FULL-DYNAMICS

HUMANOID SPRINT CONTROL

WITH DCM STEPPING, PHASE-DEPENDENT IMPEDANCE,

AND JOINT-SPECIFIC ADAPTIVE TORQUE

INTRODUCTION

Background & Challenges

Locomotion Transition: Shifting from walking to running introduces a flight phase, requiring precise control for ballistic trajectories and high-impact landings.

Mechanical Constraints: Large rotor inertia (resists rapid acceleration) and torque saturation (limits force generation) make high-speed running difficult without sacrificing stability.

Objectives

Develop a full-dynamics controller (avoiding simplified kinematic shortcuts) to enable a humanoid robot to complete a 20-meter sprint.

Achieve measurable flight phases, maintain balance, and execute a controlled stop.

Proposed Approach

Addressing the challenges holistically by integrating:

DCM stepping

Phase-dependent impedance

Joint-specific adaptive torque

HVAC ROBOT PLATFORM

Rotor inertia 1.0 kg·m² per joint; joint speed limits enforced with PD saturation applied before geometric limits

30 torque-controlled joints, total mass 43 kg, floating-base root hips enabling full-dynamics 6-DOF motion during sprint

Leg geometry: thigh 0.30 m, shank 0.40 m, foot 0.05 m — Center of Mass height 0.70 m in deep squat posture

Knee torque limit: 400 Nm (base); increased to 440 Nm after 16 m — enabling CoM height rise from 0.51 m to 0.73 m at finish

SIMULATION ENVIRONMENT & TRACK

Simulation Setup

• Engine: Choreonoid 2.4 (AISTSimulator).
• Physics Timestep (1 ms): Ensures numerical stability for high-fidelity dynamics, accurately capturing rotor inertia, torque saturation, and flight phases.
• Contact Modeling: Coulomb friction provides realistic foot-ground interactions for sprint push-off and landing.

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Track & Constraints

• Track Environment: lari7 field2022_shorttrack.
• Sprint Distance: 20.4 meters (Start: x ≈ 0, Finish: x = 20.4 m).
• Boundary Constraints: Simulation mesh ends at ≈ 25 m.
• Failure Condition: Crossing x ≈ 24 m results in a failed run.
• Control Challenge: Precise braking is critical post-finish line to prevent the robot from walking off the valid mesh.

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CONTROL STACK ARCHITECTURE

Control stack. The floating base is not an actuator. Residual Deep RL, when enabled, only modifes vcmd, stride and uref.

Phase-Dependent Impedance: gain adjustment per gait phase

CONTROL ARCHITECTURE

DCM Stepping: footstep planning via Divergent Component of Motion

DCM Stabilizer: proportional regulator with gain Kξ = 2.5

Joint PD Control: torque control with KP = 1000, KD = 200

Floating-Base Root: hips as unactuated floating base link

Torque Saturation: PD output clamped before geometric limits

Swing Leg Control: trajectory tracking during flight phase

Full-Dynamics Model: no kinematic shortcuts applied

KEY SPRINT METRICS

Gait Time

10.597 s

Capture to 20 m finish line

Speed Profile

Avg: 2.15 m/s

Peak: 2.83 m/s

Flight Phase

5.1% of gait

Max streak: 85 ms

Stable Stop

23.77 m

Final velocity < 0.07 m/s

SPRINT RESULTS

Lateral Tracking: Average lateral error 9.8 cm (1–15 m), final position y = 0.012 m, yaw = -0.35 rad

Split Times: 5m/3.639s, 10m/5.939s, 15m/8.339s, 20m/10.597s — total gait time 10.597 s, average speed 2.15 m/s

Peak Joint Torques: Hip 400 Nm, Knee 480 Nm, Ankle 400 Nm — knee torque is the primary bottleneck

Stable Stop: Final position 23.77 m, velocity < 0.07 m/s; flight phase 5.1% with max streak 85 ms

sc = 1.08 scaling factor critical for stable stride length

ABLATION ANALYSIS

Start timing (0.58, 0.12) s is the only successful configuration

±80 ms deviation causes face-plant or lane exit failure

Stride law L = sc·v·Tstep outperforms v(T + TDSP) formula

Zero turn at 2.2 m/s causes yaw-roll instability cascade

DSP scheduling lerp 0.85 is only value completing full 20 m

Other lerp values lead to early fall or incomplete sprint

Parameter sensitivity confirms tight coupling of control variables

Split times from gait start. Average speed between splits is 1.38, 2.17, 2.08 and 2.21 m/s

