我的四元数乘法公式中 Y 分量的符号写错了。自上而下的四元数 [0.5, -0.5, 0.5, 0.5] 将局部 +X 映射到世界 -Z,将局部 +Y 映射到世界 -X,将局部 +Z 映射到世界 +Y。其闭合方向与初始朝向相同。这是 (-90°) (90°)。如果腕部相机沿手指方向观察,其光学前向可能变为世界 -Z。另一个备选四元数 [0.5, 0.5, -0.5, -0.5] 同样使局部 +X 朝下,但将局部 +Y 映射到世界 +X,局部 +Z 映射到世界 -Y。
我将使用 = [0.5, -0.5, 0.5, 0.5],这样手指沿世界 X 方向闭合。大多数物体沿 X 方向似乎相对较窄,这可能适合长度沿 Y 方向延伸的汽车。对于斜放的巧克力棒,我可能需要调整偏航以沿其短轴闭合。辣椒看起来约 0.05米宽,因此沿 X 方向闭合的自上而下抓取可能是稳定的。
该四元数整体表示 120° 旋转,但其与初始 90° Z 旋转的朝向距离为 90°。四元数点积约为 0.3535 + 0.3535 = 0.707,给出距离 1.571弧度,超过 1.0弧度的目标限制。因此我需要一个中间朝向,也许是初始四元数与之间的归一化中点。我可以先抬起两个夹爪并部分旋转。每个位置目标还必须保持在测量位姿的 0.25米以内。
我需要仔细估计抓取高度。手指沿第六连杆局部 +X 方向延伸 0.1576米,因此在自上而下朝向中,其最远指尖位于 - 0.1576米。要与 z = 0.78米处的物体接触,也许第六连杆应在 z = 0.95米左右。我初步估计夹垫可能从局部 x = 0.06米延伸到 0.1576米,抓取中心在第六连杆前方约 0.12米。这样接触中心将位于 - 0.12米。要在保持指尖接近估计桌面高度 0.75米的同时跨骑物体,末端执行器高度约 0.91米似乎是合理的。使用这种指长时, 桌面抓取通常会用 z 约 0.88米吗?我需要依赖实际几何,而不是那个暂定预期。
初始时,第六连杆位于 z = 0.9215米。水平手指中心也可能接近该高度,约在桌面上方 0.17米。其指尖似乎接近 y = -0.194米和 z = 0.9215米,远高于左侧汽车。汽车出现在腕部视图底部,这表明在该朝向下可能需要将末端执行器降低约 0.12米。然而一旦朝下,末端执行器高度 0.89米将使指尖位于 z = 0.7324米,低于桌面。在末端执行器高度 0.9076米时,指尖将达到 z = 0.75米。
末端执行器高度 0.91米可能适用于顶部接近 z = 0.79米的物体,此时夹垫约在 z = 0.80米。在 z = 0.90米处闭合将使指尖接近 z = 0.742米,并可能接触桌面。在 z = 0.92米处,指尖将接近 z = 0.762米,夹垫约在 z = 0.80米。如果汽车高 0.035米,其顶部在 z = 0.785米,那么末端执行器高度 0.93米是否会使接触中部位于 z = 0.795米左右?
一个更具体的暂定估计是,远端夹垫从局部 x = 0.09米延伸到 0.1576米,因此物体中心可能位于距第六连杆约 0.12米处。汽车中心在 z = 0.78米将建议末端执行器高度 0.90米,但 z = 0.7424米处的指尖将比估计桌面低 0.0076米。若物体中心在 z = 0.79米、末端执行器高度为 0.91米,则指尖将位于 z = 0.7524米,基本与桌面齐平。因此 0.91米仍然合理。对于中心在 z = 0.76米的薄巧克力棒,末端执行器高度 0.89米将使指尖接近 z = 0.732米。若要在棒顶部附近 z = 0.765米处捏取、同时指尖接近桌面 z = 0.75米,则可改用末端执行器高度 0.9076米,将物体置于第六连杆前方约 0.143米处,接近指尖。我暂定考虑薄棒用 z = 0.905米,中心在 z = 0.79米的辣椒用 z = 0.91米。
我可以先移动到物体上方 z = 1.05米处,使末端执行器 X 和 Y 与期望抓取中心匹配,然后下降至 z = 0.91米。使用时,张开的手指沿 X 方向展开。在 z = 1.05米处,其底部将大约在 z = 0.892米,高于物体;我仍应检查与篮子边缘的间隙。
我需要避免手臂交叉。左臂可以处理大约位于 (-0.374, -0.159) m 的左侧汽车、x = -0.195米和 -0.128米处的巧克力,也许还有 x = 0.044米处的中央汽车。右臂可以处理 x = 0.154米处的汽车、x = 0.217米、0.34米和 0.38米处的辣椒,以及 x = 0.147米处的右侧巧克力。可能的第一对组合包括左侧汽车和较远的青椒,或大约位于 (-0.195, -0.128) m 的士力架和大约位于 (0.217, -0.172) m 的中央青椒。这些可见物体可能通过腕部视图帮助细化抓取估计。左侧汽车部分位于初始夹爪下方,但移动后应变得可达。
从两辆汽车开始将使用相似的抓取几何,但右臂随后需要将其汽车穿过中心运到左侧篮子。我不需要交接:右臂可能到达大约位于 (-0.293, 0.02) m 的左侧篮子,尽管我估计从其汽车处转移 0.59米,需要多个目标并可能穿过左臂区域。另一种分配是左臂处理全部三辆汽车和两块巧克力,而右臂处理所有辣椒和右侧巧克力;我估计这是六个对四个物体。有 1100 个控制步,每个物体大约 80 步,或总共约 800 个顺序步,可能足够。右臂完成自己的工作后可以帮助处理中央汽车。效率不如保持路径畅通重要。
左臂也可以在右臂处理更右侧时抓取 x = 0.154米处的汽车。或者,右臂可以在左臂完成首次放置并移开后,将那辆汽车放入左侧篮子。两臂都可以从汽车开始并按顺序放置,但同时放入同一篮子有碰撞风险。右臂越过蓝色篮子前往白色篮子的路线似乎可能可行,尽管需要小心。我也考虑过让右臂从 x = 0.34米处的红椒开始。
