumstances  While some preferences can be incorporated into the path-planning process, accommodating dynamic user preferences in real-time remains challenging 
In this paper, we propose a way to enable robots to adapt to human preferences dynamically by leveraging real-time feedback to inform decision-making  In this work, we tackle the problem of robot navigation in which the robot cannot observe the goal or the preferred path to the goal, but must make navigation decisions that are influenced by humans through recommended actions 
Prior work has explored how to adapt to a human's preference through feedback, but such approaches often require a high level of intervention, which can be time-consuming and impractical in real-world scenarios  To optimize the use of human input and quickly infer the human's preference, Fig  : An autonomous robot navigates in a simulated classroom towards a goal location (pink circle) 
At the start of its mission, it receives direction indications (arrows) from a human that indicate which path it should take to get to the goal  In this scenario, the human wants the robot to go around the desks on the right side of the classroom  A robot that does not reason over path preferences (green) will take the shortest path to the goal regardless of the human's input 
Our method (blue) infers the human's path preference from these indications and adapts to their recommendations  we propose an approach that leverages probabilistic representations of human preference and incorporates real-time feedback  Previous research by Bajcsy et al  considered an online adaptation problem in a manipulation task, where the person can apply forces to the robot to indicate their preferences 
By allowing the robot to continue its task while taking into account a probabilistic representation of human preference, their approach does not require frequent inputs  Building on this idea, we adopt a similar approach to adapt to a human's preference in the context of a robot autonomously navigating through a known environment, such as a cluttered office space 
Specifically, we focus on allowing the human to influence the robot's trajectory with respect to obstacles, by providing guidance on preferred routes or paths, while the robot continues to execute its task  Paths can be represented using homotopy classes   However, homotopies can pose computational challenges when used to encode and infer human preferences 
When the robot maintains a belief over homotopy classes, the inference problem can become exponentially complex with the number of obstacles in the space  Additionally, when the goal is unknown, the number of variables increases with the number of candidate destinations  This complexity can render the decision-making problem intractable 
Our solution is to encode path preference based on a partitioning of the environment into polytopes   This representation allows path preferences to be expressed as sets of preferred transitions between adjacent polytopes  Paths belonging to different homotopy classes correspond to different sequences of transitions 
By leveraging conditional independence assumptions, we can make the Bayesian inference problem tractable  These assumptions exploit the fact that human actions provide information about the path in a piece-wise manner  For example, indicating a preference for navigating around a particular obstacle only provides information about the local area and not the entire path 
Finally, after updating its belief representation over the human's preference, the robot can adapt to indications by replanning online  Our contributions are as follows  • We formulate the human-robot collaboration problem as a Partially Observable Markov Decision Process (POMDP) where both the goal of the task and the human's path preference are unknown random variables 
• We propose an encoding of a human's path preference using a partitioning of the environment into polytopes, along with conditional independence assumptions that make the Bayesian inference problem tractable to infer the task goal and path preference online  • Through simulations in two environments of different sizes and complexity, we show that our method is effective for solving problems where the robot must reach a goal that is unknown a-priori while simultaneously adapting to a human's indications 
Our method shows higher success rates compared to baseline approaches when the human inputs are sparse  Our approach enables a robot to make effective navigation decisions in collaboration with a human, even when the goal and path preference are not known in advance, and with minimal human input  In recent years, there has been a growing interest in shared autonomy and interactive systems, where humans and robots work together to accomplish tasks 
Several approaches have been proposed to address the challenge of enabling effective collaboration between human and robot agents while still achieving high task performance  Losey et al  and Jeon, Losey, and Sadigh propose a framework where a human operator is given control of a task-relevant latent action space while an autonomous system handles the rest 
Dragan and Srinivasa present a formalism for arbitrating between a user's input and a robot's policy when both human and robot share control of the same action space  Cognetti et al  [7] provide a method for real-time modifications of a path,       Fig  : We model the intent inference problem with the above diagram 
At each step in time, the robot receives an observation ot from the human conditioned on its current location st, the intended goal g, and the human's path preference θ  The robot updates its belief over g and θ and transitions to a next location st+1  while Hagenow et al  present a method that allows an outside agent to modify key robot state variables and blends the changes with the original control 
