A Generalized Theory of Load Distribution in Redundantly-actuated Robotic Systems

This paper discusses null-space wrench components in parallel manipulators. We examine the adaptation of the two most common characterizations of these components in grasp-like systems, namely, interaction forces and internal loads, to parallel manipulators with actuation redundancy. We identify critical oversights in the existing literature on the subject, resolve ambiguities related to the definitions of interaction forces and internal loads, and provide explicit methods for synthesizing equilibrating and manipulating joint torque vectors. A case study is also provided to justify the validity of our novel methods and correct erroneous results reported in the literature.

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.

While contact-rich manipulation requires deliberate regulation of interaction forces, recent approaches to robot manipulation learning predominantly represent actions as target positions or poses. Even methods that incorporate force sensing either use it solely as an observation or, when predicting forces as part of the output, rely on a hybrid force controller. In this paper, we propose an imitation learning policy that predicts wrenches as its sole action output for direct use by a pure force controller. Our studies suggest that force-domain imitation learning depends critically on data collection, with force-feedback teleoperation improving policy performance by capturing the operator's deliberate force regulation. Using Action Chunking with Transformers (ACT) as the base architecture, we train single-task models on bilateral wrench demonstrations and evaluate them on five contact-rich manipulation tasks. The wrench policy matches or outperforms position-based baselines across all tasks, with gains varying according to the degree of deliberate force regulation each task requires. Cross-condition ablations show that the bilateral data collection interface and the wrench action space each contribute independently to performance. To support further research, we will release over 1000 wrench-action demonstrations spanning these tasks on a companion website upon publication.