串行机械臂的任务分布感知配重综合与约束协同设计
Task-Distribution-Aware Counterweight Synthesis and Constrained Co-Design for Serial Manipulators
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中文总结 AI 辅助
本文提出任务分布感知的配重综合框架，通过闭式最优解和仿射负载扩展，结合质量-半径约束协同设计，显著提升机械臂任务空间覆盖率。
中文摘要 AI 辅助
被动配重是简单的重力补偿装置，但根据单一姿态选择的配重通常并非机械臂实际执行构型和任务的最优选择。本文开发了一个任务分布感知的综合框架，其中操作分布$\rho(q)$被显式地纳入设计。对于配重力矩$p=m_c r_c$，其重力力矩为$-gp\phi(q)$，加权均方残差重力力矩具有闭式最小化解$p^*=E_\rho[\tau_g\phi]/(gE_\rho[\phi^2])$。若负载重力力矩关于负载质量是仿射的，则最优解也是仿射的：$p^*(m_p,\rho)=p_0^*(\rho)+m_pK_p(\rho)$。对于固定的静态力矩，增加的配重惯量为$I_c=pr_c$，而质量为$m_c=p/r_c$，因此除非指定物理约束，质量-半径选择是不确定的。以一个修复的三连杆机械臂作为案例研究。在$r_c=0.20$ m时，零负载等效最优值在均匀关节空间操作为0.672 kg，近似均匀任务空间操作为0.683 kg，代表性拾取-放置任务族为0.713 kg，高重力偏置分布为0.952 kg，仅由操作分布引起的变化超过40%。非支配前沿表明，优选的质量-半径对取决于声明的工程界限。以额定力矩为参考的全关节筛选将零负载可行任务空间覆盖率从无补偿时的78.1%提高到均匀分布设计的93.7%。集总质点轨迹研究给出了从非常激进运动时的无配重到运动减慢时更强补偿的初步交叉。这些执行器和动力学结果是工程后果研究，而非物理验证。
英文摘要
Passive counterweights are simple gravity compensators, but a counterweight selected from a single pose is not generally optimal for the configurations and tasks a manipulator actually executes. This paper develops a task-distribution-aware synthesis framework in which the operating distribution $ρ(q)$ enters the design explicitly. For a counterweight moment $p=m_c r_c$ with gravity torque $-gpϕ(q)$, the weighted mean-square residual gravity torque has the closed-form minimizer $p^*=E_ρ[τ_gϕ]/(gE_ρ[ϕ^2])$. If payload gravity torque is affine in payload mass, the optimum is also affine: $p^*(m_p,ρ)=p_0^*(ρ)+m_pK_p(ρ)$. For fixed static moment, added counterweight inertia is $I_c=pr_c$ while mass is $m_c=p/r_c$, so mass-radius selection is underdetermined unless physical constraints are specified. A recovered three-link manipulator is used as a case study. At $r_c=0.20$ m, zero-payload equivalent optima are 0.672 kg for uniform joint-space operation, 0.683 kg for approximately uniform task-space operation, 0.713 kg for a representative pick-and-place family, and 0.952 kg for a high-gravity-biased distribution, a change of more than 40% caused solely by the operating distribution. Nondominated fronts show that preferred mass-radius pairs depend on declared engineering bounds. A rated-torque-referenced all-joint screen increases zero-payload feasible task-space coverage from 78.1% without compensation to 93.7% for the uniform-distribution design. A lumped point-mass trajectory study gives a provisional crossover from no counterweight at very aggressive motion to stronger compensation as motion slows. These actuator and dynamic results are engineering consequence studies rather than physical validation.
发表机构
- College of Engineering and Information Technology, University of Dubai（迪拜大学工程与信息技术学院）
机构由 AI 辅助整理，请以论文原文为准。