However, a common challenge of these approaches is the high level of intervention required from humans  Best and Fitch propose a method for predicting an agent's intended trajectory from observations  Rather than maintaining a belief over the agent's future path, they infer the agent's intended goal among a set of candidate locations at the boundary of the space 
This approach provides information on where the agent is heading and generates a distribution of candidate future trajectories for the agent  Inferring the goal of the task among a discrete set of candidates is also relevant to the area of shared autonomy  Javdani, Srinivasa, and Bagnell propose a formalism for shared control of a robotic arm, where the robot must assist the human in picking up an object but needs to infer which object the human has chosen from joystick inputs 
Planning with homotopy class constraints is useful in problems where the robot's requirements are given with respect to obstacles, and Yi, Goodrich, and Seppi consider topological constraints provided by human operators  Bhattacharya propose an efficient algorithm for solving pathplanning problems under homotopic constraints 
However, the number of homotopy classes for a given problem can be infinite, and as the robot changes location and updates its representation of the world, carrying out inference over homotopy classes in a dynamic environment requires recomputing the set of homotopies at every iteration, making the belief update challenging 
Prior work has addressed the challenge of shared autonomy by considering how robots can infer a human's intended goal, or how they can infer the preferred path to a goal  However, we argue that inferring the goal and the path as separate problems can lead to over-confidence in incorrect beliefs about the user's preferences 
To illustrate this point, consider the following scenario: a robot and a human are collaborating to move an object from one end of a room to Fig  : Using the hyperplanes composing the H-representation of each obstacle, we construct a hyperplane arrangement of the obstacle-free space (a)  We define the human's preference for the robot's one step action choices as the posterior distribution (given all human input up to that point) over transitions from the current to the neighboring polytopes, i e  edges on the graph 
Each time the robot transitions to a new polytope, the set of neighbor polytopes and the distribution over human preferences are updated  another, but there is an obstacle in the way  The human would like the robot to take a path around the obstacle on the left, even though the goal is on the right  If the robot only infers the goal from the human's inputs, it may incorrectly assume that the goal is on the right, and become over-confident in this belief 
On the other hand, if the robot only infers the preferred path, it may mistakenly assume that the goal is on the left, leading to a failure in completing the task  To overcome these challenges, our work proposes a joint inference approach that considers both the human's intended goal and their preferred path to that goal 
Specifically, we model the human's preference over different homotopy classes and leverage a conditional independence assumption to provide a tractable solution  In our approach, we assume that the human's inputs are noisily rational conditioned on both the goal and the preference  By jointly inferring the goal and path preference, we can avoid over-confidence in incorrect beliefs about the user's preferences, leading to improved system performance 
We consider the problem of robot navigation in a known environment to an unknown destination, where a human can intervene and provide a heading direction to the robot using a joystick or force cues  The human also has a preference on which path the robot should take with respect to obstacles, and our objective is for the robot to understand the human's intentions and execute the task with minimal interventions 
Let g be a discrete random variable denoting the goal of the task, belonging to a set of candidates Ω g , and let θ be a discrete-valued random variable representing the human's path preference, belonging to a set of possible preferences Θ  The physical location of the robot at time index t is denoted by s t ∈ R 2 , and the robot's action at time index t, belonging to some action space A, is denoted by a t  
The transition model T (s t+1 | s t , a t ) is deterministic, meaning the robot has full control over its future location  At any time step, the human may provide an observation to the robot  When the human intervenes, the robot receives a direction (heading angle) that can be mapped to a future location in space 
More specifically, we map the direction to an intended location, which is the resulting robot location after advancing in the indicated direction for one time step  For simplicity, we consider that the robot directly makes an observation o t of the location indicated by the human  We assume that the robot has a stochastic observation model for the human P (o t | s t , g, θ) that is conditioned on both the goal of the task g and the human's preferred path θ 
We further assume that having chosen a goal and path preference, the human takes actions to noisily minimize a cost function C g,θ that measures the cost of moving from the robot's current location to the goal along the preferred path  For example, C g,θ (s t , o t ) can be the length of the shortest path from location s t to the goal g after taking a first step to o t , and constrained by path preference θ 
We use C g,θ to induce a probability distribution over observations, given by: where γ h is a hyperparameter that designates the rationality coefficient  This model assumes the human will pick the lowest cost action with the highest probability and the likelihood of an action decreases exponentially with the increase in cost  
Our inclusion of the path preference θ sets our approach apart from   The model is shown in fig  represented as a Bayesian Network 

