Energy-Efficient Bipedal Locomotion

Independent 2D simulation, 3D PPO and gait-energy analysis, and simulation–hardware timing diagnosis.

Research case study · Robot learning & mechanics

I independently developed a 2D biped simulation environment, trained and evaluated 3D PPO locomotion policies for LIMX TRON 1A in Isaac Gym, and analyzed gait coordination, joint power, and cost of transport. I also diagnosed and corrected inconsistent simulation and execution time bases in MuJoCo–hardware comparisons.

Historical human and TRON hip, knee, and ankle angle traces across the gait cycle
Human–TRON joint-angle comparisons from the project’s historical analysis material. Red: human reference. Green: TRON. These are original plotted traces, cropped and arranged for this page; they are not a new experiment.
Period
Jul 2025 – Dec 2025
Role
Research Assistant
Platform
LIMX TRON 1A · Isaac Gym · MuJoCo
  • BuildIndependent 2D simulationRigid-body dynamics, contact, PD actuation, and PPO.
  • Train3D locomotion policiesPPO training and evaluation with reward and control tuning.
  • AnalyzeGait and joint mechanicsHuman references, torque, power, and transport cost.
  • DiagnoseSimulation–hardware timingSingle-joint tests exposed inconsistent time bases.

01 / Build

Independent 2D Simulation

I independently developed a planar biped environment with rigid-body dynamics, foot–ground contact, and PD actuation, and implemented PPO training to study gait- and energy-related reward designs.

The reduced model made the control loop easier to inspect: a policy selected joint-position targets, the PD controller generated limited joint torques, and contact forces determined the response at the feet. This provided a setting for examining how reward choices affected joint behavior.

Animated recorded TRON2d planar rollout with blue left leg, red right leg, and a camera following the moving base
Recorded TRON2d simulation, re-rendered with the project’s own visualization script at the recorded timing. Blue and red identify the left and right legs; green markers indicate contact and center of mass. This is a simulation-state replay, not physical-robot footage. Open GIF.

02 / Train

3D PPO Locomotion Training

For the LIMX TRON 1A, I trained PPO policies using the lab’s Isaac Gym framework, tuning reward terms and control parameters. My contribution centered on policy training and analysis within that framework.

The control loop links observations of the robot and its commanded motion to joint-position targets. PD gains and torque limits determine how those targets become motion; gait- and energy-related rewards influence which behavior training favors.

Still frame of the recorded TRON trajectory, shown when reduced motion is preferred
Recorded Isaac Sim body and joint states, replayed with the original TRON meshes in MuJoCo. The motion follows saved simulation data; MuJoCo provides the visualization here, not an independent policy-transfer test. GIF version.

03 / Analyze

Gait-Cycle Analysis

I collected and processed hip, knee, and ankle trajectories and developed gait-cycle visualizations against human walking references. Comparing the joints over a cycle made it possible to examine coordination and identify differences that a scalar reward could hide.

A cycle runs from one foot’s touchdown to its next touchdown, with toe-off separating stance and swing. Event alignment matters: a timing shift can otherwise look like a change in joint behavior.

Human referenceTRONAngle: degrees · Torque: N·m/kg

Hip pitch

Compare the timing and extent of hip motion alongside the associated joint moment.

Original human and TRON hip pitch angle traces over a 0 to 100 percent gait cycle
Hip pitch angle · gait cycle [%]
Original human and TRON hip pitch torque traces over a 0 to 100 percent gait cycle
Hip pitch torque · gait cycle [%]

Knee pitch

Inspect stance flexion and the larger swing-phase excursion together with knee torque.

Original human and TRON knee pitch angle traces over a 0 to 100 percent gait cycle
Knee pitch angle · gait cycle [%]
Original human and TRON knee pitch torque traces over a 0 to 100 percent gait cycle
Knee pitch torque · gait cycle [%]

Ankle pitch

Compare ankle posture and moment through stance and the transition into swing.

Original human and TRON ankle pitch angle traces over a 0 to 100 percent gait cycle
Ankle pitch angle · gait cycle [%]
Original human and TRON ankle pitch torque traces over a 0 to 100 percent gait cycle
Ankle pitch torque · gait cycle [%]

Source: Zuojun project notes, PDF p. 31, used as historical team analysis material. The curves, axis scales, and normalization are preserved. Their underlying samples and cycle count were not recovered for this page; the faint traces are not relabeled as a confidence or standard-deviation band. Touchdown/toe-off alignment was requested in the notes, but has not been independently re-established for these extracted plots. Select any plot to inspect it at full size.

04 / Interpret

Diagnosing Joint-Level Inefficiency

The historical gait discussion connected differences in joint motion to the effort required in each phase. I used this kind of joint-level analysis to look beyond whether the robot remained upright and followed a command.

