Dynamically Stable 3D Quadrupedal Walking with Multi-Domain Hybrid System Models and Virtual Constraint Controllers

Hybrid systems theory has become a powerful approach for designing feedback controllers that achieve dynamically stable bipedal locomotion, both formally and in practice. This paper presents an analytical framework 1) to address multi-domain hybrid models of quadruped robots with high degrees of freedom, and 2) to systematically design nonlinear controllers that asymptotically stabilize periodic orbits of these sophisticated models. A family of parameterized virtual constraint controllers is proposed for continuous-time domains of quadruped locomotion to regulate holonomic and nonholonomic outputs. The properties of the Poincare return map for the full-order and closed-loop hybrid system are studied to investigate the asymptotic stabilization problem of dynamic gaits. An iterative optimization algorithm involving linear and bilinear matrix inequalities is then employed to choose stabilizing virtual constraint parameters. The paper numerically evaluates the analytical results on a simulation model of an advanced 3D quadruped robot, called GR Vision 60, with 36 state variables and 12 control inputs. An optimal amble gait of the robot is designed utilizing the FROST toolkit. The power of the analytical framework is finally illustrated through designing a set of stabilizing virtual constraint controllers with 180 controller parameters.Comment: American Control Conference 201

Multifunction tests of a frequency domain based flutter suppression system

The process is described of analysis, design, digital implementation, and subsonic testing of an active control flutter suppression system for a full span, free-to-roll wind tunnel model of an advanced fighter concept. The design technique uses a frequency domain representation of the plant and used optimization techniques to generate a robust multi input/multi output controller. During testing in a fixed-in-roll configuration, simultaneous suppression of both symmetric and antisymmetric flutter was successfully shown. For a free-to-roll configuration, symmetric flutter was suppressed to the limit of the tunnel test envelope. During aggressive rolling maneuvers above the open-loop flutter boundary, simultaneous flutter suppression and maneuver load control were demonstrated. Finally, the flutter damping controller was reoptimized overnight during the test using combined experimental and analytical frequency domain data, resulting in improved stability robustness

Performance Regulation and Tracking via Lookahead Simulation: Preliminary Results and Validation

This paper presents an approach to target tracking that is based on a variable-gain integrator and the Newton-Raphson method for finding zeros of a function. Its underscoring idea is the determination of the feedback law by measurements of the system's output and estimation of its future state via lookahead simulation. The resulting feedback law is generally nonlinear. We first apply the proposed approach to tracking a constant reference by the output of nonlinear memoryless plants. Then we extend it in a number of directions, including the tracking of time-varying reference signals by dynamic, possibly unstable systems. The approach is new hence its analysis is preliminary, and theoretical results are derived for nonlinear memoryless plants and linear dynamic plants. However, the setting for the controller does not require the plant-system to be either linear or stable, and this is verified by simulation of an inverted pendulum tracking a time-varying signal. We also demonstrate results of laboratory experiments of controlling a platoon of mobile robots.Comment: A modified version will appear in Proc. 56th IEEE Conf. on Decision and Control, 201

First Steps Towards Full Model Based Motion Planning and Control of Quadrupeds: A Hybrid Zero Dynamics Approach

The hybrid zero dynamics (HZD) approach has become a powerful tool for the gait planning and control of bipedal robots. This paper aims to extend the HZD methods to address walking, ambling and trotting behaviors on a quadrupedal robot. We present a framework that systematically generates a wide range of optimal trajectories and then provably stabilizes them for the full-order, nonlinear and hybrid dynamical models of quadrupedal locomotion. The gait planning is addressed through a scalable nonlinear programming using direct collocation and HZD. The controller synthesis for the exponential stability is then achieved through the Poincaré sections analysis. In particular, we employ an iterative optimization algorithm involving linear and bilinear matrix inequalities (LMIs and BMIs) to design HZD-based controllers that guarantee the exponential stability of the fixed points for the Poincaré return map. The power of the framework is demonstrated through gait generation and HZD-based controller synthesis for an advanced quadruped robot, —Vision 60, with 36 state variables and 12 control inputs. The numerical simulations as well as real world experiments confirm the validity of the proposed framework