Exponentially Stabilizing Controllers for Multi-Contact 3D Bipedal Locomotion

Models of bipedal walking are hybrid with continuous-time phases representing the Lagrangian stance dynamics and discrete-time transitions representing the impact of the swing leg with the walking surface. The design of continuous-time feedback controllers that exponentially stabilize periodic gaits for hybrid models of underactuated 3D bipedal walking is a significant challenge. We recently introduced a method based on an iterative sequence of optimization problems involving bilinear matrix inequalities (BMIs) to systematically design stabilizing continuous-time controllers for single domain hybrid models of underactuated bipedal robots with point feet. This paper addresses the exponential stabilization problem for multi-contact walking gaits with nontrivial feet. A family of parameterized continuous-time controllers is proposed for different phases of the walking cycle. The BMI algorithm is extended to the multi-domain hybrid models of anthropomorphic 3D walking locomotion to look for stabilizing controller parameters. The Poincaré map is addressed and a new set of sufficient conditions is presented that guarantees the convergence of the BMI algorithm to a stabilizing set of controller parameters at a finite number of iterations. The power of the algorithm is ultimately demonstrated through the design of stabilizing virtual constraint controllers for dynamic walking of a 3D humanoid model with 28 state variables and 275 controller parameters

Exponentially Stabilizing Controllers for Multi-Contact 3D Bipedal Locomotion

Models of bipedal walking are hybrid with continuous-time phases representing the Lagrangian stance dynamics and discrete-time transitions representing the impact of the swing leg with the walking surface. The design of continuous-time feedback controllers that exponentially stabilize periodic gaits for hybrid models of underactuated 3D bipedal walking is a significant challenge. We recently introduced a method based on an iterative sequence of optimization problems involving bilinear matrix inequalities (BMIs) to systematically design stabilizing continuous-time controllers for single domain hybrid models of underactuated bipedal robots with point feet. This paper addresses the exponential stabilization problem for multi-contact walking gaits with nontrivial feet. A family of parameterized continuous-time controllers is proposed for different phases of the walking cycle. The BMI algorithm is extended to the multi-domain hybrid models of anthropomorphic 3D walking locomotion to look for stabilizing controller parameters. The Poincaré map is addressed and a new set of sufficient conditions is presented that guarantees the convergence of the BMI algorithm to a stabilizing set of controller parameters at a finite number of iterations. The power of the algorithm is ultimately demonstrated through the design of stabilizing virtual constraint controllers for dynamic walking of a 3D humanoid model with 28 state variables and 275 controller parameters

Hierarchical and Safe Motion Control for Cooperative Locomotion of Robotic Guide Dogs and Humans: A Hybrid Systems Approach

This paper presents a hierarchical control strategy based on hybrid systems theory, nonlinear control, and safety-critical systems to enable cooperative locomotion of robotic guide dogs and visually impaired people. We address high-dimensional and complex hybrid dynamical models that represent collaborative locomotion. At the high level of the control scheme, local and nonlinear baseline controllers, based on the virtual constraints approach, are designed to induce exponentially stable dynamic gaits. The baseline controller for the leash is assumed to be a nonlinear controller that keeps the human in a safe distance from the dog while following it. At the lower level, a real-time quadratic programming (QP) is solved for modifying the baseline controllers of the robot as well as the leash to avoid obstacles. In particular, the QP framework is set up based on control barrier functions (CBFs) to compute optimal control inputs that guarantee safety while being close to the baseline controllers. The stability of the complex periodic gaits is investigated through the Poincare return map. To demonstrate the power of the analytical foundation, the control algorithms are transferred into an extensive numerical simulation of a complex model that represents cooperative locomotion of a quadrupedal robot, referred to as Vision 60, and a human model. The complex model has 16 continuous-time domains with 60 state variables and 20 control inputs

Hierarchical and Safe Motion Control for Cooperative Locomotion of Robotic Guide Dogs and Humans: A Hybrid Systems Approach

This letter presents a hierarchical control strategy based on hybrid systems theory, nonlinear control, and safety-critical systems to enable cooperative locomotion of robotic guide dogs and visually impaired people. We address high-dimensional and complex hybrid dynamical models that represent collaborative locomotion. At the high level of the control scheme, local and nonlinear controllers, based on the virtual constraints approach, are designed to induce exponentially stable dynamic gaits. The local controller for the leash is assumed to be a nonlinear controller that keeps the human in a safe distance from the dog while following it. At the lower level, a real-time quadratic programming (QP) is solved for modifying the local controllers of the robot as well as the leash to avoid obstacles. In particular, the QP framework is set up based on control barrier functions (CBFs) to compute optimal control inputs that guarantee safety while being close to the local controllers. The stability of the complex periodic gaits is investigated through the Poincaré return map. To demonstrate the power of the analytical foundation, the control algorithms are transferred into an extensive numerical simulation of a complex model that represents cooperative locomotion of a quadrupedal robot, referred to as Vision 60, and a human model. The complex model has 16 continuous-time domains with 60 state variables and 20 control inputs