## 2 Materials and Methods  
### Biomechanical and Metabolic Data  
This study involved a secondary analysis of a previously reported dataset focused on the impact of a bilateral semi-rigid hip exoskeleton on gait characteristics [34]. The hip exoskeleton was a semi-rigid model designed to assist hip extension with a temporal force-tracking controller that applied sinusoidal torque profiles at specified times during the stride cycle [34]. This controller independently adjusted torque profiles for each leg. The torque assistance ranged in magnitude, with peak torques of 0.06 to 0.12 N\(\cdot\)m/kg. The desired timing for assistance termination varied from 21% to 49% of the gait cycle. This variable end timing and magnitude allowed us to explore the impact of assistance timing on reducing the metabolic cost [34]. The exoskeleton interfaced with participants via a waist belt and thigh cuffs positioned above the knees, allowing for targeted torque application across the hip joint. Adjustable straps ensured a secure, customized fit, and the device's lightweight, flexible design allowed for natural hip flexion and extension with minimal gait restriction. In brief, ten adults without a known disability (four males, six females; age: 27.6 \(\pm\) 5.9 years; body mass: 65.3 \(\pm\) 13.1 kg; height: 1.66 \(\pm\) 0.08 m; BMI: 23.39 \(\pm\) 4.10) enrolled in an Institutional Review Board-approved study. Participants were selected based on inclusion criteria that ensured they had no known musculoskeletal or neurological conditions that might influence gait patterns. Each performed 12 walking trials on a force plate-instrumented treadmill (Bertec, Columbus, OH, USA) at 1.25 m/s. During one trial, participants did not wear the exoskeleton. During 11 trials, participants walked while wearing a hip exoskeleton designed to assist hip motion. At the same time, the magnitude and timing of the extensor torque assistance were manipulated from no assistance to a peak torque of 0.12 (N\(\cdot\)m/kg). Oxygen consumption and carbon dioxide production were measured using indirect calorimetry (K5, Cosmed, Rome, Italy), and breath-by-breath data in the final two minutes were used to estimate the steady-state metabolic rate under each walking condition in watts per kilogram (W/kg). Three-dimensional lower extremity kinematics were recorded (VICON Vero, Oxford Metrics, Yarnton, UK; 120 Hz) from 23 reflective markers placed on the skin, a tight-fitting suit, and the exterior surface of the shoes over anatomical landmarks. Inverse kinematics were used to estimate joint kinematics from the marker data, limiting ankle and knee motion to a single degree of freedom (flexion and extension) while allowing three degrees of freedom for the hip. Ground reaction forces (GRFs), recorded (2000 Hz) using force plates embedded in the treadmill, were normalized to each participant's body mass (N/kg). Kinematic and kinetic data were used within OpenSim (version 4.0, SimTK, San Jose, CA, USA; [35; 36]) to calculate joint moments, normalized to each participant's body mass (N\(\cdot\)m/kg). We used the same software for gait validation tests, a widely recognized tool for simulating and analyzing musculoskeletal dynamics. In brief, the calibration for motion capture involved placing reflective markers on anatomical landmarks to establish a local coordinate system [20]. Before data collection, a static calibration trial was performed with the participant upright to align marker positions accurately with joint centers. For force measurements, the embedded force plates underwent zeroing and calibration with known weights to ensure precise ground reaction force readings. Calibration was repeated regularly throughout data collection to maintain accuracy and consistency in motion capture and force measurement systems. A laboratory-based global coordinate system was used, with the \(x\)-axis in the anterior-posterior, the \(y\)-axis in the medial-lateral, and the \(z\)-axis in the vertical directions.