Load-Capacity-Constrained Arm-Angle Planning for a Centrally Driven Humanoid Robotic Arm

This paper presents a load-capacity-constrained arm-angle planning method for a centrally driven humanoid robotic arm. Joint-range and singularity constraints are projected into the one-dimensional arm-angle domain to form a geometric feasible set. A static load-capacity constraint is derived from gravity torque, the Jacobian-transpose mapping of a known endpoint load, and individual actuator-torque limits, and is projected into the same domain. Continuous arm-angle values are then selected along a prescribed Cartesian path within the intersection of the geometric and mechanical feasible sets. In a heavy-load simulation, the maximum output-power metric decreased by 13.3%, and the energy value decreased from 30.60 J to 22.95 J (25.0%). In a prototype proof-of-principle test with a 13 N payload (approximately 1.33 kg), each trajectory was executed three times; the controller-recorded shoulder peak was approximately 1.83% lower, and the recorded energy value decreased from 30.378 J to 28.85 J (5.03%). The prototype values are descriptive because run-level statistics and measurement uncertainty are unavailable, and the experiment covers only one payload and one path. The results support the proposed static, load-capacity-aware planning principle for the tested slow-motion conditions but do not establish general performance or real-time suitability.