This article presents a layered control approach for real-time trajectory planning and control of robust cooperative locomotion by two holonomically constrained quadrupedal robots. A novel interconnected network of reduced-order models, based on the single rigid body (SRB) dynamics, is developed for trajectory planning purposes. At the higher level of the control architecture, two different model predictive control (MPC) algorithms are proposed to address the optimal control problem of the interconnected SRB dynamics: centralized and distributed MPCs. The distributed MPC assumes two local quadratic programs that share their optimal solutions according to a one-step communication delay and an agreement protocol. At the lower level of the control scheme, distributed nonlinear controllers are developed to impose the full-order dynamics to track the prescribed reduced-order trajectories generated by MPCs. The effectiveness of the control approach is verified with extensive numerical simulations and experiments for the robust and cooperative locomotion of two holonomically constrained A1 robots with different payloads on variable terrains and in the presence of disturbances. It is shown that the distributed MPC has a performance similar to that of the centralized MPC, while the computation time is reduced significantly.

Although legged robots are becoming more nonlinear with higher degrees of freedom (DOFs), the centralized nonlinear control methods required to achieve stable locomotion cannot scale with the dimensionality of these robots. This paper investigates time-varying decentralized feedback control architectures based on hybrid zero dynamics (HZD) that stabilize dynamic legged locomotion with high degrees of freedom. By conforming to the natural symmetries present in the robot's full-order model, three decentralization schemes are proposed for control synthesis, namely left-right, front-hind and diagonal. Our approach considers the strong nonlinear interactions between the subsystems and relies only on the intrinsic communication of the body's translation and rotational data that is readily available. Further, a quadratic programming (QP) based feedback linearization is employed to compute the control inputs for each subsystem. The effectiveness of the HZD-based decentralization scheme is demonstrated numerically for the stabilization of forward and inplace walking gaits on an 18 DOF robot.

This paper aims to develop time-varying virtual constraint controllers that allow stable and agile bounding gaits for full-order hybrid dynamical models of quadrupedal locomotion. As opposed to state-based nonlinear controllers, time-varying controllers can initiate locomotion from zero velocity. Motivated by this property, we investigate the stability guarantees that can be provided by the time-varying approach. In particular, we systematically establish necessary and sufficient conditions that guarantee exponential stability of periodic orbits for time-varying hybrid dynamical systems utilizing the Poincaré return map. Leveraging the results of the presented proof, we develop time-varying virtual constraint controllers to stabilize bounding gaits of a 14 degree of freedom planar quadrupedal robot, Minitaur. A framework for choosing the parameters of virtual constraint controllers to achieve exponential stability is shown, and the feasibility of the analytical results is numerically validated in full-order simulation models of Minitaur.

This paper presents the foundations of a MATLAB framework for dynamic modeling and simulation of closed kinematic chain (CKC) mechanisms, with a particular focus on implementation with legged locomotive mechanisms. As such, the framework supports both floating-base and fixed-base systems. Through the use of singular perturbation theory, various CKC mechanisms can be modeled so that constraint errors asymptotically converge to zero, thus avoiding the numerical drift that plagues commonly used methods. A functional API and the relevant core commands necessary to construct a model are presented. Two robotic legs incorporating CKC mechanisms are utilized as case studies, and simulations of each leg performing a dynamic monopedal gait are illustrated.

This paper presents the mechanical design and analysis of a novel leg mechanism that has only one active degree of freedom (DOF). The proposed mechanism is intended towards simplifying the mechanical and control complexity identified with the robotic legs implemented on quadrupedal platforms capable of dynamic locomotion. First, a survey of high-speed and reduced DOF legged robotic systems is presented to elucidate the design challenges and determine system requirements. Drawing from these requirements, a novel design of a six-bar leg mechanism with a single DOF is proposed. The novelty of the mechanism lies in its ability to trace a path that accommodates the execution of trot-gait by the quadrupedal platform realized by integrating the proposed leg. The kinematics of the mechanism is formulated and a multi-body model is used to perform a series of case studies on the sensitivity of the foot trajectory to the leg's dimensional parameters. Preliminary work on optimization of the foot trajectory is then performed. This research will ultimately assist the future design of quadrupedal robots to test the ability of spatial robotic tails in stabilizing and maneuvering the platform.