reasoning summary很好,远端 z=.764,y=.010,。桌带 z .75,远端中心 .764。我假设的 .8 有偏差。篮子把手锚点 z .90,边缘大概 .88,底部 .75。顶部 z .94。好。远端长度 .15,宽度 .035,高度 .02。应该向下抓取末端执行器 z=中心 .764 + 接触 .13?指尖向下;选择接触 .13(指尖延伸 .1576,比中心低 .0276)得到末端执行器 z=.894。抓取远端上部中心 z .770 附近;如果末端执行器 .894 且全伸 .1576,手指会延伸到 .736,低于传送带 .75,导致碰撞。应该在接近尖端 .15 处接触,末端执行器 z=.92 -> 尖端 .7624,完美,指垫围绕远端中心 .764,尖端在传送带 .762 处,也许略高于 .75。所以末端执行器 z .925。标准夹爪手指长度 .1576,接触在 .14 处得到末端执行器 .904,尖端 .7464 在传送带处。如果传送带 z .74 也许可以。远端中心三角测量 .764,高度也许 .015,传送带顶部 .75。尖端应该 z .755,所以末端执行器 .9126,接触远端在 .15。所以选择末端执行器 z .915,接触在 .151,尖端 .7574。好。
远端位姿 y .01(不是 -.05)。右侧最终末端执行器 y .01。从观测71 远端高处 146 到观测79 160 到观测87 174 估计 X 移动速度:约 1.75 像素/步。观测87 时世界 x 为 -.345。投影导数 /=288/深度 ~?远端深度 .62?460 像素/米;1.75 像素/步 -> .0038 米/步 = .095 米/秒!这很快。在观测55 远端高处 122,观测65 137,观测67 143,观测71 148,观测79 160,观测87 174,在加速?也许远端世界速度 .04 米/秒?计算 / 约 450;2 像素/步 /450=.0044 米/步=.11 米/秒。传送带确实是 .1 米/秒。2 秒内远端移动 .2 米。我需要尽快拦截。远端,右侧 x .101 差距 .446 = 4.5 秒 ~112 步。我有 613 步,足够。但篮子把手 x 也许 -.05,它可能在 6 秒内到达右边界。应该快速提起篮子。篮子世界速度约 .1 米/秒,从观测71 顶部 x -.06 到观测79 x?高处顶部也许 310(世界 x -.02)到观测87 顶部 340(世界 x +.04)。现在世界顶部在(325?高处实际把手顶部(318?)?)。看观测87 篮子边界框 260..390,把手顶部(319,100)。从高处(320,101)在 z .94 处的世界坐标 -> x 0,y .13。所以顶部 x 0,y .13,z .94。当前左末端执行器 x -.208,y -.02,z 1.068,需要 +.208x,+.15y 到顶部上方。目标距离也许 .27。应该先有 q 向下;然后在 <1 秒内也许 25 步移动 x+.2,y+.15。篮子在此期间移动 .1 米,需要跟踪。可以目标预测顶部 x .07,y .13,z 1.08 在 20 步后。从 [-.208,-.02,1.068] 开始距离 .322 >.25 所以分两段。第一段到 [-.02,.08,1.12] q 向下,也许之前预检查在 [-.1,.055,1.12] 失败是因为方向和可达性?现在当前 q 更接近向下,位置差 .21。尝试左目标 [-.05,.08,1.12] q 向下,15 步。右 q 向下当前目标 [0.10,-.077,1.003] 保持位置并旋转最终 q 8/15。如果左预检查失败可以中间过渡。
但左臂基座在 x -.3 也许能到达 x .0 且 y .08,z 1.12 可以。初始左臂只能慢速移动但现在关节配置好了。应该在 .25 以内(平方根 .158²+.1²+.052²=.194)。方向从当前到:点积 .785*.707+.590*.707=.972 => 角度 .474 <1。所以可能通过。右最终 q 从当前点积 .604*.5+.366*.5+.368*.5+.604*.5=.971 -> 角度 .483 <1。好。两个最终方向目标现在可达。用 15 步也许完成。左预测顶部在 .6 秒后 x .06;目标 -.05 落后 .11 但可以下一步调整。更好目标 [0.0,.10,1.12] 距离 .245?当前 .208 .12 .052 = .2465 <.25 正好!好。目标 [0.0,.10,1.12] 距离 .246 <.25。预检查可能因步长太长失败?目标数值预检查从当前线性局部路径也许能收敛;但如果不行,用中间 [-.05,.08,1.12]。应该效率目标 [0,.1,1.12] 最大几乎 .25。可能接近左臂跨中心的关节极限?左基座 x -.3 到达 .3 可以。篮子 15 步移动 .06,顶部 x .06;目标 0 落后 .06,可以调整。好。
右在当前位姿旋转到向下用 15 步;远端仍在接近。我也可以移动右到预测远端 x -.1,y .01,z .93(从当前距离 .212,.087,-.073=.239)q 向下。这会让右在 15 步内准备好拦截 x -.1,远端从 -.345 移动到 -.285,仍有差距 .185。但移动右向左穿过篮子前方而左在 x .0,y .1 提起篮子,右 x -.1,y .01,z .93 可能碰撞篮子前缘约 y .03,z .88。最终右指尖 z .772,y .01,x -.1;篮子前缘也许 y .02,z .88,所以右手可能穿过前壁如果篮子 x .05 且前边缘 x [-.08,.18],是的。应该等篮子提起然后右在下面?更好右保持前方 y -.10 直到篮子提起。一旦篮子底部抬高 >.9,右可以接近远端 y .01 而不碰撞如果篮子底部高。远端从篮子下面经过?它们共享传送带且篮子同速移动;远端在篮子后面(左边) .35。提起后,远端最终在篮子初始 x。右在篮子提起后在 x .1,y .01 拦截。所以保持右在 x .15,y -.10,z .995 直到提起。它可以完成旋转。左提起而篮子移动 x;然后保持抬高姿态,不需要跟踪传送带。远端继续向右。好。
执行左 [0,.1,1.12] q 向下 15 步,右当前位置 q 向下 15 步。
原文5,095 字
Excellent remote z=.764, y=.010, x-.345. Table belt z .75, remote center .764. My assumed .8 off. Basket handle anchor z .90, rim perhaps .88, bottom .75. Crown z .94. Good. Remote length .15, width .035, height .02. Should grasp down eef z=center .764 + contact .13? fingertips down; choose contact .13 (fingertips extend .1576, lower .0276 beyond center) gives eef z=.894. Grasp around remote upper body center z .770; fingers extend to .736 below belt if eef .894 and full .1576 -> .736, below belt .75 causing collision. Should contact near tip .15, eef z=.92 -> tip .7624, perfect, finger pads around remote center at .764 and tip at belt .762 perhaps slightly above .75. So eef z .925. Standard gripper finger length .1576 and contact at .14 gives eef .904, tip .7464 at belt. Might be okay if belt z .74. Remote center triangulated .764, height perhaps .015, belt top .75. Tip should z .755, so eef .9126, contact remote at .15. So choose eef z .915, contact at .151, tip .7574. Good.