Inference

At each time step where the human provides an observation, the posterior P (g, θ) is given through the Bayesian update We note that the number of Bayesian updates required at each iteration to update the belief is equal to the cardinality of Ω g × Θ  In addition, each Bayesian update involves computing C g,θ (  
,   ) in eq  ( ), which involves solving an optimization problem (such as a shortest path problem)  In section IV, we propose a specific encoding of preference θ for resolving eq  ( ), while ensuring the number of computations of the cost C g,θ ( ,  ) per update does not grow exponentially with the number of obstacles 

Decision Making

We consider a navigation problem where the robot receives reward according to the model R(s t , g, θ, a t )  We wish to find the optimal policy π that maximizes the expected discounted sum of future rewards, with discount factor γ  The above problem is a Partially Observable Markov Decision Process (POMDP)  
In this section, we propose an encoding of human's path preference θ for computing the posterior in eq  ( )  Devifrom the concept of homotopy classes, we define the preference according to a partitioning of the environment into polytopes, as shown in fig  , creating a hyperplane arrangement of the space 
Hyperplane arrangements have been used by Vincent and Schwager in the context of Neural Network verification  In our setting, we leverage this representation to define path preferences as preferred transitions between adjacent regions of the space 

Hyperplane Arrangement

We assume a two-dimensional environment composed of m polytopic obstacles, each defined by their half-space representation (H-representation) where A i ∈ R di×2 and b i ∈ R di , and where d i is the number of edges (hyperplanes) composing polytope i  Let n = i d i be the total number of hyperplanes  We leverage each obstacle's H-representation to construct a hyperplane arrangement of the environment as shown in fig 
 e  a partitioning of the space into polytopes  More specifically, each location in space belongs to a polytope j for which we can write an H-representation of the form where α j i ∈ {−1, 1} di is a vector specific to polytope j and obstacle i corresponding to the relative position of any point in the set with respect to each hyperplane in O i  
Fig  : Intent inference model in a hyperplane arrangement of the obstacle free space  We spatially decompose the preference θ into a set of preferred neighboring polytopes per region of the space  Within each polytope j, the human preference pj is a discrete distribution over the preferred neighbor in N (j) 
We assume that for a location st belonging to polytope j, and given goal g and preference pj, the observation ot and any other preference p i,i =j are conditionally independent  Concatenating elements from each obstacle's Hrepresentation, we can write polytope j's H-representation as where Some of the constraints in eq  ( ) (corresponding to rows of A, b and α j ) are redundant, i e  the set P j does not change upon their removal 
We can further reduce the Hrepresentation of a polytope to include only non-redundant constraints  By removing the rows corresponding to redundant constraints, we obtain new matrices A j e , b j e and α j e such that we can write the polytope's reduced H-representation as The non-redundant constraints correspond to edges of the polytope 
In other words, as the robot continually moves in space, the first hyperplane that it will cross upon exiting the polytope will correspond to one of the polytope's nonredundant constraints  Vincent and Schwager outline an iterative method for removing redundant constraints by solving n linear programs 
We use this method in practice for computing α j e for each polytope  We can now characterize each polytope by a vector α j e ∈ {−1, 1} n j e , where n j e ≤ n is the number of essential constraints of the polytope  The polytopes P j partition the environment into a hyperplane arrangement 

Path Preference

In this section, we provide a definition of preference θ according to a graphical representation of the environment based on the hyperplane arrangement  Under this representation, a path preference corresponds to a set of preferred transitions  In other words, for each polytope in the space, the human will have a preference to which neighboring polytope they wish to transition 
Let G := (V, E) be an undirected graph, where vertices are obstacle-free polytopes, and edges connect two adjacent polytopes  Each polytope is described by a unique vector α j as defined in eq  ( )  Two polytopes are adjacent if they share non-redundant constraints (rows in eq  ( )) corresponding to the same hyperplane (i e  they are on opposite sides of the hyperplane) 
Let N (v) be the set of neighbors of a vertex v  For each vertex, we denote p v the discrete-valued random variable describing which edge in N (v) the human intends to transition to  Using this formalism, we define a path preference as the set of preferred transitions over all nodes in the graph, Let m θ = v∈V |N (v)| be the cardinality of Θ, and m g = |Ω g | the number of possible goals 
A priori, the number of Bayesian updates required to update the belief at every iteration should be m θ × m g   Now, let us assume the conditional independence relationships described by the new problem diagram in fig    More specifically, we introduce the assumption that conditioned on a robot location s t , the goal g, and the preference for the corresponding vertex p v in the graph, the observation o t and the preference for any other vertex are conditionally independent 
In other words, the observations the human provides can be defined conditioned only on the robot location, the goal, and the human's preference for its current vertex p v   By introducing this assumption, each update step only requires updating the joint (p v , g), reducing the number of cost computations to |N (v)| × m g  
We can notice that by introducing this assumption, we removed the direct relationship between the number of polytopes in the environment and the complexity of the Bayesian update in eq  ( )  In practice, components of θ are not mutually independent  For example, if the human preference at a vertex v 1 is
, it is unlikely that the human will also prefer p v2 = (v 2 , v 1 ) (turning back)  We can improve our model by assuming a dependent relationship between preferences for adjacent edges, which does not significantly increase the complexity of the inference problem  An interesting property of our encoding is that any two paths that belong to different homotopy classes will cross different sequences of polytopes, i e  they correspond to a different sequence of edges on G 
This can be proved by contradiction  Let us suppose that two continuous trajectories ξ 1 and ξ 2 , with the same start and end points and that do not intersect any obstacle, traverse the same regions in G in the same order  From the construction of the hyperplane arrangement, each polytope that the paths traverse through is obstacle-free 
Therefore, within each polytope, there is no obstacle in the area located in between the portions of ξ 1 and ξ 2 that belong to the region  A smooth transformation of ξ 1 into ξ 2 can be obtained by transforming each portion of ξ 1 belonging to the polytopes it intersects into the corresponding portion of ξ 2 for the same polytopes, where the extremities of the trajectory portions are connected to one another along the polytope's edges (where the same edge is crossed by both paths) 
Along this transformation, the paths do not intersect any obstacle, and therefore ξ 1 and ξ 2 belong to the same homotopy class 

