更近的视图似乎显示左侧有两根条状物,使物体总数达到八个:三块巧克力棒、三个辣椒和两辆小车。白色条状物被左侧夹爪部分遮挡,大约位于图像 x = 113–146、y = 266–294 处。它是否已经位于张开的手指之间,与手指的局部 +X 方向对齐,从而在旋转后易于抓取?手指在约 z = 0.92米处水平,而条状物在桌面上靠近 z = 0.76米,因此它可能只是由于相机透视才看起来位于手指之间。该指令适用于每个类别的所有物体。
我需要一个高效的双臂计划。我可以用左臂抓取左侧的金色条状物,同时用右臂抓取紫色条状物,然后将它们依次放入左侧篮子。同时将两者运送到那里可能导致手臂交叉。另一种可能的分配是左臂处理三根左侧条状物和红辣椒,而右臂处理紫色条状物、右侧绿辣椒以及黄色和红色小车。1100 步的预算对于串行操作可能足够,但可达范围可能限制任一分配。
篮子中心大约在 x = -0.32米、0米和 +0.32米处。将紫色巧克力棒从右侧移到左侧篮子可能需要交接。左臂能否从靠近 x = -0.3米的基座直接抓取位于 x = 0.31米处的它,跨度约 0.6米?相反,右臂从其估计基座 x = +0.3米到左侧篮子的 x 间距为 0.62米。那可能不可达,尤其是加上向前的距离。也许最大可达范围约为 0.7米,不过我还在考虑的可达范围大约为 0.55米或 0.65米。
右末端执行器起始于 [0.3, -0.35, 0.92] m 附近,因此接近 [0.31, -0.1, 0.9] m 附近的紫色条状物似乎很直接。到达 [-0.32, 0.05, 1.0] m 附近的左侧篮子可能需要距基座约 0.8米,超出假设的 0.6米可达范围。一种替代方案是将紫色条状物放在 x = 0米处一个空旷的中间或前方区域,然后让左臂将其拾起。另一种是测试右臂通过中间位姿的直接路径,同时让左臂停靠在更左和更靠后的位置。我应该使用运动学预检查,而不是假设任一臂都能到达每个篮子。
基座位置不确定。两臂具有对称的零值关节配置,第六连杆靠近 [±0.3, -0.352, 0.922] m。基座可能靠近 x = ±0.3米、y = -0.65米,或者也许是 y = -0.6米和 z = 0.8米。若右基座在 [0.3, -0.6] m 而左侧篮子在 [-0.32, 0.02] m,水平距离将是平方根(0.62² + 0.62²) = 0.877米,在这些可达范围假设下我会认为这是不可能的。基座在 y = -0.45米会使初始第六连杆仅向前约 0.1米。高机位图像似乎将基座放在其底部角落附近,大约 x = 0 或 640、y = 480;用 z = 0.8米投影表明 y 大约在 -0.6米。在该假设下,从右到左的距离约为 0.88米。从 [-0.3, -0.6] m 的基座直接用左臂拾取紫色条状物将跨越 x 方向约 0.61米和 y 方向 0.5米,即约 0.79米,似乎也太远。如果篮子更靠近 y = 0.1米而基座靠近 y = -0.4米,距离可能反而约为 0.7米。仅凭这些估计我无法确定可达范围。
x = -0.16米附近的红色小车和 x = -0.046米附近的中间绿辣椒看起来适合左臂;x = 0.065米附近的黄色小车和 x = 0.28米附近的右侧绿辣椒看起来适合右臂。红辣椒在 x = -0.292米附近,金色条状物也许在 x = -0.27米,白色条状物也许在 x = -0.4米,紫色条状物在 x = 0.31米。我一度怀疑部分被遮挡的白色形状是否是夹爪装饰,但现在我认为它是一根单独的条状物。分拣包括右侧巧克力向左、右侧辣椒到中间、左侧小车向右,因此可能需要跨过或转移物体。
对机器人几何形状的进一步视觉估计并不能解决这个问题。基座可以设想在 x = ±0.3米、y = -0.8米附近,可达范围 0.9米,或者臂长可能在 0.6米左右。在高机位图像中,白色上臂似乎靠近像素 (0, 403),黑色前臂向腕部延伸靠近 (90, 280)。左基座可能靠近 [-0.3, -0.75, 0.3] m,或者手臂可能安装在 y = -0.7米、z = 0.6米附近,有两个约 0.3米的连杆和约 0.6米的水平可达范围。那会使 y = 0.03米附近的篮子向前约 0.73米,即使在同一侧也显然超出可达范围,尽管该任务本应是可达的。像素 (0, 420) 附近的表观基座不在与物体相同的世界平面上,因此我无法可靠地推断其位置。我可以读取相机参数,但我不得访问模拟器内部或另一个控制器。我将使用测得的末端执行器位姿和预检查来继续。