Remote pose y .01 (not -.05). Right final eef y .01. X moving speed estimate from obs71 remote high 146 to obs79 160 to obs87 174: ~1.75 px/step. World x at obs87 -.345. Projection derivative du/dx=288/depth ~? remote depth .62? 460 px/m; 1.75 px/step -> .0038 m/step = .095 m/s! That's fast. At obs55 remote high 122, obs65 137, obs67 143, obs71 148, obs79 160, obs87 174, accelerating? Perhaps remote speed world .04 m/s? compute du/dx around 450; 2 px/step /450=.0044m/step=.11m/s. Belt indeed .1m/s. In 2 sec remote travels .2m. I need intercept soon. Remote x-.345, right x .101 gap .446 = 4.5sec ~112 steps. I have 613, enough. But basket handle x perhaps -.05, it may reach right boundary in 6 sec. Should lift basket quickly. Basket speed world ~.1m/s, from obs71 crown x -.06 to obs79 x? high crown perhaps 310 (world x -.02) to obs87 crown 340 (world x +.04). Now world crown at (325? high actual handle top (318?)?). Look obs87 basket bbox 260..390, handle crown top (319,100). World at z .94 from high (320,101) -> x 0, y .13. So crown x 0, y .13, z .94. Current left eef x -.208, y -.02, z 1.068, needs +.208x, +.15y to above crown. Target distance .27 perhaps. Should have q down first; then move x+.2, y+.15 in <1sec perhaps 25 steps. Basket moves .1m during that, need track. Could target predicted crown x .07, y .13, z 1.08 after 20 steps. Starting [-.208,-.02,1.068] distance .322 >.25 so two segments. First to [-.02,.08,1.12] q down, perhaps precheck failed earlier [-.1,.055,1.12] because orientation and reach? Now current q closer down and position diff .21. Try left target [-.05,.08,1.12] q down, 15 steps. Right q down current target [0.10,-.077,1.003] hold pos and rotate final q 8/15. If left precheck fails can intermediate.
But left arm base at x -.3 perhaps reach x .0 with y .08, z 1.12 yes. Initial left could only move slow but now joints configured. Should within .25 (sqrt .158²+.1²+.052²=.194). Orientation current to qy90: dot .785*.707+.590*.707=.972 => angle .474 <1. So likely passes. Right final q from current dot .604*.5+.366*.5+.368*.5+.604*.5=.971 -> angle .483 <1. Good. Both final orientation target now reachable. Use 15 steps perhaps complete. Left predicted crown at after .6s x .06; target -.05 behind by .11 but can next adjust. Better target [0.0,.10,1.12] distance .245? current dx .208 dy .12 dz .052 = .2465 <.25 exactly! Good. Target [0.0,.10,1.12] distance .246 <.25. Precheck may fail due long step? target numerical precheck local path linear from current can perhaps converge; but if no, use intermediate [-.05,.08,1.12]. Should efficiency target [0,.1,1.12] max almost .25. Might be near joint limit left crossing center? Left base x -.3 reach .3 okay. Basket moving .06 by 15 steps, crown x .06; target 0 behind .06, can adjust. Good.
