This work investigates a data-driven template model for trajectory planning of dynamic quadrupedal robots. Many state-of-the-art approaches involve using a reduced-order model, primarily due to computational tractability. The spirit of the trajectory planning approach in this work draws on recent advancements in the area of behavioral systems theory. Here, we aim to capitalize on the knowledge of well-known template models to construct a data-driven model, enabling us to obtain an information rich reduced-order model. In particular, this work considers input-output states similar to that of the single rigid body model and proceeds to develop a data-driven representation of the system, which is then used in a predictive control framework to plan a trajectory for quadrupeds. The optimal trajectory is passed to a low-level and nonlinear model-based controller to be tracked. Preliminary experimental results are provided to establish the efficacy of this hierarchical control approach for trotting and walking gaits of a high-dimensional quadrupedal robot on unknown terrains and in the presence of disturbances.

This letter develops, theoretically justifies, and experimentally implements an optimization-based nonlinear control methodology for stabilizing quadrupedal locomotion. This framework utilizes virtual constraints and control Lyapunov functions (CLFs) in the context of quadratic programs (QPs) to robustly stabilize periodic orbits for hybrid models of quadrupedal robots. Properties of the proposed QP are studied wherein sufficient conditions for the continuous differentiability of the controller are presented. Additionally, this letter addresses the robust stabilization problem of the orbits based on the Poincar é sections analysis and input-to-state stability (ISS). The proposed controller is numerically and experimentally validated on the A1 quadrupedal robot with 18 degrees of freedom to demonstrate the robust stability of trotting gaits against external disturbances and unknown payloads.

Template-based reduced-order models have provided a popular methodology for real-time trajectory planning of dynamic quadrupedal locomotion. However, the abstraction and unmodeled dynamics in template models significantly increase the gap between reduced-and full-order models. This letter presents a computationally tractable robust model predictive control (RMPC) formulation, based on convex quadratic programs (QP), to bridge this gap. The RMPC framework considers the single rigid body model subject to a set of unmodeled dynamics and plans for the optimal reduced-order trajectory and ground reaction forces (GRFs). The generated optimal GRFs of the highlevel RMPC are then mapped to the full-order model using a lowlevel nonlinear controller based on virtual constraints and QP. The proposed hierarchical control framework is employed for locomotion over rough terrains. We leverage deep reinforcement learning to train a neural network to compute the set of unmodeled dynamics for the RMPC framework. The proposed controller is finally validated via extensive numerical simulations and experiments for robust and blind locomotion of the A1 quadrupedal robot on different terrains.

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Walking is an integral indicator of human health commonly investigated while walking overground and with the use of a treadmill. Unlike fixed-speed treadmills, overground walking is dependent on the preferred walking speed under the individuals’ control. Thus, user-driven treadmills may have the ability to better simulate the characteristics of overground walking. This pilot study is the first investigation to compare a user-driven treadmill, a fixed-speed treadmill, and overground walking to understand differences in variability and mean spatiotemporal measures across walking environments. Participants walked fastest overground compared to both fixed and user-driven treadmill conditions. However, gait cycle speed variability in the fixed-speed treadmill condition was significantly lower than the user-driven and overground conditions, with no significant differences present between overground and user-driven treadmill walking. The lack of differences in variability between the user-driven treadmill and overground walking may indicate that the user-driven treadmill can better simulate the variability of overground walking, potentially leading to more natural adaptation and motor control patterns of walking.

The primary goal of this paper is to develop a formal foundation to design nonlinear feedback control algorithms that intrinsically couple legged robots with bio-inspired tails for robust locomotion in the presence of external disturbances. We present a hierarchical control scheme in which a high-level and real-time path planner, based on an event-based model predictive control (MPC), computes the optimal motion of the center of mass (COM) and tail trajectories. The MPC framework is developed for an innovative reduced-order linear inverted pendulum (LIP) model that is augmented with the tail dynamics. At the lower level of the control scheme, a nonlinear controller is implemented through the use of quadratic programming (QP) and virtual constraints to force the full-order dynamical model to track the prescribed optimal trajectories of the COM and tail while maintaining feasible ground reaction forces at the leg ends. The potential of the analytical results is numerically verified on a full-order simulation model of a quadrupedal robot augmented with a tail with a total of 20 degrees of freedom. The numerical studies demonstrate that the proposed control scheme coupled with the tail dynamics can significantly reduce the effect of external disturbances during quadrupedal locomotion.

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