EXPERIMENTS

We evaluate our model on a simulated navigation task where the robot must reach a goal that is unknown a priori while respecting the path preferences indicated by a human  The robot navigates in a grid world containing obstacles  The transition model is deterministic: the robot selects an adjacent location on the grid to reach at the next time step 
The robot is also allowed to take diagonal actions  Each location s t in the map can be mapped to a vertex v t ∈ G  Therefore, the actions leading to locations mapped to different vertices correspond to edges on the graph  We note f (s t , a t ) the edge crossed by taking action a t from location s t  
The robot is given a mission time limit T max for reaching the goal  In this problem, we assume that the human selects actions to noisily minimize a cost function C g,θ , where θ is defined as per eq  ( ), corresponding to the length of the shortest path to the goal constrained by the preference (where the robot is only allowed to make transitions on G along preferred edges) 
More specifically, where δ(s t , g | o t , p vt ) designates the length of the shortest path from s t to g passing by o t and constrained by preference p vt   This is a slight variant of the cost function proposed by Best and Fitch , where we add in a conditioning on the path preference  We compute costs by running the A path planning algorithm on the environment maps (grid worlds with diagonal actions) and impose preference constraints by pruning invalid transitions from the search tree 
Reward model  At each step in time, the robot receives a reward which is a sum of three components: a goal-specific reward a preference-specific reward or penalty We compute solutions to the POMDP defined in section III-B with the online solver POMCP , and with the particularity that within the rollouts, the robot does not expect to collect human inputs 
Each time a solution is computed, the robot takes an action and may receive an observation  If it does, it updates its belief distribution over the unknown problem variables and resolves the POMDP over a receding horizon 

Baselines

• Goal only  The robot solves the POMDP while ignoring the effects of path preference  Similarly to , we assume the human is taking action to minimize a goaldependent cost C g (s t , o t ) = δ(s t , g | o t ), where the conditioning on the preference is removed  We also omit the path preference's contribution to the reward R pref  
• Compliant  The robot complies with the human input, but does not take an initiative  If the user stops providing information, the robot continues in the last direction indicated for 5 time steps (conserving its momentum), then stops  • Blended  We designed an arbitration function to decide between our proposed policy (accounting for path preferences) and the user's recommendation when the robot receives inputs 
Our metric to evaluate confidence in the robot's prediction for the purpose of arbitration is the entropy of the intention distribution H(g, p i ), where p i denotes the preferred neighbor for the current region  Because our representation of the world is discrete, the arbitration is given by a step function 
Denoted by U , the action corresponding to the human's input, and P , the robot's prediction for the optimal action, we write the policy where we chose h = 1 6 as the confidence threshold 

Results

When evaluating the algorithm, we consider that a run is successful if the robot reached the goal within its allocated mission time T max and only made transitions between graph vertices corresponding to the human's preferences  We vary the time delay between human inputs, from constant guidance (∆ T = 1) to only a single observation (∆ T ≥ T max ) 
Success rates  Table I reports the success rates for experiments conducted over six randomly sampled problem instances and 50 runs per instance in Map 1 (fig  )  When the human provides inputs at every iteration, the compliant policy shows the highest success rates  However, as ∆ T increases, the compliant robot is not able to accomplish the task within the allotted time as it does not receive sufficient inputs to do so, and performance decreases compared to the autonomous baselines 
We find that in these runs, accounting for path preference consistently improves performance compared with the goal-only baseline  Results also show that blending the user's input with the robot's policy (Path Preference + Blend) when the human provides information leads to improved performance  Belief entropy 
Figure shows a challenging problem instance where the directions the human provides do not align directly with the shortest path to the goal  By ignoring the effects of preferences in the problem model (goal only), the robot quickly infers from observations that the upper left goal is less likely than others (P (g) drops) 
The strong decrease in entropy shows that the robot becomes overconfident in this prediction  Overconfidence in an incorrect goal will prevent the agent from finding the correct goal once the human's indications directly align with it, as it needs to correct for the wrong predictions, as shown in the path realization (fig 
)  In this realization, the goal-only method (green robot) fails to search the upper left area within the allotted time  By accounting for path preferences in its model, the blue robot's entropy over the goal distribution decreases more steadily, allowing for it to leverage the human's latest observations and reach the goal successfully 
shows an over-confident prediction (shown by the strong reduction in belief entropy) that the correct goal is less likely, making it more difficult to reach the correct goal compared to a method that accounts for path preference  Computation time  In table II we provide the time required to solve the POMDP, and the time required to update the robot's belief as it receives new observations 
We compute solutions on three maps: a simple 10 × 10 grid world with 8 polytopes (fig  ), a 10 × 10 grid world with 56 polytopes (fig  ), and a 20×20 grid world with 73 polytopes (fig  )  The latter environment being larger, we increase the mission time and the depth of the search tree in POMCP from T max = 30 (Map 1 and Map 2) to T max = 60 (Map 3) 
We do not notice an increase in the time required to update the robot's belief with an increase in problem complexity, which is consistent with our observation that the complexity of the Bayesian update should not increase with the number of obstacles or polytopes  On the contrary, the belief update time on Map 2 and Map 3, containing more obstacles, is reduced compared to the first map 
More obstacles result in fewer iterations when solving the constrained shortest path problem with A   Adding constraints due to the obstacles and polytopes reduces the size of the A search tree  C  Limitations Simulation environments  In our simulations, we hardcoded the preference policy over the maps (e g  in Map 1, go around the table counter-clockwise) 
We randomly sampled problem instances (start and goal locations, and goal options) to reduce the bias introduced by these preference choices  To best evaluate and compare the different approaches, it would be best to sample preferences among a distribution of preferences chosen by a human (for example, from benchmarks resulting from a collection of data) 
Creating such a benchmark is an interesting direction for future work  Hyperplane arrangement construction  The main limitation of our approach is that the size and geometry of each polytope depends strongly on the geometry of the obstacles, as seen in fig    Because of this, the robot can make predictions over preferences that are too refined compared with the topology of the environment 
A direct consequence is that when the size of the polytopes is small, the information provided by the human can be incorrectly interpreted as a preference on the robot's immediate action  Our method can be improved by changing the structure of the hyperplane arrangement so that it relies on the topology of the environment, but does not vary strongly with the geometry of the features in the environment 
For this purpose, topometric maps and region construction algorithms are promising directions  We presented an approach for encoding and inferring a human's path preference in an environment with obstacles  By leveraging a partitioning of the space into polytopes and a stochastic observation model, our method allows for joint inference over the goal and path preference even when both are unknown a-priori 
Our experiments on an unknown-goal navigation problem with sparse human interventions demonstrate the effectiveness of our approach and its suitability for online applications  The time required to update the robot's belief does not increase with the complexity of the environment, which further highlights the practicality of our method 