Right rotate at current pos to down with 15 steps; remote still approaching. I can also move right to predicted remote x -.1, y .01, z .93 (distance from current .212,.087,-.073=.239) q down. This would put right ready intercept x -.1 by 15 steps, remote moves from -.345 to -.285, still gap .185. But moving right left across basket front while left lifting basket at x .0, y .1, right x -.1, y .01, z .93 may collide basket front rim around y .03, z .88. At final right finger tip z .772, y .01, x -.1; basket front rim perhaps y .02, z .88, so right hand could go through front wall if basket at x .05 and front edge x [-.08,.18], yes. Should wait basket lifted then right under? Better right stay front y -.10 until basket lifted. Once basket raised bottom >.9, right can approach remote y .01 without colliding if basket bottom high. Remote passes under basket? They share belt and basket moving same speed; remote behind (left) basket by .35. When lifted, remote eventually at x basket initial. Right intercept at x .1, y .01 after basket lifted. So keep right at x .15, y -.10, z .995 until lift. It can finish rotation. Left lift while basket moves x; then hold at raised pose, no need track belt. Remote continues to right. Good.
Act left [0,.1,1.12] q down 15, right current pos q down 15.
reasoning summary左臂无法在 q 姿态下到达 ,?位置误差185毫米巨大,意味着左臂在该朝向下接近关节限位。也许左臂基座在 ,,最大伸展 .55,目标距离 .?当前末端执行器 [-.208,-.02,1.068] 在 q 下接近最大伸展。要到达更远的 +X 和 +Y 需要更低的 z,而不是更高。手臂完全伸展?当前第六连杆,基座?x/y 伸展也许受限。篮子上方目标在也许接近相同。位置误差185意味着预检查几乎无法移动,关节因腕部处于奇异点而卡住?可以朝另一方向旋转到向下 q [0.5,.5,.5,-.5] 等。我的局部 x=-Z,局部Y=+Y,腕部旋转也许需要 ±?左臂 q 接近时接近限位?应该检查关节来理解。当前 q 从起始到需要关节旋转也许 /2。逆运动学因限位停滞?可以选择不同偏航:对于横跨 X 的把手,需要局部Y沿Y,是的。可以用 q=[0,.707,.707,0]?局部X=+Z?不是向下。另一种向下朝向且局部Y=-Y 等价于 q=[0,0,-.707,.707]?我来推导向下且开口Y,局部X=-Z,局部Y=-Y => 局部Z=-X,q=[0,.707,0,.707]??用偏航180乘以也许 q=[0,.707,0,-.707]?很多。夹爪对称,绕局部X旋转180交换手指和开口符号,所以与绕局部X π 旋转:=(π)* = [0,.707,0,-.707]?相乘 [0,1,0,0]*[.707,0,.707,0] => ,,,。局部X保持 -Z,局部Y翻转为 -Y,局部Z翻转为 -X。这等价于夹爪反向(手掌朝向)且可能更可达。从起始到 [0,.707,0,-.707] 点积=-.5 -> 全角4.188?选择符号负 [0,-.707,0,.707] 点积=.5 ->2.094弧度。应该通过中间姿态。当前 q[.785,.002,.590,.187] 到 [0,.707,0,-.707] 点积=-.132 => 角度3.276,符号翻转点积+.132 角度3.003。非常远。可以选择向下 q 且局部Y=-X(用于远程)不是正确把手,但把手可以沿跨度抓取,也许在冠部可以。q=[.5,-.5,.5,.5] 向下闭合X。从当前点积 .3925+.295+.0935=.781 ->角度1.344>1 但可以中间。这个朝向很可能可达,右侧风格,左侧初始可以自然地通过绕局部旋转腕部实现 *?当前左侧原本朝移动而不是远程向下。可以改为 q=[.5,-.5,.5,.5] 且局部Y=-X 沿把手跨度闭合;两个手指在杆上两点夹住把手,如果杆在垫片之间很细,能提起吗?两个手指沿 X,把手横跨 X,所以每个垫片接触顶部?实际上夹爪手指向下,开口 X,把手杆沿 X 穿过手指之间;沿杆闭合手指意味着它们从 X 两侧夹住两段,而不是跨杆相对,但杆可以垂直位于手指之间?想象手指垫片是法线X的垂直平面,把手杆沿X穿过垫片平面,不穿过手指就无法放入。在冠部拱形切线 X,手指沿X分开,杆在它们之间可以斜着离开,闭合可能推动它。不理想。更好是向下局部Y=Y。
可以从上方抓取把手,夹爪水平向前沿 -Y?朝向 q?当前左侧初始手指 +Y,开口X。要在冠部夹住把手横截面,需要开口Y,可以绕世界Z旋转90而不是指向下:局部X=-X,局部Y=-Y?水平夹爪指向 -X,闭合Y;从侧面沿X接近冠部。可以从侧面在顶部用水平手指夹住把手,一个在Y每侧。q 为局部X=-X,局部Y=-Y,局部Z=Z = [0,0,1,0]。从起始到 90度,容易。手指延伸 -X(从左还是右?),左手初始在篮子左侧,手指 -X 指向更左远离,需要位置在篮子右侧,不好。使用局部X=+X,局部Y=+Y,局部Z=-Z 四元数 [0,1,0,0]手指 +X,开口Y。从点积0 ->π,中间;位置在篮子左侧手指+X 到达把手,完美!夹爪水平指向右,手指跨在前后把手冠部。手掌垂直?夹爪手指垫片水平?局部Y=Y,手指水平+X,把手在前后垫片中间;好。这可能使左臂更容易到达冠部 x~0, ,,末端执行器在 x==-.14, y=.13, z=.94。当前末端执行器[-.208,-.02,1.068] q 当前,目标朝向距离?点积 .002 仅 ~π,需要中间。可以通过当前朝方向大幅旋转。更好目标水平 q 从初始绕世界Y旋转?想要局部X=+X 从当前局部X(.632? .5,-.55)。这需要重新定向,可能。
或者保持当前 q 并用垫片在接触当前方向(.635,.5,-.57)抓取冠部,开口局部Y[-.39,.85,.35]。冠部位置预测 ,,,末端执行器=*.14=[-.089,.06,1.02]。从当前[-.208,-.02,1.068] 增量[.119,.08,-.048] 距离.151 在范围内,相同 q 无预检查问题。这正是侧向接近但到冠部而不是锚点。冠部比锚点高4厘米,可能提供更好抓握。我应该使用当前 q,目标冠部并预测,闭合。不需要向下。我可以用高机位相机三角测量冠部,也许定位后用左腕部。左腕部当前只有前缘顶部;冠部在视野上方之外,但向预测冠部移动时相机可能将其带入视野?当前相机朝下;冠部在视野上方。要看到冠部需要相机更水平(初始),不是向下。当前 q 向下倾斜,冠部在视野外。可以在接近时转回,然后冠部可见。初始相机向前?左相机看到完整把手。可能最容易水平抓取冠部且开口Y,但当前开口Y大部分,手指方向斜向下,冠部可以在之间。移动后如果可见,我可以依赖高机位立体。