我将首先用两个张开的夹爪接近左侧金色条状物和右侧紫色条状物,旋转朝向自上而下的抓取,同时保持在 z = 0.98米的高处。在物体附近我应该使用 1–3 个控制步,但对于空旷空间中这种较大的旋转,我可以考虑 5–10 步。每个目标必须保持在测得位置的 0.25米以内。
金色条状物的高机位图像中心大约在像素 (180, 289)。假设它平放在 z = 0.762米处,估计 x 接近 -0.277米;使用 z = 0.76米得到大约 [-0.28, -0.207, 0.76] m。另一个暂定的 x 估计是 -0.276米。紫色条状物的中心大约为 [0.31, -0.096, 0.767] m。我考虑过金色条状物的接近目标为 [-0.275, -0.20, 0.94] m,紫色条状物为 [0.31, -0.096, 0.96] m。从取整的初始右位姿 [0.3, -0.352, 0.922] m 出发,后者距离 0.259米,超过 0.25米的限制,因此我需要一个中间位置。
预期的自上而下四元数按顺序为 [0.5, -0.5, -0.5, 0.5]。它与初始四元数 [0.707, 0, 0, 0.707] 的点积约为 0.354 + 0.354 = 0.707,给出约 1.571弧度的朝向差,超过 1.0弧度的限制。我将把旋转分成两个动作。中间四元数约为 [0.6533, -0.2706, -0.2706, 0.6533],从起始朝向旋转约 45°,即 0.785弧度。我最初考虑中间位置 [-0.285, -0.25, 0.97] m 和 [0.31, -0.22, 0.97] m,用 6–8 步,然后在第二个动作中完成旋转和接近。
对于紫色条状物,它沿环境 Y 方向较长,沿环境 X 方向闭合似乎是合适的。金色条状物在图像中沿对角线向右下方延伸;其估计的世界长轴分量大约为 = 0.04米和 = -0.1米。我最终应将闭合方向定向为垂直于该轴,但其偏航仍需决定。从圆形红辣椒和右侧绿辣椒开始是另一种可能,因为两者都去中间篮子,但我更倾向于先处理外侧的扁平巧克力棒。
移动手臂后,我应该使用腕部视图和三角测量来细化物体位置,尤其是白色条状物在遮挡减少后。它在初始左腕部图像底部大约 x = 200–250、y = 440 或更大处部分可见。
我将使用当前观测进行中间接近。在检查四元数时,我一度得到 [0.9239, -0.2706, -0.2706, 0.9239],但那是错误的。将初始和最终四元数相加得到 [1.207, -0.5, -0.5, 1.207];用我估计的范数 1.863,归一化结果约为 [0.648, -0.268, -0.268, 0.648]。对于中间旋转,将 (-45°) = [0.9239, -0.3827, 0, 0] 乘以 (90°) = [0.707, 0, 0, 0.707] 得到 [0.6533, -0.2706, -0.2706, 0.6533],具有单位范数。我将对两臂都使用该四元数。
选定的目标为左臂 [-0.28, -0.25, 0.98] m 和右臂 [0.31, -0.20, 0.98] m,均为张开状态。我估计目标距离左臂约 0.10米、右臂约 0.16米,朝向变化为 0.785弧度。六步可能足以完成部分运动,但在每个控制步 0.1弧度的朝向增量下,旋转需要约八步;位置增量为 0.02米。我将请求八步。
原文8,285 字
The closer view appears to show two bars on the left, bringing the total to eight objects: three chocolate bars, three peppers, and two cars. The white bar is partly occluded by the left gripper and appears around image x = 113–146, y = 266–294. Could it already be between the open fingers, aligned with their local +X direction, making it easy to grasp after rotation? The fingers are horizontal at about z = 0.92 m while the bar is on the table near z = 0.76 m, so it may only appear between them because of the camera perspective. The instruction applies to all objects of each category.