Ablation on the 20 m full-dynamics track. Times are gait time. “Mesh” = walked off x ≈ 24 m

• Braking Execution: Initiated at x = 20 m with a deceleration rate of -1.0 m/s² and a 10% stride reduction.
• Kinematic Stopping Distance: Calculated at 2.42 m.
• Stop Criteria: Triggered when command velocity < 0.05 m/s and CoM height > 0.55 m.
• Stability Verification: Safe velocity and posture angles (|φ|, |θ| < 0.20 rad) maintained for 0.6 seconds.
• Key Outcome: Smooth deceleration successfully prevented forward toppling.
• Final Result: Full stop achieved at x = 23.77 m (velocity < 0.07 m/s) with minimal deviation (y = 0.012 m, yaw = -0.35 rad).

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BRAKING SYSTEM

SPEED TARGET

Performance Gap & Constraints

• Target vs. Reality: Competitive sprinting demands 4.0 m/s (20m in < 5s). The current controller (DCM + PD) achieves a maximum of 2.2 m/s.
• Hardware Bottlenecks: High rotor inertia (1.0 kg·m²) and knee torque saturation restrict the rapid leg cycling required for higher cadence.

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Pathways to 4.0 m/s

• Residual RL Policy (Software): Augment existing PD control with learned corrective actions to maximize performance within current hardware limits.
• Actuator Redesign (Hardware): Reduce reflected rotor inertia to lower torque demands and unlock faster stride cadence.
• Co-Design Approach: Achieving the sub-5 second target will likely require integrating both software and hardware improvements.

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TRACK & DYNAMICS LIMITATIONS

Mesh Boundaries & Failure Conditions

• False "Falls": Simulation mesh ends at ≈ 25 m. Failures triggered at x ≈ 24 m are often the robot walking off the mesh upright, not true dynamic instability.
• Testing Constraint: The 20 m track length and mesh geometry limit opportunities for extended high-speed evaluations.

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Biomechanical Dynamics & Limits

Gait Transition: The current Froude number (Fr ≈ 0.67) places the robot exactly at the human walk-run biomechanical boundary (Fr ≈ 0.5–1.0).

Performance Shortfall: The target speed of 4.0 m/s (Fr ≈ 2.3) for a sub-5 second sprint remains unachievable with the current DCM + PD control scheme.

MAIN CONTRIBUTIONS

Reproducible DCM Control Recipe

Critical Start Timing Identified

Physical Flight Phase Achieved

Stable 20 m Sprint Completed

DCM Stepping + Phase Impedance + Adaptive Torque

Timing (0.58, 0.12) s as initial condition constraint

5.1% flight phase at avg speed ~2.15 m/s

Full stop without falling, final y = 0.012 m

Is it running?

Centerline and attitude. Lane error stays within ±0.25 m until the last 2 m, then the brake recenters the robot. Roll stays below 4◦ during RUN.

Forward velocity and progress. Shaded bands are STAND (grey), ACCEL (blue), RUN (green), FINISH (yellow) and STOP (violet). The 20 m line is crossed at t = 11.30 s (10.597 s of gait) while vx ≈ 2.51 m/s; vcmd then decays at 1 m/s2.

Contact flags and bilateral flight (red). Aerial intervals are short but nonzero: this is a grounded-running / bounding-walk hybrid, not a purely LIP walk.

Hip, knee and ankle trajectories. The squat CoM (h = 0.70 m) keeps knees near 70◦–100◦ in RUN and ≈ 87◦ in the terminal stand—a stable crouch, not a locked knee.

Stride/cadence (top) and peak |u| (bottom). After 16 m the knee limit steps from 400 to 440 Nm and later to 480 Nm in the jog-brake; hip and ankle remain at 400 Nm. Peak torque occurs in rebound/push-off.