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

opty: Software for Trajectory Optimization and Parameter Identification Using Direct Collocation

opty is a tool for describing and solving trajectory optimization and parameter identification problems based on symbolic descriptions of ordinary differential equations and differential algebraic equations that describe a dynamical system. The motivation for its development resides in the need to solve optimal control problems of biomechanical systems. The target audience is engineers and scientists interested in solving nonlinear optimal control and parameter identification problems with minimal computational overhead

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

Continuous Stairs Climbing Control Design for Bipedal Robots

While robotics technology advances and more real-world applications are used in the industry, legged robots, unlike robotic arms or wheeled robots, are not widely utilized despite their various benefits, such as improved movement performance in complex terrains. This could be due to several limitations in both hardware and software. This paper focuses on developing a reliable and efficient control algorithm for bipedal robots walking on long, continuous stairs. This enhancement aims to increase their movability in real-world scenarios, fully utilizing their advantages of better operation and relatively less space requirement in complex terrain compared to traditional wheeled robots. To enable bipedal robots to walk on continuous stairs, the paper proposes improvements to the traditional Angular Momentum Linear Inverted Pendulum (ALIP) planner. These improvements enable the 2D planar five-link walker robot, RABBIT, to handle vertical and horizontal displacement of the center of mass (COM) and to calculate foot displacement as a trajectory in the simulator. The findings suggest that the modified traditional dynamical model for bipedal robots requires fewer resources to generate control algorithms. As the working environment, stairs, a reparative environment, this offers an advantage with utilizing Bezier approximation to regulate the swing-foot and COM displacement trajectory onto the bipedal model itself. This work highlights the advantage from model-based approach that it takes less time and inputs to generate the control algorithms and the transparency during the simulation comparing to the black box-like process of the learning-based approaches, but with an inherent limitation of lacking versatility. And for LIP model specifically, without introducing other policies or methodologies, it is insufficient to handle the vertical displacement of the COM for bipedal robots.No embargoAcademic Major: Mechanical Engineerin

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