I need an efficient dual-arm plan. I could grasp the left gold bar with the left arm and the purple bar with the right arm simultaneously, then place them into the left basket sequentially. Transporting both there simultaneously could cause the arms to cross. Another possible assignment is for the left arm to handle the three left bars and the red pepper, while the right arm handles the purple bar, right green pepper, and yellow and red cars. The 1100-step budget may be enough for serial manipulation, but reach could constrain either assignment.
The basket centers are approximately x = -0.32 m, 0 m, and +0.32 m. Moving the purple chocolate bar from the right side to the left basket may require a handoff. Could the left arm pick it directly at x = 0.31 m from a base near x = -0.3 m, spanning about 0.6 m? Conversely, the right arm would have an x separation of 0.62 m from its estimated base at x = +0.3 m to the left basket. That may be unreachable, especially with the forward distance included. Perhaps the maximum reach is around 0.7 m, though I am also considering an ARX X5 reach of roughly 0.55 m or 0.65 m.
The right end effector starts near [0.3, -0.35, 0.92] m, so approaching the purple bar near [0.31, -0.1, 0.9] m seems straightforward. Reaching the left basket near [-0.32, 0.05, 1.0] m might require about 0.8 m from the base, beyond an assumed 0.6 m reach. One alternative is to place the purple bar in a clear middle or front area at x = 0 m, then have the left arm pick it up. Another is to test a direct right-arm route through intermediate poses while keeping the left arm parked farther left and back. I should use kinematic prechecks rather than assume either arm can reach every basket.
The base locations are uncertain. Both arms have symmetric, zero-valued joint configurations, with link6 near [±0.3, -0.352, 0.922] m. The bases might be near x = ±0.3 m, y = -0.65 m, or perhaps y = -0.6 m and z = 0.8 m. With a right base at [0.3, -0.6] m and the left basket at [-0.32, 0.02] m, the horizontal distance would be sqrt(0.62² + 0.62²) = 0.877 m, which I would consider impossible under these reach assumptions. A base at y = -0.45 m would put the initial link6 only about 0.1 m forward. The high image appears to put the bases near its bottom corners, around x = 0 or 640, y = 480; projecting with z = 0.8 m suggests y around -0.6 m. Under that hypothesis, the right-to-left distance is about 0.88 m. A direct left-arm pickup of the purple bar from a base at [-0.3, -0.6] m would span approximately 0.61 m in x and 0.5 m in y, or about 0.79 m, also seemingly too far. If the baskets were closer to y = 0.1 m and the bases near y = -0.4 m, the distance might instead be about 0.7 m. I cannot settle reach from these estimates alone.
The red car near x = -0.16 m and middle green pepper near x = -0.046 m look suitable for the left arm; the yellow car near x = 0.065 m and right green pepper near x = 0.28 m look suitable for the right arm. The red pepper is near x = -0.292 m, the gold bar perhaps x = -0.27 m, the white bar perhaps x = -0.4 m, and the purple bar x = 0.31 m. I briefly wondered whether the partly obscured white shape was a gripper decoration, but I now take it to be a separate bar. Sorting includes a right-side chocolate going left, a right-side pepper going to the middle, and a left-side car going right, so reaching across or transferring objects may be necessary.