ground_truth: Online documentation, QuecPython community, online support: QQ group 445121768.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the effect of accounting for path preference on the robot's belief update?

Read the following text and answer briefly.

Context 4:  The process is repeated for all the couplings obtaining then a fully connected adjacency matrix  The results here presented are obtained with $\lambda = 0 01$ 
   For the minimization we have used the MATLAB routine \emph{minFunc\_2012}\cite{min_func}  
      
      \begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{Jor11_2D_l2_JR_soJR_TPJR}
    	\caption{Top panels: instances of single site coupling reconstruction for the case of $N=64$ XY spins on a 2D lattice with ordered $J$ (left column) and bimodal distributed $J$ (right column)  
    	
    	Bottom panels: sorted couplings }
    	\label{PL-Jor1}
    \end{figure}

   
To produce the data by means of numerical Monte Carlo simulations a system with $N=64$  spin variables  is considered on a deterministic 2D lattice with periodic boundary conditions  
Each spin has then connectivity $4$, i e , we expect to infer an adjacency matrix with $N c = 256$ couplings different from zero  
The dynamics of the simulated model is based on the Metropolis algorithm and parallel tempering\cite{earl05} is used to speed up the thermalization of the system 
The thermalization is tested looking at the average energy over logarithmic time windows and
the acquisition of independent configurations
starts only after the system is well thermalized 

   For the values of the couplings we considered two cases: an ordered case, indicated in the figure as  $J$ ordered (e g , left column of Fig  \ref{PL-Jor1}) where the couplings can take values $J_{ij}=0,J$, with $J=1$, 
   and a quenched disordered case, indicated in the figures as  $J$ disordered (e g , right column of Fig  \ref{PL-Jor1})
   where the couplings can take also  negative values, i e , 
    $J_{ij}=0,J,-J$, with a certain probability   The results here presented were obtained with bimodal distributed $J$s: 
   
    $P(J_{ij}=J)=P(J_{ij}=-J)=1/2$   The performances of the PLM have shown not to depend on $P(J)$  
   
    We recall that in Sec  \ref{sec:plm} we used the temperature-rescaled notation, i e , $J_{ij}$ stands for $J_{ij}/T$  
   
    To analyze the performances of the PLM, in Fig  \ref{PL-Jor1} the inferred couplings, $\mathbb{J}^R_{\rm inf}$, are shown on top of the original couplings,  $\mathbb{J}^R_{\rm true}$ 
     The first figure (from top) in the left column shows  the $\mathbb{J}^R_{\rm inf}$ (black) and the $\mathbb{J}^R_{\rm tru}$ (green) for a given spin
     at temperature $T/J=0 7$ and number of samples  $M=1024$  PLM appears to reconstruct the correct couplings, though zero couplings are always given a small inferred non-zero value  
     In the left column of Fig   \ref{PL-Jor1},  both the $\mathbb{J}^R_{\rm{inf}}$ and the $\mathbb{J}^R_{\rm{tru}}$ are sorted in decreasing order and plotted on top of each other  
     We can clearly see that $\mathbb{J}^R_{\rm inf}$ reproduces the expected step function  Even though the jump is smeared, the difference between inferred couplings corresponding to the set of non-zero couplings 
     and to the set of zero couplings can be clearly appreciated 
     Similarly, the plots in the right column of Fig  \ref{PL-Jor1} show the results obtained for the case with  bimodal disordered couplings, for the same working temperature and number of samples  
     In particular, note that the algorithm infers half positive and half negative couplings, as expected 
     
     
\begin{figure}
\centering
\includegraphics[width=1\linewidth]{Jor11_2D_l2_errJ_varT_varM}
\caption{Reconstruction error $\mbox{err}_J$, cf  Eq  (\ref{eq:errj}), plotted as a function of temperature (left) for three values of the number of samples $M$ and  as a function $M$ (right) for three values of temperature in the ordered system, i e , $J_{ij}=0,1$  
The system size is $N=64$ }
\label{PL-err-Jor1}
\end{figure}