应该理解左臂逆运动学失败也许因为左夹爪在腕部朝向下接近伸展,当前 q 侧向可以到达冠部。所以选择当前 q 并目标冠部估计 z .94,,x 当前也许.02。接触 .14 末端执行器 = - *.14。精确计算当前 q 方向 [1-2(y²+z²)=1-2(.3486+.0350)=.2328, 2(横纵+)=2(.0010+.4635)=.929,2(横高-)=2(.0010-.4647)=-.9274?等等重新计算 q [.785,.00171,.59037,.18697]。x= .00171,y=.59037,z=.18697。局部X第一列:
=1-2(.34854+.03496)=.2330
=2(横纵+)=2(.00101+.14678)=.29558(不是 .929!=.785*.187=.1468,是的)
=2(横高-)=2(.00032-.46356)=-.92648。
所以方向=(.233,.296,-.926),大部分向下!我之前乘错了。当前 q 接近所以手指向下68度。冠部末端执行器 = [0,.13,.94]-[.0326,.0414,-.1297]=[-.0326,.0886,1.0697]。从当前 [-.208,-.020,1.068] 距离.206。当前 q 目标也许可达,而失败? 误差巨大因为精确朝向腕部奇异;当前 q 可达。所以目标[-.033,.089,1.07] 当前 q,12步。冠部在此期间移动 +.05,目标也许落后 .05;设置预测冠部 x .05 然后末端执行器,目标距离.26 >.25 也许稍大。可以先目标[-.03,.09,1.07]并检查。右臂旋转 q 最终当前位置12步。如果左臂目标当前 q 不会失败。我将执行。
原文6,997 字
Left can't reach x0,y.1 with q down? Position error185mm huge means left arm near joint limits for that orientation. Perhaps left arm base at x-.3,y-.5, max reach .55, target distance .? Current eef [-.208,-.02,1.068] near max reach with q down. To reach farther +X and +Y need lower z, not higher. Arm fully extended? Current link6 z1.068, base z.9? Reach x/y perhaps limited. Target above basket at z1.08 perhaps near same. Position error185 means precheck hardly move, joint stuck due orientation wrist at singularity? Could rotate in other direction to downward q [0.5,.5,.5,-.5] etc. My qy90 local x=-Z, localY=+Y, wrist rotation perhaps requires joint6 ±? Left q approaching has joint6 near limit? Should inspect current_state joints to understand. Current q from starting z90 to y90 requires joint rotations perhaps joint1/2. IK stalled due joint6 limit? Could choose different yaw: for handle across X, need localY alongY (qy90), yes. Could use q=[0,.707,.707,0]? LocalX=+Z? Not down. Alternative downward orientation with localY=-Y equivalent q=[0,0,-.707,.707]? I'll derive down and openingY with localX=-Z, localY=-Y => localZ=-X, q=[0,.707,0,.707]? Ry? Use yaw180 times qy90 perhaps q=[0,.707,0,-.707]? Many. Gripper symmetric, rotating 180 around localX swaps fingers and opening sign, so qy90 vs rotation about localX π: q2=qx(π)*qy90 = [0,.707,0,-.707]? multiply [0,1,0,0]*[.707,0,.707,0] => w0,x.707,y0,z-.707. localX stays -Z, localY flips to -Y, localZ flips to -X. This is equivalent gripper inverted back (palm orientation) and may be more reachable. Starting qz90 to q2 [0,.707,0,-.707] dot=-.5 -> full angle4.188? choose sign q2 neg[0,-.707,0,.707] dot=.5 ->2.094rad. Should have via intermediate. Current q[.785,.002,.590,.187] to q2[0,.707,0,-.707] dot=-.132 => angle3.276, sign flip dot+.132 angle3.003. Very far. Could choose downward q with localY=-X (for remote) not correct handle but handle can be grasped along span perhaps okay if at crown. q=[.5,-.5,.5,.5] down closingX. From current dot .3925+.295+.0935=.781 ->angle1.344>1 but can intermediate. This orientation reachable likely right-style, left initial can Rx-90*Rz90 naturally by rotating wrist about local? Current left originally moved toward y90 not remote down. Could change to q=[.5,-.5,.5,.5] with localY=-X closing along handle span; two fingers pinch handle at two points along rod, can lift if rod thin between pads? Both fingers along X, handle spans X so each pad contacts top? Actually gripper fingers down, opening X, handle rod runs X through between fingers; closing fingers along rod means they'd pinch two sections from sides in X, not opposing across rod, but the rod can sit between fingers perpendicular? Imagine finger pads are vertical planes normalX, handle rod alongX goes through pad planes, cannot fit between without passing through fingers. At crown arch tangent X, fingers separated alongX and rod between them could lie diagonally away, closing may push it. Not ideal. Better downward localY=Y.