A schematic cycle from touchdown through stance, toe-off, swing, and next touchdown, without measured phase durations
Phase sequence redrawn for this page. The observations below summarize the discussion on PDF p. 33; they are interpretations to investigate, not experimentally isolated causal effects.
Stance

Support knee

A flexed stance posture coincides with sustained knee effort in the plotted cycle. This motivates checking how support posture affects joint loading.

Swing

Swing knee

The larger flexion excursion motivates examining acceleration and deceleration effort. The notes also raise possible joint-limit interaction as a hypothesis.

Transition

Ankle / push-off

Ankle posture and push-off need to be considered alongside knee motion when interpreting propulsion and foot-clearance demands.

Mechanical energy: from a joint trace to work

Joint power combines torque with angular velocity. Integrating power over the same time interval connects a gait pattern to mechanical work; torque alone cannot establish energy consumption.

Joint powerPj(t) = τj(t) · q̇j(t)Torque in N·m and angular velocity in rad/s give power in W.

Mechanical workW+ = ∫ Σj max(Pj, 0) dtPositive work differs from absolute work ∫ Σ|Pj| dt and net work ∫ ΣPj dt.

Mechanical CoTCoT = W / (m · g · d)The chosen work definition, mass, traveled distance, and evaluation interval must accompany the value.

Mechanical CoT is not electrical or battery CoT. No numeric CoT result is reported here because a matching source record and calculation protocol have not been established.

05 / Compare

Cross-Simulator Evaluation

I participated in Isaac Gym–MuJoCo transfer and evaluation, comparing joint position, velocity, and torque to investigate differences in system response. Mechanical-power and CoT analysis provided additional ways to examine locomotion efficiency.

Motion

Position and velocity traces reveal changes in excursion, timing, and tracking under a matched command.

Actuation

Torque traces put similar-looking motion in context: PD response, saturation, and loading can differ.

Energy

Power and work must use the same interval and accounting convention before comparing transport cost.

Archived MuJoCo SF_TRON1 viewer showing the robot mesh and named joint controls
Archived MuJoCo model view from the retained project files. This screenshot documents the TRON model setup; it does not establish a matched-policy transfer result. Paired trajectory overlays require a separately identified comparison record.

06 / Reconstruct

Hardware Data & 3D Motion Replay

I processed physical-robot joint-angle and body-pose data and developed 3D motion replays. In MuJoCo–hardware comparisons, I used single-joint sinusoidal tests to diagnose and correct inconsistent simulation and execution time bases.

A measured-data replay helps inspect coordination and posture over time. It reconstructs a recorded motion; it does not by itself demonstrate a controller running on hardware or validate a simulator’s dynamics.

Simulation–Hardware Timing Diagnosis

I used single-joint sinusoidal tests to investigate timing differences between simulated and measured joint responses. The historical diagnostic record showed an effective approximately 2-ms execution interval despite nominal 1-ms simulation steps. I traced the discrepancy to inconsistent simulation and execution time bases and corrected the comparison timing.

The nominal step describes simulated time; the execution interval describes elapsed wall-clock time. Keeping these time bases distinct is necessary before interpreting a difference in joint-response timing.

Historical single-knee sinusoidal test overlay with simulation and hardware position, velocity, torque, and command traces as labeled in the original legend
Original signal overlay from the single-knee sinusoidal test in Zuojun PDF, p. 8. The original axes, legend, and signal scaling are preserved. This historical test illustrates the investigation; it is not a before-and-after error benchmark.

The timing finding is documented in the historical notes on pp. 7–8. A numerical before-and-after trajectory error has not been independently reconstructed from the retained logs.

  1. RecordJoint angles and body pose
  2. AlignTiming, joint order, and coordinate frames
  3. ReconstructRobot geometry and 3D motion
  4. CompareSelected simulation and measured signals

What This Work Taught Me

Locomotion analysis needs more than a reward curve or a convincing animation. Gait phase tells me when a joint acts; torque and velocity explain its mechanical role; energy accounting defines what an efficiency number means. Comparing models and measurements then reveals which parts of that explanation survive a change of platform.

About the evidence on this page

The contribution statements follow my October 2026 CV’s account of the July–December 2025 project. The human–TRON curves come from historical team notes supplied for this case study (Zuojun PDF, p. 31); the gait diagnostic observations draw on p. 33, and the single-joint timing test and time-base finding come from pp. 7–8. My responsibility for the timing diagnosis and correction was confirmed separately from the authorship of the team notes. The gait-phase diagram was newly drawn as a schematic. The 2D and 3D animations were re-rendered from retained simulation records; their generation and source-run details are recorded separately from the historical project period. Team plots are not attributed to me as sole author.

The curves preserve the original plotted data, while the animations reproduce saved simulation states. No new walking benchmark, hardware efficiency result, or numerical sim-to-sim agreement is claimed. The remaining reserved areas identify the records needed for joint-power analysis and a verified hardware replay.