In order to analyze the effects of the number of samples and of the temperature regimes, we plot in Fig  \ref{PL-err-Jor1} the reconstruction error, Eq  (\ref{err}), as a function of temperature for three different sample sizes $M=64,128$ and $512$  
The error is seen to sharply rise al low temperature, incidentally, in the ordered case, for  $T<T_c \sim 0 893$, which is the Kosterlitz-Thouless transition temperature of the 2XY model\cite{Olsson92}  
 However, we can see that if only $M=64$ samples are considered, $\mbox{err}_J$ remains high independently on the working temperature  
 In the right plot of Fig  \ref{PL-err-Jor1},  $\mbox{err}_J$ is plotted as a function of $M$ for three different working temperatures $T/J=0 4,0 7$ and $1 3$  As we expect, 
 $\mbox{err}_J$  decreases as $M$ increases  This effect was observed also with mean-field inference techniques on the same model\cite{Tyagi15} 

To better understand the performances of the algorithms, in Fig  \ref{PL-varTP-Jor1} we show several True Positive (TP) curves obtained for various values of $M$ at three different temperatures $T$  As $M$ is large and/or temperature is not too small,  we are able to reconstruct correctly all the couplings present in the system (see bottom plots) 
The True Positive curve displays how many times the inference method finds a true link of the original network  as a function of the index of the vector of sorted absolute value of reconstructed couplings $J_{ij}^{\rm inf}$  
The index $n_{(ij)}$ represents the related spin couples $(ij)$  The TP curve is obtained as follows: 
first  the values $|J^{\rm inf}_{ij}|$ are sorted in descending order and  the spin pairs $(ij)$ are ordered according to the sorting position of $|J^{\rm inf}_{ij}|$  Then,
     	a cycle over the ordered set of pairs $(ij)$, indexed by $n_{(ij)}$, is performed, comparing with the original network coupling $J^{\rm true}_{ij}$ and verifying whether it is zero or not  The true positive curve is computed as
\begin{equation}
\mbox{TP}[n_{(ij)}]= \frac{\mbox{TP}\left[n_{(ij)}-1\right] (n_{ij}-1)+ 1 -\delta_{J^{\rm true}_{ij},0}}{n_{(ij)}}
\end{equation}
As far as $J^{\rm true}_{ij} \neq 0$, TP$=1$  As soon as the true coupling of a given $(ij)$ couple in the sorted list is zero, the TP curve departs from one  
In our case, where the connectivity per spin of the original system is  $c=4$ and there are $N=64$ spins, we know that we will have  $256$ non-zero couplings   
     	If the inverse problem is successful, hence, we expect a steep decrease of the TP curve when  $n_{ij}=256$ is overcome 

In Fig  \ref{PL-varTP-Jor1}
it is  shown that,  almost independently of $T/J$, the TP score improves as $M$ increases  Results are plotted for three different temperatures, $T=0 4,1$ and $2 2$, with increasing number of samples $M = 64, 128,512$ and $1024$ (clockwise)  
We can clearly appreciate the improvement in temperature if the size of the data-set is not very large: for small $M$, $T=0 4$ performs better  
When $M$ is high enough (e g , $M=1024$), instead, the TP curves do not appear to be strongly influenced by the temperature 

\begin{figure}[t!]
	\centering
	\includegraphics[width=1\linewidth]{Jor11_2D_l2_TPJR_varT_varM}
	\caption{TP  curves  for 2D short-range ordered $XY$ model with $N=64$ spins at three different values of $T/J$ with increasing - clockwise from top - $M$ }
	\label{PL-varTP-Jor1} 
\end{figure} 

\subsection{$XY$ model with complex-valued couplings}
For the complex $XY$ we have to contemporary  infer $2$ apart coupling matrices,  $J^R_{i j}$ and $J^I_{i j}$   As before, a system of $N=64$ spins is considered on a 2D lattice 
For the couplings we have considered both ordered and bimodal disordered cases 
In Fig  \ref{PL-Jor3}, a single row of the matrix $J$ (top) and the whole sorted couplings (bottom) are displayed for the ordered model (same legend as in Fig  \ref{PL-Jor1}) for the real, $J^R$ (left column), and the imaginary part, $J^I$   

\begin{figure}[t!]
	\centering
\includegraphics[width=1\linewidth]{Jor3_l2_JRJI_soJRJI_TPJRJI}
	\caption{Results related to the ordered complex XY model with $N=64$ spins on a  2D lattice  Top: instances of  single site reconstruction for the real, JR (left column), and
		the imaginary, JI (right column), part of $J_{ij}$  Bottom: sorted values of JR (left) and JI (right) }
		
