Supplementary Material for: Rapid predictive simulations with complex musculoskeletal models suggest that diverse healthy and pathological human gaits can emerge from similar control strategies Antoine Falisse, Gil Serrancol´ ı, Christopher L. Dembia, Joris Gillis, Ilse Jonkers, and Friedl De Groote Journal of the Royal Society Interface Experimental data The subject (female; age: 35 years; height: 170 cm; mass: 62 kg) was instrumented with 45 retro-reflective skin-mounted markers. Three-dimensional marker coordinates were recorded (100 Hz) using a ten-camera motion capture system (Vicon, Oxford, UK). Ground reaction forces and electromyography (EMG) data were recorded (1000 Hz) using two force plates (AMTI, Watertown, USA) and a wireless EMG acquisition system (Cometa Mini Wave, Milano, Italy), respectively. Ground reaction forces were low-pass filtered (6 Hz) using a second-order dual-pass Butterworth filter. EMG data was collected from 14 muscles (peroneus brevis and longus, tibialis anterior, gastrocnemius lateralis and medialis, soleus, vastus lateralis and medialis, adductor longus, rectus femoris, tensor fascia latae, gluteus medius, hamstrings lateralis and medialis) and was processed by band-pass filtering (20-400 Hz), full-wave rectification, and low-pass filtering (10 Hz) using a second-order dual-pass Butterworth filter. Smooth approximations We performed smooth approximations of the contact and metabolic energy models to allow having twice continuously differentiable models, which are required when using gradient-based optimization [1]. We performed smooth approximations of conditional if statements using hy- perbolic tangent functions. For example, the following if statement : y =  0, x<d a, x ≥ d (1) can be approximated by: f =0.5+0.5 tanh(b(x − d)), (2) y = af, (3) where b is a parameter that determines the smoothness of the transition. Optimal control problem formulation We applied direct collocation to solve the optimal control problems underlying the predictive simulations. We sought to find the states, controls, and static (i.e., time-independent) parame- ters that minimized a cost function subject to dynamic and path constraints. 1