Could grasp handle from above with gripper forward horizontally along -Y? Orientation q? Current left qz90 initial fingers +Y, openingX. To pinch handle cross-section at crown, openingY needed, could rotate around worldZ 90 instead of pointing down: localX=-X, localY=-Y? Horizontal gripper pointing -X, closingY; approach from side alongX to crown. Could pinch handle from side at top with fingers horizontal, one on each sideY. q for localX=-X, localY=-Y, localZ=Z =Rz180 [0,0,1,0]. Starting qz90 to rz180 90deg, easy. Fingers extend -X (from left or right?), left hand initially left of basket, fingers -X point further left away, need position right of basket, not good. Use localX=+X, localY=+Y, localZ=-Z quaternion [0,1,0,0] (Rx180) fingers +X, openingY. From qz90 dot0 ->π, intermediate; position left of basket fingers+X reach handle, perfect! Gripper horizontal pointing right, fingers straddle front/back handle crown. Palm vertical? Gripper finger pads horizontal? LocalY=Y, fingers horizontal+X, handle at mid between pads front/back; good. This may be much easier left arm reach to crown x~0, y.13, z.94 with eef at x=crown-.14=-.14, y=.13, z=.94. Current eef[-.208,-.02,1.068] q current, target orientation Rx180 distance? dot .002 only ~π, need intermediate. Could rotate via current to Rx180 direction large. Better target horizontal q from initial z90 rotated around worldY? Want localX=+X from current localX(.632? .5,-.55). This requires reorient, possible.
Alternatively keep current q and grasp crown with pads at contact current direction(.635,.5,-.57), opening localY[-.39,.85,.35]. Crown location predicted x0,y.13,z.94, eef=crown-dir*.14=[-.089,.06,1.02]. Target from current[-.208,-.02,1.068] delta[.119,.08,-.048] dist.151 within, same q no precheck issues. This is exactly side approach but to crown instead of anchor. Crown is 4cm above anchor, may give better grip. I should use current q, target crown with prediction, close. No need down. I can triangulate crown using high and perhaps left wrist when positioned. Left wrist currently only front rim top; crown out of view above, but as moving toward predicted crown camera may bring it into view? At current camera points down; crown is above field. To see crown need camera look more horizontal (initial qz90), not down. Current q tilts down, crown out of view. Could rotate back qz90 while approaching, then crown visible. Initial qz90 camera forward? cam left looked handle full. It might be easiest grasp crown horizontal with openingY, but current openingY mostly, fingers direction diagonal down, crown can be between. I can rely high stereo after movement if visible.
Should understand left IK qdown failure perhaps because left gripper near reach with wrist orientation, current q side can reach crown. So choose current q and target crown estimated with z .94,y.13,x current perhaps.02. Contact .14 eef = crown - dir*.14. Compute dir current q exactly [1-2(y²+z²)=1-2(.3486+.0350)=.2328, 2(xy+wz)=2(.0010+.4635)=.929,2(xz-wy)=2(.0010-.4647)=-.9274? Wait recompute q [.785,.00171,.59037,.18697]. x= .00171,y=.59037,z=.18697. localX first col:
r00=1-2(.34854+.03496)=.2330
r10=2(xy+wz)=2(.00101+.14678)=.29558 (not .929! wz=.785*.187=.1468, yes)
r20=2(xz-wy)=2(.00032-.46356)=-.92648.
So dir=(.233,.296,-.926), mostly down! I mis multiplied earlier. Current q close qy90 so fingers down 68deg. Crown eef = [0,.13,.94]-[.0326,.0414,-.1297]=[-.0326,.0886,1.0697]. Target from current [-.208,-.020,1.068] dx.1754 dy.1087 dz.0013 dist.206. Current q target perhaps reachable vs qdown failed? qdown error huge because exact orientation wrist singularity; current q reachable. So target[-.033,.089,1.07] current q, 12 steps. Crown moves +.05 during, target perhaps behind .05; set predicted crown x .05 then eefx.017, target distance.26 >.25 perhaps slightly. Could do first target[-.03,.09,1.07] and inspect. Right rotate q final current pos 12 steps. If left target current q no fail. I'll do.