	\label{PL-Jor3}
\end{figure}
 
 
  \section{PLM with Decimation}
 \label{sec:res_dec}
 

\begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_tPLF_varT_varM}
    	\caption{Tilted Pseudolikelyhood, ${\cal L}_t$, plotted as a function of decimated couplings  Top: Different ${\cal L}_t$ curves obtained for different values of $M$ plotted on top of each other  Here $T=1 3$  The black line indicates the expected number of decimated couplings, $x^*=(N (N-1) - N c)/2=1888$  As we can see, as $M$ increases, the maximum point of ${\cal L}_t$ approaches $x^*$  Bottom: Different ${\cal L}_t$ curves obtained for different values of T with $M=2048$  We can see that, with this value of $M$, no differences can be appreciated on the maximum points of the different  ${\cal L}_t$ curves }
   	\label{var-$t$PLF}
   \end{figure}

\begin{figure}[t!]
    \centering
    \includegraphics[width=1\linewidth]{Jor1_dec_tPLF_peak_statistics_varM_prob eps}
    	\caption{Number of most likely decimated couplings, estimated by the maximum point of $\mathcal{L}_t$, as a function of the number of samples $M$  We can clearly see that the maximum point of $\mathcal{L}_t$ tends toward $x^*$, which is the right expected number of zero couplings in the system }  
    	\label{PLF_peak_statistics}
    \end{figure}
      
      For the ordered real-valued XY model we show in Fig  \ref{var-$t$PLF}, top panel, the outcome on the tilted pseudolikelyhood, $\mathcal{L}_t$ Eq  \eqref{$t$PLF}, of the progressive decimation: from a fully connected lattice  down to an empty lattice  The figure shows the behaviour of $\mathcal{L}_t$ for three different data sizes $M$  A clear data size dependence of the maximum point of  $\mathcal{L}_t$, signalling the most likely value for decimation, is shown  For small $M$ the most likely number of  couplings is overestimated and for increasing $M$ it tends to the true value, as displayed in Fig  \ref{PLF_peak_statistics}   In the bottom panel of Fig  \ref{var-$t$PLF} we display instead different 
 $\mathcal{L}_t$ curves obtained for three different values of $T$ 
  Even though the values of $\mathcal{L}_t$ decrease with increasing temperature, the value of the most likely number of decimated couplings appears to be quite independent on $T$ with $M=2048$ number of samples 
In Fig  \ref{fig:Lt_complex} we eventually display the tilted pseudolikelyhood for a 2D network with complex valued ordered couplings, where the decimation of the real and imaginary coupling matrices proceeds in parallel, that is, 
when a real coupling is small enough to be decimated its imaginary part is also decimated, and vice versa 
One can see that though the apart errors for the real and imaginary parts are different in absolute values, they display the same dip, to be compared with the maximum point of $\mathcal{L}_t$ 
     
       \begin{figure}[t!]
    	\centering
      	\includegraphics[width=1\linewidth]{Jor3_dec_tPLF_new}
      	\caption{Tilted Pseudolikelyhood, ${\cal L}_t$, plotted with the reconstruction errors for the XY model with $N=64$ spins on a 2D lattice  These results refer to the case of  ordered and complex valued couplings  The full (red) line indicates ${\cal L}_t$  The dashed (green) 
      		and the dotted (blue) lines show the reconstruction errors (Eq  \eqref{eq:errj}) obtained for the real and the imaginary couplings respectively  We can see that both ${\rm err_{JR}}$ and ${\rm err_{JI}}$ have a minimum at $x^*$ }
          	\label{fig:Lt_complex}
    \end{figure}

\begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_JR_soJR_TPJR}
   	\caption{XY model on a 2D lattice with $N=64$ sites and real valued couplings  The graphs show the inferred (dashed black lines) and true couplings (full green lines) plotted on top of each other  The left and right columns refer to the
   		 cases of ordered and bimodal disordered couplings, respectively  Top figures: single site reconstruction, i e , one row of the matrix $J$  Bottom figures: couplings are plotted sorted in descending order }  
   	\label{Jor1_dec}
   \end{figure}
   
\begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{Jor3_dec_JRJI_soJRJI_TPJRJI}
    	\caption{XY model on a 2D lattice with $N=64$ sites and ordered complex-valued couplings 
    		The inferred and true couplings are plotted on top of each other  The left and right columns show the real and imaginary parts, respectively, of the couplings  Top figures refer to a single site reconstruction, i e , one row of the matrix $J$  Bottom figures report the couplings sorted in descending order }
    	\label{Jor3_dec}
    \end{figure}
    
       







       \begin{figure}[t!]
     	\centering
     	\includegraphics[width=1\linewidth]{MF_PL_Jor1_2D_TPJR_varT}
     	\caption{True Positive curves obtained with the three techniques: PLM with decimation, (blue) dotted line,  PLM with $l_2$ regularization, (greed) dashed line, and mean-field, (red) full line   These results refer to real valued ordered couplings with $N=64$ spins on a 2D lattice  The temperature is here $T=0 7$ while the four graphs refer to different sample sizes: $M$ increases clockwise }
     	\label{MF_PL_TP}
     \end{figure}
    
