Controlling a simple model of bipedal walking to adapt to a wide range of target step lengths and step frequencies

Abstract We tested whether the same principles of actuation and control that support steady-state walking are sufficient for robust, rapid gait adaptation over a wide range of step lengths and frequencies. We begin by demonstrating that periodic limit cycle gaits exist at combinations of step frequency and step length that span the full range of gaits achievable by humans. We demonstrate that open-loop local stability is not enough to rapidly transition to target gaits because some gaits in the gait space are unstable and the stable gaits have slow convergence rates. Next, we show that actuating with only one push-off and one hip spring of fixed stiffness cannot fully control the walker in the entire gait space. We solve this by adding a second hip spring with an independent stiffness with respect to the first one to actuate the second half of the swing phase. This allowed us to design local feedback controllers that provided rapid convergence to target gaits by making once-per-step adjustments to push-off and hip spring stiffnesses. To adapt to a range of target gaits that vary over time, we interpolated between local controllers. This policy performs well, accurately tracking rapidly varying combinations of target step length and step frequency with human-like response times across a wide range of human achievable gaits. To test whether this policy is biologically plausible, we use it with supervised learning to train an artificial neural network to perform nearly identical control. Author Summary People can rapidly adapt their walking gaits. In this study, we used a modeling approach to study whether control of walking adaptation is identical to control of steady state walking. We first demonstrate that the model can produce human-like gaits over a wide range of step lengths and step frequencies. However, we found that unlike steady state walking, the model does not transition between gaits quickly or reliably. To address this, we introduced an additional actuation to control the swing leg and used feedback control that applies once-per-step adjustments to the actuations. This enabled the model to rapidly converge to target gaits, even when the targets changed from one step to the next. To test whether this policy is biologically plausible, we use it with supervised learning to train an artificial neural network to perform nearly identical control. This work provides insights into the mechanisms of walking adaptation and has potential implications for the design of adaptive control in robotic and wearable assistive systems.

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