Energy-Efficient Arm Reaching for a Humanoid Robot via Deep Reinforcement Learning with Identified Power Models

Accurate prediction of electrical power consumption is essential for energy-aware motion planning, battery management, and thermal monitoring in battery-powered humanoid robots. This letter presents a physics-based, linear-in-parameters model for the electrical power consumption of the seven-degree-of-freedom left arm of the UnitreeG1 humanoid robot. The proposed formulation combines actuator loss terms with a baseline-torque correction that captures changes in gravity-compensation load and enables accurate prediction of negative net power trajectories. Pairwise interaction terms are introduced to model power coupling during simultaneous multi-joint motion. Model parameters are identified from experimental data collected on a physical UnitreeG1 using onboard power measurements as the regression target. Across 897 trajectories covering single-joint and coordinated arm motions at multiple speed levels, the identified model achieves $R^2 = 0.933$ with an RMSE of 1.07 (W). Validation on 46 trajectories executed at previously unseen speeds yields $R^2 = 0.965$, demonstrating strong generalisation beyond the identification dataset. Analysis of the identified parameters reveals distinct power-consumption characteristics across the arm, with viscous friction dominating most joints (shoulder pitch and all three wrist joints), copper losses dominating shoulder yaw and the elbow, and shoulder roll uniquely dominated by Coulomb friction.

This paper studies energy-aware manipulation as a physically grounded learning problem. We define a joint-space mechanical-work proxy from joint torque and angular displacement, and train a differentiable energy predictor that estimates this work from robot states and actions. The predictor converts a non-differentiable simulator-side physical quantity into a differentiable regularizer for fine-tuning a pretrained manipulation policy. We instantiate the framework with RVT-2 on RLBench and evaluate 12 manipulation tasks involving object contact, articulated motion, placement, pushing, and sweeping. The proposed fine-tuning reduces the average mechanical work from 208.8J to 204.4J (i.e., 2.1% reduction), while the mean task success rate also increases slightly from 86.2% to 86.9%. These results show that work-aware policy optimization can suppress physically inefficient motion without requiring an explicit differentiable dynamics model.

Multi-objective reinforcement learning for humanoid robots must coordinate locomotion and manipulation within a single policy. A natural design choice is whether to use a single (unified) critic that estimates the combined value of all objectives, or separate (dual) critics with disjoint reward signals. We present a controlled comparison on the Unitree G1 humanoid (23 active DoF) in NVIDIA Isaac Lab, training loco-manipulation policies through a sequential curriculum spanning 13 levels from stationary reaching to walking with variable-orientation targets. In standardized evaluation, dual-critic policies reach targets 3.5$\times$ faster (6.5 vs. 22.6 simulation steps), achieve 2$\times$ higher throughput (14.3 vs. 7.0 validated reaches per 1,000 steps), and attain higher validated reach rates (65.2% vs. 53.8%) compared to the unified-critic policy. Notably, additional anti-gaming reward mechanisms provide no further improvement beyond the architectural change alone (60.9% vs. 65.2%). These results have direct implications for the emerging paradigm of RL fine-tuning of imitation-learned policies: when refining a pre-trained manipulation policy with RL, a unified critic risks suppressing the learned behavior through competing locomotion gradients. These findings demonstrate that critic architecture is a primary - and often overlooked - design choice in multi-objective humanoid RL, with greater impact than reward engineering on reaching efficiency.