Predictive gait simulations currently do not account for environmental or internal noise. We describe a method to solve predictive simulations of human movements in a stochastic environment using a collocation method. The optimization is performed over multiple noisy episodes of the trajectory, instead of a single episode in a deterministic environment. Each episode used the same control parameters. The method was verified on a torque-driven pendulum swing-up problem. A different optimal trajectory was found in a stochastic environment than in the deterministic environment. Next, it was applied to gait to show its application in predictive simulation of human movement. We show that, unlike in a deterministic model, a nonzero minimum foot clearance during swing is predicted by a minimum-effort criterion in a stochastic environment. The predicted amount of foot clearance increased with the noise amplitude. (C) 2020 Elsevier Ltd. All rights reserved.