左侧的木质玩具看起来像一只兔子,右侧被部分遮挡的玩具可能是同一种。看起来有两个手表、两个木质玩具和两个辣椒需要分拣。
我需要在两条机械臂之间分配工作,同时考虑可达范围。左臂能否直接将青椒运到位于 x = 0.26米的右侧篮子?从 x = -0.3米移动到 x = +0.26米跨越 0.56米。0.25米的目标距离限制允许中间运动,但整体可达范围和逆运动学仍可能阻止这次转移。我最初考虑让左臂直接处理青椒,或者让右臂去抓取它而左臂分拣手表。然而,位于 x = -0.339米的青椒对左臂是可及的,而右侧篮子远在工作区另一侧。通过中心进行转移似乎更好。
我估计机械臂基座在 x = ±0.3米,可能 y = -0.6米。初始末端执行器在 y = -0.352米,z = 0.922米;桌面物体大约在 y = -0.1米,篮子大约在 y = -0.007米。我的理解是的可达范围约为 0.55米。基于这个假设,从左基座到右侧篮子的 0.56米水平位移,加上大约 0.6米的 y 方向距离,使得直接转移不可能。我应该按侧分配工作,并通过中心交换青椒。
暂定的分配是:左臂将木质兔子从大约 x = -0.23米,y = -0.20米移到靠近 x = 0,y = 0 的中间篮子,x 方向变化约 0.23米。右臂可以将其兔子从 x = 0.36米,y = -0.20米移到那个篮子。这需要 x 方向约 0.36米;在右基座位于 x = 0.3米且可达范围约 0.6米的情况下可能可行,不过 y 方向位移也很重要。我认为中间篮子对两条臂都是可及的。左臂可以将位于 x = 0.015米和 x = 0.084米的两个手表分拣到位于 x = -0.26米,y = -0.007米的左侧篮子。右臂可能也能到达 x = 0.015米的手表,但左臂可以处理两个。右臂将把黄椒从 x = 0.206米,y = -0.114米移到位于 x = 0.266米,y = -0.007米的右侧篮子。
对于位于 x = -0.339米,y = -0.119米的青椒,左臂可以将其暂放在靠近中心前方的桌面上,位置为 x = 0.05米,y = -0.25米,然后右臂可以抓取它并放入右侧篮子。我也考虑过让左臂将其保持在 x = 0.03米,y = -0.26米附近,同时右臂靠近。无论哪种转移都需要避开手表和木质玩具,并且在清除一些物体后可能更容易。
一个有用的四轮计划是:第一,左臂暂放青椒,同时右臂分拣黄椒;第二,左臂分拣其木质玩具,同时右臂分拣暂放的青椒;第三,左臂分拣第一个手表,同时右臂分拣其木质玩具;第四,左臂分拣第二个手表,同时右臂保持空闲。我需要确保右臂能够从上方抓取暂放的辣椒并安全运输。
我仍然需要更好地估计桌面和物体的高度。在高机位相机图像中,青椒的顶部大约在像素 y = 222,底部大约在 y = 249。我暂时假设桌面高度为 0.75米,并对木质玩具使用 z = 0.79米。这些高度并非从观测中得知。典型值可能是桌面在 z = 0.75米,物体中心大约在 z = 0.78–0.82米,但我应该在抓取前用腕部相机和测量的增量运动来细化估计。能否从篮子或机器人坐标推断桌面平面?能否对多个相机中可见的物体进行三角测量?初始左腕视图显示青椒,右腕视图显示黄椒,高机位视图显示所有物体。手表可能只在高机位视图中可见,因此移动相机可能有帮助。
我必须使用观测图像、标定和测量的末端执行器位姿,而不是底层网格位置或模拟器内部信息。投影已知的夹爪几何形状可能有助于检查深度估计。初始左末端执行器位置是测量的,其旋转是可用的,腕部相机外参可能与其有固定关系。移动后的额外视图可以提供物体深度线索。
我应该确定用于自上而下抓取的夹爪方向。当前四元数 [0.707, 0, 0, 0.707] 表示绕世界 Z 轴旋转 90 度:局部 X 指向世界 +Y,局部 Y 指向世界 -X,局部 Z 指向世界 +Z。因此手指沿世界 +Y 方向延伸,并沿世界 -X 方向张开。在第六连杆位于 y = -0.352米,z = 0.922米且手指延伸约 0.157米的情况下,指尖大约在 y = -0.194米,z = 0.922米。高机位相机中的夹爪大约在 x = -0.3米,y = -0.23米。
左腕标定给出光学 X 沿世界 X,光学 Y 大约为 [0, -0.5, -0.866],光学 Z 大约为 [0, 0.866, -0.5]。因此相机朝前下方看,其前向方向大约等于 0.866 世界 Y 减去 0.5 世界 Z。在初始方向上,局部 +X 是世界 +Y。