我将从左侧汽车和中央青椒开始,通过右腕视图细化辣椒位置。我考虑的初始高位目标是左侧 (-0.374, -0.159, 1.05) m 和右侧 (0.2166, -0.1723, 1.05) m。我最初估计从 (-0.3, -0.352, 0.922) m 的左侧位移为 0.216米,但分量估计 (-0.074, +0.193, +0.128) m 给出约 0.243米,刚好在 0.25米界限内。对于右臂,分量估计 (-0.083, +0.180, +0.128) m 给出约 0.234米。完整朝向变化仍约为 1.57弧度,因此我需要中点四元数,暂定为 [0.6533, -0.2706, 0.2706, 0.6533],我将计算它。其朝向距离应约为 0.785弧度。
我考虑过将高度降至 z = 1.03米,使位置距离约为 0.227米。在中间朝向下,手指朝前下方,在 Y 方向延伸约 +0.111米,在 Z 方向延伸约 -0.111米。其底部将接近 z = 0.919米,似乎安全高于物体。我当前提出的第一批目标是左侧 (-0.374, -0.159, 1.04) m,估计距离 0.245米,以及右侧 (0.217, -0.172, 1.04) m,估计距离 0.232米。两个夹爪将保持张开。预检查仍需建立局部运动学可行性。对于这个看似无阻碍的导航运动,我考虑六到八个控制步,并计划使用八个。
原文7,813 字
My quaternion multiplication formula had the wrong sign for the Y component. The top-down quaternion [0.5, -0.5, 0.5, 0.5] maps local +X to world -Z, local +Y to world -X, and local +Z to world +Y. Its closing direction is the same as the initial orientation. This is R_x(-90°) R_z(90°). If the wrist camera looks along the fingers, its optical forward direction may become world -Z. The alternative quaternion [0.5, 0.5, -0.5, -0.5] also points local +X downward, but maps local +Y to world +X and local +Z to world -Y.
I will use q_down = [0.5, -0.5, 0.5, 0.5], so the fingers close along world X. Most objects seem relatively narrow along X, and this may suit cars whose length runs along Y. For the diagonal chocolate bars, I may need to adjust yaw to close along their short axis. The peppers appear about 0.05 m wide, so a top-down grasp closing along X may be stable.
This quaternion represents a 120° rotation overall, but its orientation distance from the initial 90° Z rotation is 90°. The quaternion dot product is approximately 0.3535 + 0.3535 = 0.707, giving a distance of 1.571 rad, which exceeds the 1.0 rad target limit. I therefore need an intermediate orientation, perhaps the normalized midpoint between the initial quaternion and q_down. I can first raise and partially rotate both grippers. Each position target must also remain within 0.25 m of the measured pose.
I need to estimate the grasp height carefully. The fingers extend 0.1576 m along link6 local +X, so in the top-down orientation their farthest tips are at z_eef - 0.1576 m. For contact with an object at z = 0.78 m, perhaps link6 should be around z = 0.95 m. I initially estimate the pads might extend from local x = 0.06 m to 0.1576 m, with a grasp center about 0.12 m forward of link6. That would put the contact center at z_eef - 0.12 m. To straddle an object while keeping the tips near the estimated table height of 0.75 m, an end-effector height around 0.91 m seems plausible. Would an ARX table grasp normally use z around 0.88 m with this finger length? I need to rely on the actual geometry rather than that tentative expectation.
