Task-Distribution-Aware Counterweight Synthesis and Constrained Co-Design for Serial Manipulators

arXiv:2609.15082v1 Announce Type: cross Abstract: 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 rho(q) enters the design explicitly. For a counterweight moment p=m_c r_c with gravity torque -gpphi(q), the weighted mean-square residual gravity torque has the closed-form minimizer p^=E_rho[au_gphi]/(gE_rho[phi^2]). If payload gravity torque is affine in payload mass, the optimum is also affine: p^(m_p,rho)=p_0^*(rho)+m_pK_p(rho). 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.

Source: arXiv cs.LG | 2026-09-15