对于自上而下的抓取,局部 X 应指向世界 -Z,局部 Y 在合适的闭合方向上水平。我可以选择局部 Y 沿世界 X 或世界 Y。取局部 X = (0, 0, -1) 和局部 Y = (1, 0, 0),局部 Z 是它们的叉积,即世界 -Y。以这些轴为列写出的旋转矩阵是 [[0, 1, 0], [0, 0, -1], [-1, 0, 0]]。我不确定四元数:我考虑过的可能性包括 [0.5, 0.5, -0.5, 0.5]、[0.5, -0.5, 0.5, 0.5],以及其他常见的自上而下形式,如 [0.5, 0.5, 0.5, -0.5]。我应该用科学计算库计算它,而不是凭记忆选择一个。
腕部相机的前向方向大约为 0.866 局部 X 减去 0.5 局部 Z。其光学 X 是 -局部 Y,光学 Y 大约为 -0.5 局部 X 减去 0.866 局部 Z。如果局部 X 指向下方,局部 Z 沿世界 -Y,相机前向变为 0.5 世界 Y 减去 0.866 世界 Z。它仍会从垂直方向向前看 30 度,这应该能让它看到夹爪稍前方的物体。
辣椒的球茎直径似乎约为 0.07米,高度约为 0.08米。围绕上半部分进行自上而下的抓取,手指垂直延伸并跨球茎宽度闭合,可能可行。我应该选择适合形状的偏航角。在初始左腕图像中,青椒大约在像素 (225, 356),张开的黑色手指占据左下和右下边缘。夹爪当前水平朝前,因此需要在辣椒上方接近时向下转动。
一个可能的左臂接近方式是大约 x = -0.335米,y = -0.12米,z = 0.99米。从当前位姿估计的距离是平方根(0.035² + 0.232² + 0.068²) = 0.243米,勉强在 0.25米限制内。所需的旋转约为 1.57弧度,超过 1.0弧度的方向限制,因此需要中间方向。我可以先以当前方向移动到 y = -0.27米,z = 1.0米,然后在两步内向下转 90 度,同时朝 y = -0.12米移动。我需要避开辣椒和篮子。当前手指延伸到 y = -0.194米,而辣椒在 y = -0.119米,z = 0.80米附近;在其上方抬高并前进似乎没有障碍。
对于位于 x = 0.206米,y = -0.114米附近的黄椒,右臂可以类似地从 (0.3, -0.352, 0.922) m 移动到 (0.21, -0.25, 1.00) m,然后向下转并接近 y = -0.11米。两个辣椒可以在第一轮并行抓取,但它们的中心需要更精确的定位。
我应该比较在假设高度下青椒底部和顶部的投影。其底部可能在像素 (148, 249)。在桌面 z = 0.75米的情况下,我暂估计其地面位置接近 x = -0.337米,y = -0.14米。我早先的中心投影使用像素 (148, 236) 和 z = 0.82米,得到 y = -0.119米。底部在像素 y = 249 且 z = 0.75米时给出 y = -0.148米,而顶部在像素 y = 221 且 z = 0.83米时可能给出 y = -0.083米。这些估计需要检查。在原始高机位图像中,青椒大致跨越像素 y = 220–249,其中心大约在 y = 233,木质玩具跨越 y = 265–293。篮子底部大约在像素 y = 211;它们的中心平面 y 坐标仍不清楚。也许消失几何可以帮助确定桌面高度。我怀疑桌面顶部在 z = 0.75米或 0.78米,但这仍然是一个假设。
我将首先投影已知的夹爪几何形状,并与图像比较。在第六连杆 z = 0.9215米处,0.1576米的局部 X 手指延伸指向世界 +Y,给出近似左指尖位置 [-0.2995, -0.1947, 0.9215] m。这是否投影到像素 y = 243 附近的黑色指尖附近?手指似乎从像素 (100, 285) 和 (145, 287) 附近的基部延伸到 (90, 244) 和 (147, 244) 附近的指尖。我现在应该计算它们的投影和候选的向下四元数。
原文9,018 字
The left wooden toy looks like a bunny, and the partly occluded toy on the right may be the same kind. There appear to be two watches, two wooden toys, and two peppers to sort.
