Local Stability of PD Controlled Bipedal Walking Robots

  title={Local Stability of PD Controlled Bipedal Walking Robots},
  author={Shishir Kolathaya},
We establish stability results for PD tracking control laws in bipedal walking robots. Stability of PD control laws for continuous robotic systems is an established result, and we extend this for hybrid robotic systems, an alternating sequence of continuous and discrete events. Bipedal robots have the leg-swing as the continuous event, and the foot-strike as the discrete event. In addition, bipeds largely have underactuations due to the interactions between feet and ground. For each continuous… Expand
PD Tracking for a Class of Underactuated Robotic Systems With Kinetic Symmetry
Stability properties of Proportional-Derivative controlled underactuated robotic systems for trajectory tracking applications are studied and it is shown that for a subclass of robotic systems, PD tracking control laws, indeed, yield desirable tracking guarantees. Expand
Safety-Critical Kinematic Control of Robotic Systems
This paper demonstrates a purely kinematic implementation of a velocity-based CBF, and introduces a formulation that guarantees safety at the level of dynamics, through a new form of CBFs that incorporate kinetic energy with the classical forms, thereby minimizing model dependence and conservativeness. Expand
Study of Series-parallel Mechanism Used in Legs of Biped Robot
Walking is an essential ability for biped robots, and the stability of walking is affected by both mechanical structure and control algorithm. In this work, a new design of legs with low moment ofExpand
Energy based Control Barrier Functions for Robotic Systems
Control barrier function (CBF) based Quadratic Programs (QPs) were introduced in early 2014 as a means to guarantee safety in affine control systems in conjunction with stability/tracking. However,Expand
Quadrupedal Robotic Walking on Sloped Terrains via Exact Decomposition into Coupled Bipedal Robots
This paper presents a method for rapidly generating quadrupedal locomotion on sloped terrains—from modeling to gait generation, to hardware demonstration, and the ability to rapidly generate quadrupingal walking gaits on a variety of slopes. Expand
Modeling and Networked Control of Two-rigid link Robot Arm
A networked control system (NCS) is one in which controller(s), actuator(s),and sensor(s)exchange command signals and data through a limited-bandwidth communication network that may be used by otherExpand


Time dependent control Lyapunov functions and hybrid zero dynamics for stable robotic locomotion
It is shown that stable walking can be achieved through time-based implementations of state-based virtual constraints, and virtual constraints that yield hybrid zero dynamics with desired outputs that are a function of time or a state- based phase variable are considered. Expand
Stable dynamic walking over uneven terrain
A constructive control design for stabilization of non-periodic trajectories of underactuated robots, using a transverse linearization about the desired motion and providing exponential orbital stability of the target trajectory of the original nonlinear system. Expand
Bipedal Robotic Running with DURUS-2D: Bridging the Gap between Theory and Experiment
This paper uses a large-scale optimization to generate an energy-efficient running gait, formally guaranteed in the hybrid system model with an input to state stability (ISS) based control law, and implements a provably stable control implementation, resulting in bipedal robotic running. Expand
Hybrid zero dynamics of planar biped walkers
The design of exponentially stable walking controllers for general planar bipedal systems that have one degree-of-freedom greater than the number of available actuators are presented. Expand
3D dynamic walking with underactuated humanoid robots: A direct collocation framework for optimizing hybrid zero dynamics
This paper presents a methodology that allows for the fast and reliable generation of efficient multi-contact robotic walking gaits through the framework of HZD, even in the presence of underactuation, and experimentally validated the methodology on the spring-legged prototype humanoid, DURUS, showing that the optimization approach yields dynamic and stable 3D walking Gaits. Expand
Asymptotic Stability of Feedback Control Laws for Robot Manipulator
Abstract Stability and robustness analysis of various tractable and easily implementable feedback control laws for robotic systems with a single mechanical arm or a pair of master and slave robotExpand
Exponentially stabilizing continuous-time controllers for periodic orbits of hybrid systems: Application to bipedal locomotion with ground height variations
The power of this systematic approach to robustly and exponentially stabilize periodic orbits of hybrid dynamical systems arising from bipedal walking is illustrated by finding robust and stabilizing continuous-time feedback laws for walking gaits of two underactuated 3D bipingal robots. Expand
Human-inspired underactuated bipedal robotic walking with AMBER on flat-ground, up-slope and uneven terrain
Human-inspired control strategies required for achieving three motion primitives in walking-flat-ground, uneven terrain and up-slope-in an underactuated physical bipedal robot: AMBER are presented. Expand
3D Bipedal Robotic Walking: Models, Feedback Control, and Open Problems
Abstract The fields of control and robotics are contributing to the development of bipedal robots that can realize walking motions with the stability and agility of a human being. Dynamic models forExpand
Parameter Sensitivity and Boundedness of Robotic Hybrid Periodic Orbits
The ultimate boundedness of the output dynamics is established in terms of this measure via these Lyapunov functions under the assumption of stable hybrid zero dynamics on a 5-DOF underactuated bipedal robot. Expand