Further visual estimates of the robot geometry do not resolve this. The bases could conceivably be near x = ±0.3 m, y = -0.8 m with 0.9 m reach, or the arm length could be around 0.6 m. In the high image, the white upper arm appears near pixel (0, 403), with the black forearm extending toward the wrist near (90, 280). The left base might be near [-0.3, -0.75, 0.3] m, or the arms might be mounted near y = -0.7 m, z = 0.6 m with two roughly 0.3 m links and about 0.6 m horizontal reach. That would put a basket near y = 0.03 m about 0.73 m forward, apparently beyond reach even on the same side, despite the task being intended to be reachable. The apparent base near pixel (0, 420) is not on the same world plane as the objects, so I cannot infer its position reliably. I may read camera parameters, but I must not access simulator internals or another controller. I will proceed using measured end-effector poses and prechecks.
I will start by approaching the left gold bar and right purple bar with both grippers open, rotating toward a top-down grasp while staying high at z = 0.98 m. Near the objects I should use 1–3 control steps, but I can consider 5–10 steps for this larger rotation in clear space. Each target must remain within 0.25 m of the measured position.
The gold bar's high-image center is around pixel (180, 289). Assuming it lies flat at z = 0.762 m gives an estimated x near -0.277 m; using z = 0.76 m gives approximately [-0.28, -0.207, 0.76] m. Another tentative x estimate is -0.276 m. The purple bar's center is approximately [0.31, -0.096, 0.767] m. I considered approach targets of [-0.275, -0.20, 0.94] m for the gold bar and [0.31, -0.096, 0.96] m for the purple bar. From the rounded initial right pose [0.3, -0.352, 0.922] m, the latter is 0.259 m away, exceeding the 0.25 m limit, so I need an intermediate position.
The intended top-down quaternion is [0.5, -0.5, -0.5, 0.5] in wxyz order. Its dot product with the initial quaternion [0.707, 0, 0, 0.707] is approximately 0.354 + 0.354 = 0.707, giving an orientation difference of 1.571 rad, above the 1.0 rad limit. I will split the rotation across two actions. The halfway quaternion is approximately [0.6533, -0.2706, -0.2706, 0.6533], a roughly 45° rotation from the starting orientation, or 0.785 rad. I initially considered intermediate positions [-0.285, -0.25, 0.97] m and [0.31, -0.22, 0.97] m, with 6–8 steps, before completing the rotation and approach in a second action.
For the purple bar, which is long along environment Y, closing along environment X seems appropriate. The gold bar runs diagonally down and right in the image; its estimated world long-axis components are roughly dx = 0.04 m and dy = -0.1 m. I should eventually orient the closing direction perpendicular to that axis, but its yaw still needs deciding. Starting with the round red and right green peppers is another possibility, since both go to the middle basket, but I prefer the outer flat chocolate bars first.
After moving the arms, I should use the wrist views and triangulation to refine the object positions, particularly the white bar once it is less occluded. It is partly visible at the bottom of the initial left wrist image around x = 200–250, y = 440 or greater.
I will use the current observation ID for the intermediate approach. In checking the quaternion, I briefly obtained [0.9239, -0.2706, -0.2706, 0.9239], but that was incorrect. Adding the initial and final quaternions gives [1.207, -0.5, -0.5, 1.207]; with my estimated norm of 1.863, the normalized result is approximately [0.648, -0.268, -0.268, 0.648]. For the halfway rotation, multiplying qx(-45°) = [0.9239, -0.3827, 0, 0] by qz(90°) = [0.707, 0, 0, 0.707] gives [0.6533, -0.2706, -0.2706, 0.6533], with unit norm. I will use that quaternion for both arms.
The selected targets are [-0.28, -0.25, 0.98] m for the left arm and [0.31, -0.20, 0.98] m for the right arm, both open. I estimate the target distances as about 0.10 m for the left and 0.16 m for the right, with an orientation change of 0.785 rad. Six steps might suffice for some of the motion, but at an orientation increment of 0.1 rad per control step the rotation needs about eight; the position increment is 0.02 m. I will request eight steps.