This article presents a novel representation-free model predictive control (RF-MPC) framework for controlling various dynamic motions of a quadrupedal robot in three-dimensional (3-D) space. Our formulation directly represents the rotational dynamics using the rotation matrix, which liberates us from the issues associated with the use of Euler angles and quaternion as the orientation representations. With a variation-based linearization scheme and a carefully constructed cost function, the MPC control law is transcribed to the standard quadratic program form. The MPC controller can operate at real-time rates of 250 Hz on a quadruped robot. Experimental results including periodic quadrupedal gaits and a controlled backflip validate that our control strategy could stabilize dynamic motions that involve singularity in 3-D maneuvers.

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 a new Model Predictive Control (MPC) framework for controlling various dynamic movements of a quadrupedal robot. System dynamics are represented by linearizing single rigid body dynamics in three-dimensional (3D) space. Our formulation linearizes rotation matrices without resorting to parameterizations like Euler angles and quaternions, avoiding issues of singularity and unwinding phenomenon, respectively. With a carefully chosen configuration error function, the MPC control law is transcribed into a Quadratic Program (QP) which can be solved efficiently in realtime. Our formulation can stabilize a wide range of periodic quadrupedal gaits and acrobatic maneuvers. We show various simulation as well as experimental results to validate our control strategy. Experiments prove the application of this framework with a custom QP solver could reach execution rates of 160 Hz on embedded platforms.