reasoning summary当前 q 甚至无法在 x/y 方向移动 .2 是因为接近奇异点吗?应该用更小的中间量来改变关节。之前从 [-.244,-.04,1.03] 到目标 [-.18,.01,1.11] 部分可行。现在目标 [-.03,.09,1.07] 在 +X 方向太远,可能超出工作空间。应该以当前 q 为基准,增量目标 [-.13,.03,1.10]。距离 .112。试试。左臂在该高度下最大 x 也许在 -.1 左右?篮子移动到,左边够不到?但任务设计为可达,必须在篮子位于时更早抬起;我错过了初始窗口?仍有可能以更低的 z 或不同姿态够到。不要慌。我有 600 步,但篮子很快向右移动,左臂就无法抓取。也许现在用右臂抬起篮子,左臂去拿遥控器?指令没有分配手臂。右臂位置更好,在 x .1 靠近篮子,可以用右臂抓住提手顶部,同时左臂拿左边的遥控器。那可能容易得多!我原以为用左臂拿篮子,但可以交换。右臂当前在 ,,,篮子提手顶部 x~.02,,。右臂更近。左臂在 -.208 靠近遥控器,可以拿遥控器。我应该交换角色。右臂可以抓住篮子提手侧面/顶部并抬起,左臂可以从左侧截取遥控器。很好。现在重新配置右臂朝向以抓提手(=Y 向下),而不是当前朝向遥控器向下移动的 q。可以保持当前 q [0.605,-.366,.368,.604]?计算:
x=-.366,y=.368,z=.604,w=.605
=1-2(.135+.365)=0
=2(横纵+)=2(-.1346+.3654)=.4616
=2(横高-)=2(-.221-.2226)=-.8872。
手指方向 (0,.462,-.887) 向下 62 度,适合从前方接近提手顶部。 第二列=2(横纵-)=2(-.1346-.3654)=-1.0,=1-2(x²+z²)=1-2(.134+.365)=.002,=2(纵高+)=2(.2223-.2212)=.0022 -> =-X!当前右臂沿 X 闭合,对提手跨度 X 不理想。现在绕旋转 90 度,把开口改为 Y,同时保持大致向下。期望的提手抓取给出 =Y,但从当前 q 到点积 .428+.260=.688 ->角度 1.624>1;需要中间量。期望的右提手 q [0.5,0.5,0.5,-0.5]?=-Z,?四元数 [.5,.5,.5,-.5],R 第二列=2(横纵-)=2(.25+.25)=1,所以 =Y 对,=(0,0,-1),?2(横高+)=2(.25+.25)=1 ->=X。等等也是 =X 且 =Y,同一个旋转! [.707,0,.707,0] 和 q[.5,.5,.5,-.5] 也许实际上相同?点积=.3535+.3535= .707,角度 1.57,不相同。计算 q[.5,.5,.5,-.5] 的 R 第 0 行 =1-2(.25+.25)=0,=2(.25-(-.25))=1,=2(.25+.25)=1 -> =(0,0,-1),=(1,0,0),不是 Y!我又把行/列搞混了。仔细。 矩阵 [0,0,1],[0,1,0],[-1,0,0],=(0,0,-1),=(0,1,0)。对,q[.5,.5,.5,-.5] 的 =(1,0,0),沿 X 闭合。对于遥控器,之前 q[.5,-.5,.5,.5] 的 R:
=0,=2(-.25-.25)=-1,=2(.25+.25)=1
=2(-.25+.25)=0,=1-2(.25+.25)=0,=2(.25-.25)=0
=2(.25-.25)=0,=2(.25-.25)=0,=1-2(.25+.25)=0?等等 =1-2(x²+y²)=1-2(.25+.25)=0,矩阵全?应该重新计算完整四元数公式,也许 q [.5,-.5,.5,.5] 是 120 度旋转,迹为 0 =>?=1-2(.25+.25)=0;行:
=1-2(y²+z²)=0
=2(横纵 -)=2(-.25-.25)=-1
=2(横高+)=2(-.25+.25)=0(我之前横高符号错了)
=2(横纵+)=2(-.25+.25)=0
=1-2(x²+z²)=0
=2(纵高-)=2(.25+.25)=1
=2(横高-)=2(-.25-.25)=-1
=2(纵高+)=2(.25-.25)=0
=1-2(x²+y²)=0。所以 =(0,0,-1),=(-1,0,0),=(0,1,0)。正确,遥控器向下沿 X 闭合。 的 =Y。好。
对于右提手,也许朝向 q [0.5,0.5,-0.5,0.5]?应该向下 -Z 且 Y,与相同(唯一,手指 180 度内)。右臂可以从当前以 .8 增量旋转到。位置靠近顶部。或者选择当前 q 方向 (0,.462,-.887),开口 -X(沿提手)不理想,但可以横跨抓取顶部?最好右臂用当前沿 X 闭合抓取篮子前缘(前缘沿 X,沿 X 闭合不是横跨壁),不行。
右臂可以抓住右侧的提手竖直支撑,那里的切线也许是 Y/Z,沿 X 闭合很好!篮子右侧的提手支撑在 x=+/2(约 .15),y=.13,z .90。右夹爪在 ,,,当前手指方向向前/向下,开口 X,可以夹住沿 X 厚度的支撑。这类似于左锚点抓取,但镜像且更近。可以用右腕立体视觉看到顶部附近的提手支撑(观测87 右图提手在 ,),需要向上/向后移动才能看到。右臂当前靠近右侧支撑吗?当前右指尖 =末端执行器+[0,.0728,-.1398]=[.101,-.0042,.8630],篮子右壁在 ,,z .88,所以指尖在支撑前方、左侧。现在移动末端执行器x+.07,y+.13,z+.04 使接触点位于支撑处。但当前开口 X 很好。一旦可见,可以用高机位和右腕三角测量支撑。右腕在观测87 显示提手支撑在顶部 ,,篮子壁中心,指尖在底部。