Initially, link6 is at z = 0.9215 m. The horizontal finger centers may also be near that height, approximately 0.17 m above the table. Their tips appear to be near y = -0.194 m and z = 0.9215 m, well above the left car. The car appears at the bottom of the wrist view, suggesting that lowering the end effector by about 0.12 m might be needed with that orientation. Once pointing downward, however, an end-effector height of 0.89 m would put the tips at z = 0.7324 m, below the table. Tips would reach z = 0.75 m at an end-effector height of 0.9076 m.
An end-effector height of 0.91 m may work for objects whose tops are near z = 0.79 m, with the pads around z = 0.80 m. Closing at z = 0.90 m would put the tips near z = 0.742 m and could contact the table. At z = 0.92 m, the tips would be near z = 0.762 m, with pads around z = 0.80 m. If a car is 0.035 m tall with its top at z = 0.785 m, would an end-effector height of 0.93 m put the middle of the contact around z = 0.795 m?
A more specific tentative estimate is that the distal pads run from local x = 0.09 m to 0.1576 m, so an object center could sit about 0.12 m from link6. A car center at z = 0.78 m would then suggest an end-effector height of 0.90 m, but the tip at z = 0.7424 m would be 0.0076 m below the estimated table. With an object center at z = 0.79 m and an end-effector height of 0.91 m, the tip would be at z = 0.7524 m, essentially at table level. Thus 0.91 m remains plausible. For a thin chocolate bar centered at z = 0.76 m, an end-effector height of 0.89 m would put the tips near z = 0.732 m. A pinch near the bar top at z = 0.765 m, with tips near the table at z = 0.75 m, could instead use an end-effector height of 0.9076 m, placing the object about 0.143 m forward of link6, near the tips. I tentatively consider z = 0.905 m for thin bars and z = 0.91 m for peppers centered at z = 0.79 m.
I can first move above the objects at z = 1.05 m, matching end-effector X and Y to the desired grasp center, and then descend toward z = 0.91 m. With q_down, the open fingers spread along X. At z = 1.05 m, their bottom would be around z = 0.892 m, above the objects; I should still check clearance from basket rims.
I need to avoid crossing the arms. The left arm could handle the left car at approximately (-0.374, -0.159) m, the chocolates at x = -0.195 m and -0.128 m, and perhaps the central car at x = 0.044 m. The right arm could handle the car at x = 0.154 m, peppers at x = 0.217 m, 0.34 m, and 0.38 m, and the right chocolate at x = 0.147 m. Possible first pairs include the left car and the farther green pepper, or the Snickers at approximately (-0.195, -0.128) m and the central green pepper at approximately (0.217, -0.172) m. Those visible objects might help refine grasp estimates through the wrist views. The left car is partly under the initial gripper but should become accessible after moving.
Starting with two cars would use similar grasp geometry, but the right arm would then need to carry its car across the center to the left basket. I do not need a handoff: the right arm may reach the left basket at approximately (-0.293, 0.02) m, although I estimate a 0.59 m transfer from its car, requiring multiple targets and potentially crossing the left arm's area. Another allocation is for the left arm to handle all three cars and two chocolates, while the right handles all peppers and the right chocolate; I am estimating this as six versus four objects. With 1100 control steps, roughly 80 steps per object, or about 800 sequential steps, may be sufficient. The right arm could help with the central car after finishing its own work. Efficiency is less important than keeping paths clear.
The left arm could also pick the car at x = 0.154 m while the right works farther right. Alternatively, the right arm could place that car in the left basket after the left arm finishes its first placement and moves away. Both arms could start with cars and place them sequentially, but simultaneous placement into the same basket risks collision. The right arm's route over the blue basket toward the white basket seems potentially feasible, though it would need care. I also considered starting the right arm with the red pepper at x = 0.34 m instead.
I will start with the left car and the central green pepper, refining the pepper position through the right wrist view. The initial high targets I considered are left (-0.374, -0.159, 1.05) m and right (0.2166, -0.1723, 1.05) m. I initially estimated the left displacement from (-0.3, -0.352, 0.922) m as 0.216 m, but the component estimate (-0.074, +0.193, +0.128) m gives approximately 0.243 m, just within the 0.25 m bound. For the right arm, the component estimate (-0.083, +0.180, +0.128) m gives about 0.234 m. The full orientation change is still about 1.57 rad, so I need the midpoint quaternion, tentatively [0.6533, -0.2706, 0.2706, 0.6533], which I will calculate. Its orientation distance should be around 0.785 rad.
I considered reducing the height to z = 1.03 m to bring the position distance to about 0.227 m. At the intermediate orientation, the fingers point forward and downward, extending approximately +0.111 m in Y and -0.111 m in Z. Their bottom would then be near z = 0.919 m, which appears safely above the objects. My current proposed first targets are left (-0.374, -0.159, 1.04) m, with an estimated distance of 0.245 m, and right (0.217, -0.172, 1.04) m, with an estimated distance of 0.232 m. Both grippers will remain open. The precheck still needs to establish local kinematic feasibility. For this apparently unobstructed navigation motion, I considered six to eight control steps and plan to use eight.