Dynamic Humanoid Arm-Swing Motion via Trajectory Optimization Leveraging Speed–Torque Mode Switching of a Variable Chain Motor

Hiromi TadaTakuma HiraokaJin HiraiKunio KojimaKei Okada

in Proceedings of the 2026 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2026)

Elbow speed–torque trajectory through high-torque, intermediate, and high-speed modes, alongside elbow velocity histories comparing mode switching with three fixed modes.

Abstract

Achieving high athletic performance in humanoid robots requires both high joint speed and high joint torque. While transmission mechanisms have been proposed to enlarge the output envelope by varying the speed–torque characteristics, such mechanisms are disadvantageous for humanoids in terms of weight and size. Moreover, planning methods for generating dynamic humanoid motions that account for output-characteristic switching—which leads to discontinuous changes in the admissible speed–torque constraints—remain underexplored. This paper proposes a method for generating dynamic humanoid motions that exploit mode switching through trajectory optimization, using a Variable Chain Motor (VC motor) that can switch among modes with different speed–torque characteristics via an electrical circuit. Specifically, we impose the union of feasible speed–torque ranges across multiple modes as constraints on joint velocity and torque in the trajectory optimization problem. During execution on the real robot, we determine the mode at each time step based on the speed–torque profile of the optimized trajectory, enabling dynamic mode switching. We generate a dynamic arm-swing motion that maximizes forward end-effector velocity for a humanoid equipped with a VC motor at the elbow joint and validate it via real-robot experiments. We demonstrate the effectiveness of the proposed method by comparing it against fixed-output-characteristic cases, in which the actuator is used as a conventional motor.

Trajectory Optimization Exploiting VC Motor Mode Switching

VC Motor: Switching Speed–Torque Characteristics

The Variable Chain Motor (VC motor) [1] combines four small motor units. A dedicated circuit switches their winding connections between series and parallel, changing the speed–torque characteristics: more series connections provide higher torque, while more parallel connections allow higher speed.

The VC motor's four small motor units and the circuit that switches their winding connections between series and parallel.

Switchable high-torque, intermediate, and high-speed ranges of the VC motor.

Mode (a) connects four windings in series; Mode (b) connects two series pairs in parallel; Mode (c) connects all four windings in parallel.

Trajectory Optimization over All Feasible Modes

We constrain joint velocity and torque to the union of the feasible speed–torque ranges of all three modes. This lets trajectory optimization exploit high torque and high speed without introducing discrete mode variables. We then determine the mode to execute from the optimized speed–torque trajectory.

The orange boundary shows the combined feasible range.

Orange boundary marking the union of the feasible speed–torque ranges of Modes (a), (b), and (c), with torque limits, no-load speed limits, and slope minus alpha.

Constraints on joint velocity $v$ and joint torque $τ$

| v | \leq v^{max,C} and | τ | \leq \max (\begin{array}{l} \min (τ^{max,A}, - α (| v | - v^{max,A})) \\ \min (τ^{max,B}, - α (| v | - v^{max,B})) \\ \min (τ^{max,C}, - α (| v | - v^{max,C})) \end{array})

$v^{max, i}, τ^{max, i}$ : Maximum speed and torque of each mode ( $i \in {A, B, C}$ )
$α$ : Slope of the speed–torque limit
Smooth max/min approximation using LSE (log-sum-exp).

Faster Humanoid Arm Swings through Mode Switching

We equipped the left elbow of JAXON [2] with the VC motor and optimized an arm swing for maximum forward end-effector velocity. We compared mode switching with three fixed-mode conditions, then executed all four motions on the real robot.

(a) Fixed Mode: High-Torque	(b) Fixed Mode: Intermediate	(c) Fixed Mode: High-Speed	(d) Mode Switching[Proposed Method]
Optimized Trajectories

Open full-size image ↗	Open full-size image ↗	Open full-size image ↗	Open full-size image ↗
Peak End-Effector Velocity (Optimized Trajectories)
6.20 m/s	8.16 m/s	8.26 m/s	8.89 m/s+7.7% vs. (c)
Peak Elbow Velocity (Optimized Trajectories)
−3.87 rad/s	−7.65 rad/s	−9.13 rad/s	−10.06 rad/s+10.2% vs. (c)
Real-Robot Experiments

Peak End-Effector Velocity (Real-Robot Experiments)
6.20 m/s	7.95 m/s	8.24 m/s	9.01 m/s
Peak Elbow Velocity (Real-Robot Experiments)
−3.93 rad/s	−7.80 rad/s	−9.19 rad/s	−10.23 rad/s

In the optimized trajectories, switching increased peak forward end-effector velocity by 7.7% and peak elbow speed by 10.2% over the fastest fixed mode (c). On the real robot, it reached 9.01 m/s at the end-effector and −10.23 rad/s at the elbow.

With mode switching enabled in condition (d), the optimized arm swing follows (a) → (b) → (c) → (b) → (a): high-torque acceleration followed by a shift to higher-speed modes.

The real-robot log for the switching condition shows elbow velocity in orange and applied motor voltage in green. Switching to higher-speed modes kept the required voltage low even as elbow speed increased, enabling high-speed motion.

Real-robot log for the mode-switching condition: elbow velocity in orange and applied motor voltage in green, with shaded regions showing Modes (a), (b), and (c). Switching to higher-speed modes reduces the required voltage.

Citation

BibTeX

@inproceedings{tada_iros26-arm-swing,
  title     = {Dynamic Humanoid Arm-Swing Motion via Trajectory Optimization
               Leveraging Speed--Torque Mode Switching of a Variable Chain Motor},
  author    = {Tada, Hiromi and Hiraoka, Takuma and Hirai, Jin and Kojima, Kunio and Okada, Kei},
  booktitle = {2026 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)},
  year      = {2026}
}

References

[1]
H. Tada et al., “Development of Variable Chain Motor with Shape and Speed-Torque Characteristics Variability and Its Application to a Humanoid,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2025, pp. 21102–21109.
[2]
K. Kojima et al., “Development of life-sized high-power humanoid robot JAXON for real-world use,” IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), 2015, pp. 838–843.