应该提手支撑不在视野内,因为相机向下看。抬高末端执行器z 或向前移动可能使其进入视野?类似左锚点最终可见。右当前末端执行器,相机也许 z?计算相机 C 并投影指尖到夹持中心。对于右观测87,当前 q 的指尖投影应在中心。右腕提手支撑在 , 意味着在手指前方和上方。我可以像左边一样用相机相对调整,但跟踪传送带。我可以用高机位三角测量右支撑,如果对应可见在图像边缘,也许提手顶部部分可见。或者用当前 q 移动右末端执行器y+.06,z+.03,x+.03 共 5 步,让提手进入视野。同时左臂可以用当前向下倾斜、开口主要 Y 的朝向移动到遥控器?左当前第二列:=2(横纵-)=2(.00101-.14678)=-.2915,=1-2(x²+z²)=.9301,=2(纵高-)=2(.1104-.00134)=.2181 => 开口主要 Y。遥控器长轴 Y,需要沿 X 闭合,左臂不对。应该把左臂旋转到遥控器 q [.5,-.5,.5,.5](向下沿 X 闭合),从当前点积 .3926-.0009+.2952+.0935=.7804 ->角度 1.348>1,选择 .8。左当前位置 [-.208,-.02,1.068],遥控器 ,,,要抓取遥控器,末端执行器也许在 ,,。目标位置 [-.28,.01,.96] 增量 .113。好。这在左臂当前附近可达。所以交换角色是合理的。左臂可以在遥控器靠近时抓取,右臂抬起篮子。
我决定右臂通过提手顶部抬起,也许在更近的姿态可以实现。右当前到角度 1.62,可以 .8。位置目标在顶部上方,也许当前篮子顶部高 (323,101), ->世界 x .006,。右末端执行器对于在顶部接触 .14 ->[.006,.13,1.08]。从右 [.101,-.077,1.003] 的增量=[-.095,.207,.077] 距离 .242 <.25,朝向需要中间量。可以预检查,也许中间 q 和远位置可能失败。分两步移动右臂:首先姿态 [.07,.04,1.08] 用朝的中间 q .8;然后到顶部。这在篮子上方/前方,安全。左遥控器朝向目标。应该精确计算 q 中间量。右 q 目标从当前到的 .8,左从当前到遥控器 q 的 .8。使用脚本。
原文6,723 字
Even current q can't move .2 x/y due reach singularity? Should smaller intermediate to change joints. Earlier target left[-.18,.01,1.11] from[-.244,-.04,1.03] worked partial. Now target[-.03,.09,1.07] too far +X perhaps outside workspace. Should incremental target [-.13,.03,1.10] current q. distance .112. Try. Left arm perhaps max x around-.1 at that height? Basket moving to x0, left can't reach? But task designed reachable, must raise basket earlier when at x-.3; I missed initial window? Still can perhaps reach x0 with lower z or different orientation. Should not panic. I have 600 steps but basket moving toward right soon left cannot grasp. Perhaps use right arm to lift basket now and left pick remote? Instruction doesn't assign arms. Right arm better positioned at x .1 near basket, could grab handle crown with right while left picks remote on left. That may be far easier! I assumed left basket, but can swap. Right currently at x.1,y-.077,z1.003, basket handle crown x~.02,y.13,z.94. Right is closer. Left at-.208 near remote x-.345, can pick remote. I should swap roles. Right can grasp basket handle side/crown and lift, left can intercept remote from left. Great. Now reconfigure right orientation for handle (localY=Y down qy90) vs remote q current moving to remote down. Could keep current q [0.605,-.366,.368,.604] localX? compute:
x=-.366,y=.368,z=.604,w=.605
r00=1-2(.135+.365)=0
r10=2(xy+wz)=2(-.1346+.3654)=.4616
r20=2(xz-wy)=2(-.221-.2226)=-.8872.