I need to divide the work between the arms while accounting for reach. Could the left arm carry the green pepper directly to the right basket at x = 0.26 m? Moving from x = -0.3 m to x = +0.26 m spans 0.56 m. The 0.25 m target-distance limit allows intermediate motions, but overall reach and IK may still prevent the transfer. I initially considered having the left arm handle the green pepper directly, or having the right arm pick it while the left arm sorted a watch. The green pepper at x = -0.339 m is accessible to the left arm, however, and the right basket is far across the workspace. A transfer through the center seems better.
I am estimating the arm bases at x = ±0.3 m and perhaps y = -0.6 m. The initial end effectors are at y = -0.352 m, z = 0.922 m; the table objects are around y = -0.1 m and the baskets around y = -0.007 m. My understanding is that the ARX X5 reach is approximately 0.55 m. On that assumption, the 0.56 m horizontal displacement from the left base to the right basket, plus roughly 0.6 m in y, makes the direct transfer impossible. I should divide the work by side and exchange the green pepper through the center.
The tentative assignments are for the left arm to move the wooden bunny from approximately x = -0.23 m, y = -0.20 m into the middle basket near x = 0, y = 0, a change of about 0.23 m in x. The right arm can move its bunny from x = 0.36 m, y = -0.20 m into that basket. That requires about 0.36 m in x; it may be possible with the right base at x = 0.3 m and a reach around 0.6 m, though the y displacement also matters. I think the middle basket is accessible to both arms. The left arm can sort both watches, at x = 0.015 m and x = 0.084 m, into the left basket at x = -0.26 m, y = -0.007 m. The right arm could probably reach the watch at x = 0.015 m too, but the left can handle both. The right arm will move the yellow pepper from x = 0.206 m, y = -0.114 m to the right basket at x = 0.266 m, y = -0.007 m.
For the green pepper at x = -0.339 m, y = -0.119 m, the left arm can stage it on the table near the center front at x = 0.05 m, y = -0.25 m, then the right arm can pick it and place it in the right basket. I also considered having the left arm hold it near x = 0.03 m, y = -0.26 m while the right approached. Either transfer needs to avoid the watches and wooden toys, and it may be easier after some objects have been cleared.
A useful four-round schedule would be: first, the left arm stages the green pepper while the right sorts the yellow pepper; second, the left sorts its wooden toy while the right sorts the staged green pepper; third, the left sorts the first watch while the right sorts its wooden toy; fourth, the left sorts the second watch while the right remains idle. I need to make sure the right arm can grasp the staged pepper from above and transport it safely.
I still need better estimates of the table and object heights. In the high-camera image, the green pepper’s top is around pixel y = 222 and its base around y = 249. I have provisionally assumed a table height of 0.75 m and used z = 0.79 m for the wooden toys. These heights are not known from the observation. Typical values might be a table at z = 0.75 m and object centers around z = 0.78–0.82 m, but I should refine the estimates with the wrist cameras and measured incremental motion before grasping. Could the table plane be inferred from the baskets or robot coordinates? Could objects visible in multiple cameras be triangulated? The initial left wrist view shows the green pepper, the right wrist view shows the yellow pepper, and the high view shows all the objects. The watches may only be visible in the high view, so moving a camera could help later.
I must use observation images, calibration, and measured end-effector poses rather than underlying mesh positions or simulator internals. Projecting the known gripper geometry may help check depth estimates. The initial left end-effector position is measured, its rotation is available, and the wrist camera extrinsics likely have a fixed relationship to it. Additional views after moving could provide object depth cues.
