High-speed human running data are difficult to acquire, limiting the availability of motion priors for high-speed humanoid running. To reduce dependence on motion capture and retargeting, this study proposes a framework that combines trajectory optimization with reinforcement learning. A planar multibody model generates reference motions across speeds subject to contact, periodicity, and actuator constraints. The optimized motions guide the training of a three-dimensional running policy through adversarial imitation and proximal policy optimization. Hardware experiments demonstrate treadmill running by the full-size BOLT humanoid at $10\mathrm{m}/\mathrm{s}$. In $2\mathrm{s}$ simulation windows under a $10\mathrm{m}/\mathrm{s}$ forward velocity command, comparison with a policy trained on retargeted human motions shows a more balanced distribution of joint loads relative to actuator capacity. The coefficient of variation of joint root-mean-square (RMS) utilization decreases from $0.397$ to $0.317$ across twelve joints, a reduction of $20.1\%$, with a corresponding reduction of $35.6\%$ across the six leg joints. These results support trajectory optimization as an effective source of motion priors for high-speed humanoid running and demonstrate a route from reference generation to hardware deployment without high-speed human motion data.

Humanoid motion tracking provides a scalable interface for transferring kinematic human motion to whole-body robot control, but highly dynamic and contact-rich references remain difficult because underactuation and discontinuous contacts can restrict the closed-loop state distributions explored during training. External wrenches can reduce dynamic mismatch during imitation, but retaining such assistance in the final controller can compromise physical realism. This paper proposes residual-wrench-assisted reinforcement learning (RWARL), a two-stage framework that uses base residual wrenches as a temporary optimization scaffold. RWARL first solves a relaxed tracking problem with residual-wrench assistance and then anneals the residual-wrench strength while adapting early-termination bounds and segment sampling to observed training difficulty. To keep the policy adaptable as the training distribution shifts from assisted to unassisted dynamics, RWARL incorporates plasticity-preserving mechanisms during relaxation. Experiments on highly dynamic and contact-rich references show that RWARL generally improves global tracking accuracy, with the largest gains near difficult transitions where standard training tends to produce conservative behavior. Compared with the baseline, the final unassisted RWARL policies reduce global body-position tracking error by 8.6%–37.8% on the highly agile and contact-rich motions examined in this work and achieve the largest successful-frame-rate gain of 41.8 percentage points on jump twist . A closed-loop predecessor-state diagnostic further links these gains to more favorable predecessor-state distributions around critical phases. We deploy the final unassisted controllers on Unitree G1 hardware, demonstrating that the learned policies remain executable after residual assistance is removed. Together, these findings suggest that RWARL uses residual wrenches to reshape learning around difficult, low-reachability transitions, allowing the final unassisted policy to inherit better tracking behavior in phases that standard training tends to underexplore.