    \begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{MF_PL_Jor1_2D_errJ_varT_varM}
    	\caption{Variation of reconstruction error, ${\rm err_J}$, with respect to temperature as obtained with the three different techniques, see Fig  \ref{MF_PL_TP}, for four different sample size:  clockwise from top   $M=512,1024, 2048$ and $4096$ } 
    	\label{MF_PL_err}
    \end{figure}
    
     Once the most likely network has been identified through the decimation procedure, we perform the same analysis displayed in Fig  \ref{Jor1_dec}  for ordered and then quenched disordered real-valued couplings
and in Fig  \ref{Jor3_dec} for  complex-valued ordered couplings   In comparison to the results shown in Sec  \ref{sec:res_reg},
  the PLM with decimation leads to rather cleaner results  In Figs  \ref{MF_PL_err} and \ref{MF_PL_TP} we compare the performances of the PLM with decimation in respect to ones of the PLM with $l_2$-regularization  These two techniques are also analysed in respect to a mean-field technique previously implemented on the same XY systems\cite{Tyagi15} 
  
    For what concerns the network of connecting links, in Fig  \ref{MF_PL_TP} we compare the TP curves obtained with the three techniques  The results refer to the case of ordered and real valued couplings, but similar behaviours were obtained for the other cases analysed  
  The four graphs are related to different sample sizes, with $M$ increasing clockwise  When $M$ is high enough, all techniques reproduce the true network  
  However, for lower values of $M$ the performances of the PLM with $l_2$ regularization and with decimation drastically overcome those ones of the previous mean field technique  
  In particular, for $M=256$ the PLM techniques still reproduce the original network while the mean-field method fails to find more than half of the couplings  
  When $M=128$, the network is clearly reconstructed only through the PLM with decimation while the PLM with $l_2$ regularization underestimates the couplings  
  Furthermore, we notice that the PLM method with decimation is able to clearly infer the network of interaction even when $M=N$ signalling that it could be considered also in the under-sampling regime $M<N$   
 
 
In Fig  \ref{MF_PL_err} we compare the temperature behaviour of the reconstruction error 
In can be observed that for all temperatures and for all sample sizes  the reconstruction error, ${\rm err_J}$, (plotted here in log-scale) obtained with the PLM+decimation is always smaller than 
that one obtained with the other techniques  The temperature behaviour of ${\rm err_J}$ agrees with the one already observed for Ising spins in \cite{Nguyen12b} and for XY spins  in \cite{Tyagi15} with a mean-field approach:  ${\rm err_J}$ displays a minimum around $T\simeq 1$ and then it increases for very lower $T$; however,
 the error obtained with the PLM with decimation is several times smaller  than the error estimated by the other methods 



 
 

     
     \section{Conclusions}
     \label{sec:conc}


Different statistical inference methods have been applied to the inverse problem of the XY model 
After a short review of techniques based on pseudo-likelihood and their formal generalization to the model we have tested their performances against data generated by means of Monte Carlo numerical simulations of known instances
with diluted, sparse, interactions 

The main outcome is that the best performances are obtained by means of the  pseudo-likelihood method combined with decimation  Putting to zero (i e , decimating) very weak bonds, this technique turns out to be very precise for  problems whose real underlying interaction network is sparse, i e , the number of couplings per variable does not scale with number of variables 
The PLM + decimation method is compared to the PLM + regularization method, with $\ell_2$ regularization and to a mean-field-based method  The behavior of the quality of the network reconstruction is analyzed by looking at the overall sorted couplings and at the single site couplings, comparing them with the real network, and at the true positive curves in all three approaches  In the PLM +decimation method, moreover, the identification of the number of decimated bonds at which the tilted pseudo-likelihood is maximum allows for a precise estimate of the total number of bonds  Concerning this technique, it is also shown that the network with the most likely number of bonds is also the one of least reconstruction error, where not only the prediction of the presence of a bond is estimated but also its value 

The behavior of the inference quality in temperature and in the size of data samples is also investigated, basically confirming the low $T$ behavior hinted by Nguyen and Berg \cite{Nguyen12b} for the Ising model  In temperature, in particular, the reconstruction error curve displays a minimum at a low temperature, close to the critical point in those cases in which a critical behavior occurs, and a sharp increase as temperature goes to zero  The decimation method, once again, appears to enhance this minimum of the reconstruction error of almost an order of magnitude with respect to other methods 
 
The techniques displayed and the results obtained in this work can be of use in any of the many systems whose theoretical representation is given by Eq  \eqref{eq:HXY} or Eq  \eqref{eq:h_im}, some of which are recalled in Sec  \ref{sec:model}  In particular, a possible application can be the field of light waves propagation through random media and the corresponding problem of the  reconstruction of an object seen through an opaque medium or a disordered optical fiber \cite{Vellekoop07,Vellekoop08a,Vellekoop08b, Popoff10a,Akbulut11,Popoff11,Yilmaz13,Riboli14} 

 	



ground_truth: The belief entropy decreases more steadily.