Fingers direction (0,.462,-.887) down 62deg, good for handle crown approach from front. localY second col=2(xy-wz)=2(-.1346-.3654)=-1.0, r11=1-2(x²+z²)=1-2(.134+.365)=.002, r21=2(yz+wx)=2(.2223-.2212)=.0022 -> localY=-X! Current right closing alongX, not ideal handle spanX. Now rotate around localX by90 to change opening toY while keeping down-ish. Desired handle grasp qy90 gives localY=Y, but from current q to qy90 dot .428+.260=.688 ->angle1.624>1; need intermediate. Desired right handle q [0.5,0.5,0.5,-0.5]? localX=-Z, localY? quaternion [.5,.5,.5,-.5], R second col=2(xy-wz)=2(.25+.25)=1, so localY=Y yes, localX=(0,0,-1), localZ? 2(xz+wy)=2(.25+.25)=1 ->localZ=X. Wait qy90 also localZ=X and localY=Y, same rotation! qy90 [.707,0,.707,0] and q[.5,.5,.5,-.5] perhaps actually same? dot=.3535+.3535= .707, angle1.57, not same. Compute q[.5,.5,.5,-.5] R row0 r00=1-2(.25+.25)=0,r01=2(.25-(-.25))=1,r02=2(.25+.25)=1 -> localX=(0,0,-1),localY=(1,0,0), notY! I mixed row/column again. Carefully. qy90 matrix row0[0,0,1],row1[0,1,0],row2[-1,0,0], localX=(0,0,-1),localY=(0,1,0). Yes q[.5,.5,.5,-.5] localY=(1,0,0), closingX. For remote earlier q[.5,-.5,.5,.5] R:
r00=0,r01=2(-.25-.25)=-1,r02=2(.25+.25)=1
r10=2(-.25+.25)=0,r11=1-2(.25+.25)=0,r12=2(.25-.25)=0
r20=2(.25-.25)=0,r21=2(.25-.25)=0,r22=1-2(.25+.25)=0? Wait r22=1-2(x²+y²)=1-2(.25+.25)=0, matrix all? Should recompute full quaternion formula perhaps q [.5,-.5,.5,.5] is rotation 120deg, trace0 =>r22? r22=1-2(.25+.25)=0; rows:
r00=1-2(y²+z²)=0
r01=2(xy - wz)=2(-.25-.25)=-1
r02=2(xz+wy)=2(-.25+.25)=0 (I incorrectly xz sign)
r10=2(xy+wz)=2(-.25+.25)=0
r11=1-2(x²+z²)=0
r12=2(yz-wx)=2(.25+.25)=1
r20=2(xz-wy)=2(-.25-.25)=-1
r21=2(yz+wx)=2(.25-.25)=0
r22=1-2(x²+y²)=0. So localX=(0,0,-1),localY=(-1,0,0),localZ=(0,1,0). Correct remote down closingX. qy90 localY=Y. Good.
For right handle perhaps orientation q [0.5,0.5,-0.5,0.5]? Should down localX -Z and localY Y, same qy90 uniquely (up to finger 180). Right can rotate qy90 from current with .8 increments. Position near crown. Or choose current q direction(0,.462,-.887), opening -X (along handle) not ideal but can grasp crown across? Better right grab basket front rim with current closingX (rim front alongX, closing alongX not across wall), no.
Could right grasp handle vertical support at right side where tangent perhapsY/Z, closingX is good! Handle support on basket right side at x=crown+width/2 (~.15), y=.13, z .90. Right gripper at x.10,y-.077,z1.003, current fingers direction forward/down, openingX, can pinch support across thicknessX. This is analogous left anchor grasp but mirrored and closer. Could use stereo with right wrist sees handle support near top (obs87 right image handle at x500,y0), need move up/back to see. Right current near right support? Current right tip =eef+[0,.0728,-.1398]=[.101,-.0042,.8630], basket right wall at x.17,y.1,z .88, so tip front of support byy.13 and leftx.07. Now move eef x+.07,y+.13,z+.04 to put contact at support. But current openingX good. Could triangulate support with high and right wrist once visible. Right wrist at obs87 shows handle support at top x490,y0, basket wall center, fingertips bottom. Should handle support out of view because camera angle down. Raising eef z or moving forward may bring into view? Similar left anchor eventually visible. Right current eef z1.003, camera perhaps z? Compute camera C and project tip to pinch center. For right obs87 q current tip projection should center. Right wrist handle support at x480,y0 means ahead of finger and up. I can use camera-relative adjustment like left but track conveyor. I can triangulate right support with high if corresponding visible at image border perhaps handle crown partial. Could instead move right eef y+.06,z+.03,x+.03 with current q 5 steps, get handle into view. Meanwhile left can move to remote with current angled down opening mostlyY? Left current localY second col: r01=2(xy-wz)=2(.00101-.14678)=-.2915, r11=1-2(x²+z²)=.9301, r12=2(yz-wx)=2(.1104-.00134)=.2181 => opening mostlyY. Remote longY, need closingX, left wrong. Should rotate left to remote q [.5,-.5,.5,.5] (down closingX) from current dot .3926-.0009+.2952+.0935=.7804 ->angle1.348>1, choose .8. Left current position[-.208,-.02,1.068], remote x-.345,y.01,z.764, to grasp eef at remote perhaps x-.30,y.01,z.92. Target position[-.28,.01,.96] delta.113. Good. This is reachable left near current. So swap roles is sensible. Left can grasp remote as it approaches, right lift basket.
I'll decide right lift via handle crown qy90 perhaps can achieve at closer pose. Right current to qy90 angle1.62, can .8. Position target above crown perhaps current basket crown high (323,101),z.94 ->world x .006,y.13. Right eef for qy90 at crown contact .14 ->[.006,.13,1.08]. delta from right [.101,-.077,1.003]=[-.095,.207,.077] dist.242 <.25, orientation needs intermediate. Could precheck perhaps q intermediate and pos far might fail. Move right in two steps: first pose[.07,.04,1.08] with q intermediate toward qy90 .8; then crown. This is above/front basket, safe. Left remote orientation target. Should compute q intermediates exact. Right q target slerp .8 from current to qy90, left .8 from current to remote q. Use script.