I should work out the gripper orientation for a top-down grasp. The current quaternion [0.707, 0, 0, 0.707] represents a 90-degree rotation around world Z: local X points along world +Y, local Y along world -X, and local Z along world +Z. Thus the fingers extend along world +Y and open along world -X. With link6 at y = -0.352 m, z = 0.922 m and an approximate finger extension of 0.157 m, the tips are around y = -0.194 m, z = 0.922 m. The high-camera grippers appear around x = -0.3 m, y = -0.23 m.
The left wrist calibration gives optical X along world X, optical Y approximately [0, -0.5, -0.866], and optical Z approximately [0, 0.866, -0.5]. The camera therefore looks forward and down, with its forward direction equal to approximately 0.866 world Y minus 0.5 world Z. At the initial orientation, local +X is world +Y.
For a top-down grasp, local X should point along world -Z, with local Y horizontal in a suitable closing direction. I could choose local Y along world X or world Y. With local X = (0, 0, -1) and local Y = (1, 0, 0), local Z is their cross product, world -Y. The rotation matrix, written with those axes as columns, is [[0, 1, 0], [0, 0, -1], [-1, 0, 0]]. I am unsure of the quaternion: possibilities I considered include [0.5, 0.5, -0.5, 0.5], [0.5, -0.5, 0.5, 0.5], and other common top-down forms such as [0.5, 0.5, 0.5, -0.5]. I should calculate it with SciPy rather than choose one by memory.
The wrist camera’s forward direction is approximately 0.866 local X minus 0.5 local Z. Its optical X is -local Y, and optical Y is approximately -0.5 local X minus 0.866 local Z. If local X points down and local Z points along world -Y, camera forward becomes 0.5 world Y minus 0.866 world Z. It would still look 30 degrees forward from vertical, which should let it see the object slightly ahead of the gripper.
The peppers appear to have a bulb diameter around 0.07 m and a height around 0.08 m. A top-down grasp around the upper half, with the fingers extending vertically and closing across the bulb’s width, may work. I should choose the yaw to suit the shape. In the initial left wrist image, the green pepper is around pixel (225, 356), and the open black fingers occupy the lower left and right edges. The gripper currently points forward horizontally, so it needs to turn downward while approaching above the pepper.
A possible left approach is approximately x = -0.335 m, y = -0.12 m, z = 0.99 m. The estimated distance from the current pose is sqrt(0.035² + 0.232² + 0.068²) = 0.243 m, barely within the 0.25 m limit. The required rotation is about 1.57 rad, exceeding the 1.0 rad orientation limit, so an intermediate orientation is necessary. I could first move with the current orientation to y = -0.27 m, z = 1.0 m, then turn downward by 90 degrees over two steps while moving toward y = -0.12 m. I need to avoid the pepper and basket. The current fingers extend to y = -0.194 m, while the pepper is near y = -0.119 m, z = 0.80 m; raising and advancing above it appears unobstructed.
For the yellow pepper near x = 0.206 m, y = -0.114 m, the right arm could similarly move from (0.3, -0.352, 0.922) m to (0.21, -0.25, 1.00) m, then turn downward and approach y = -0.11 m. Both peppers could be grasped in parallel for the first round, but their centers need more precise localization.
I should compare projections of the green pepper’s base and top under the assumed heights. Its base may be at pixel (148, 249). With a table at z = 0.75 m, I tentatively estimate its ground position near x = -0.337 m, y = -0.14 m. My earlier center projection used pixel (148, 236) and z = 0.82 m, giving y = -0.119 m. The base at pixel y = 249 with z = 0.75 m gives y = -0.148 m, while the top at pixel y = 221 with z = 0.83 m may give y = -0.083 m. These estimates need checking. In the original high image, the green pepper spans roughly pixel y = 220–249, with its center around y = 233, and the wooden toys span y = 265–293. The basket bottoms are around pixel y = 211; their center-plane y coordinate remains unclear. Perhaps vanishing geometry could help establish the table height. I suspect the table top is at z = 0.75 m or 0.78 m, but that is still an assumption.
I will first project the known gripper geometry and compare it with the image. At link6 z = 0.9215 m, the 0.1576 m local-X finger extent points along world +Y, giving an approximate left tip position of [-0.2995, -0.1947, 0.9215] m. Does that project near the black finger tips at pixel y = 243? The fingers appear to extend from bases around pixels (100, 285) and (145, 287) to tips around (90, 244) and (147, 244). I should calculate their projections and the candidate downward quaternions now.