This paper presents a novel methodology for implementing optimized jumping behavior on quadruped robots. Our method includes efficient trajectory optimization, precise high-frequency tracking controller and robust landing controller for stabilizing the robot body position and orientation after impact. Experimental validation was successfully conducted on the MIT Cheetah 3, enabling the robot to repeatably jump onto and jump down from a desk with the height of 30" (0.76 m). The result demonstrates the advantages of the approach as well as the capability of the robot hardware itself.

This paper introduces a new robust, dynamic quadruped, the MIT Cheetah 3. Like its predecessor, the Cheetah 3 exploits tailored mechanical design to enable simple control strategies for dynamic locomotion and features high-bandwidth proprioceptive actuators to manage physical interaction with the environment. A new leg design is presented that includes proprioceptive actuation on the abduction/adduction degrees of freedom in addition to an expanded range of motion on the hips and knees. To make full use of these new capabilities, general balance and locomotion controllers for Cheetah 3 are presented. These controllers are embedded into a modular control architecture that allows the robot to handle unexpected terrain disturbances through reactive gait modification and without the need for external sensors or prior environment knowledge. The efficiency of the robot is demonstrated by a low Cost of Transport (CoT) over multiple gaits at moderate speeds, with the lowest CoT of 0.45 found during trotting. Experiments showcase the ability to blindly climb up stairs as a result of the full system integration. These results collectively represent a promising step toward a platform capable of generalized dynamic legged locomotion.

This paper presents a novel method of stabilizing hybrid models of torque-constrained, underactuated walking robots - without using nonlinear gait optimization - by leveraging properties of the mechanics of the robot. At its core, the controller stabilizes the transfer of angular momentum from one leg to the next through continuous-time control coupled with hybrid system models that capture impacts that occur at foot strike. In particular, conservation of angular momentum at impact allows for computation of the exact transfer of momentum as a function of the robot's step length and vertical center of mass velocity just prior to foot impact. This motivates the construction of continuous-time reference trajectories for the robot's step length and vertical center of mass with endpoints corresponding to a desired transfer of angular momentum. Stabilization to these trajectories results in stable walking, as indicated by numeric Poincaré analysis. The controller is implemented in simulation of a five-link, underactuated 3D robot via Model Predictive Control which provides a means of achieving walking under non-trivial actuation limits.

This paper addresses the problem of controlling underactuated bipedal walking robots in the presence of actuator torque saturation. The proposed method synthesizes elements of the Human-Inspired Control (HIC) approach for generating provably-stable walking controllers, rapidly exponentially stabilizing control Lyapunov functions (RES-CLFs) and standard model predictive control (MPC). Specifically, the proposed controller uses feedback linearization to construct a linear control system describing the dynamics of the walking outputs. The input to this linear system is designed to be the solution of a MPC-based Quadratic Program which minimizes the sum of the values of a RES-CLF-describing the walking control objectives-over a finite-time horizon. Future values of the torque constraints are mapped into the linear control system using the Hybrid Zero Dynamics property of HIC and subsequently incorporated in the Quadratic Program. The proposed method is implemented in a rigid-body dynamics simulation and initial experiments with the Durus robot.

This paper presents a method for achieving planar multi-phase, multi-contact robotic walking using human inspired control and optimization. The walking presented contains phases with differing degrees of actuation including over-actuated double support, fully-actuated single support, and under-actuated single support via heel lift. An optimization methodology for generating walking gaits using partial hybrid zero dynamics will be presented. It will be shown that this method yields periodic, multi-contact locomotion. Simulation results for the three domain walking under standard Input-Output Linearization control will be presented.

This paper employs the Human-Inspired Control framework in the formal design, optimization and implementation of controllers for 3D bipedal robotic walking. In this framework, controllers drive the robot to a low-dimensional representation, termed the partial hybrid zero dynamics, which is shaped by the parameters of the outputs describing human locomotion data. The main result of this paper is the use of partial hybrid zero dynamics in an optimization problem to compute physical constraints on the robot, without integrating the dynamics of the system, and while simultaneously yielding provably stable walking controllers for a 3D robot model. Controllers corresponding to various walking speeds are obtained through a second speed regulation optimization, and formal methods are presented which provide smooth transitions between walking speeds. These formal results are demonstrated through simulation and utilized to obtain 3D walking experimentally with the NAO robot.

This paper demonstrates the process of utilizing human locomotion data to formally design controllers that yield provably stable robotic walking and experimentally realizing these formal methods to achieve dynamically stable bipedal robotic walking on the NAO robot. Beginning with walking data, outputs---or functions of the kinematics---are determined that result in a low-dimensional representation of human locomotion. These same outputs can be considered on a robot, and human-inspired control is used to drive the outputs of the robot to the outputs of the human. An optimization problem is presented that determines the parameters of this controller that provide the best fit of the human data while simultaneously ensuring partial hybrid zero dynamics. The main formal result of this paper is a proof that these same parameters result in a stable hybrid periodic orbit with a fixed point that can be computed in closed form. Thus, starting with only human data we obtain a stable walking gait for the bipedal robot model. These formal results are validated through experimentation: implementing the stable walking found in simulation on NAO results in dynamically stable robotic walking that shows excellent agreement with the simulated behavior from which it was derived.

This paper presents an approach to the development of bipedal robotic control techniques for multiple locomotion behaviors. Insight into the fundamental behaviors of human locomotion is obtained through the examination of experimental human data for walking on flat ground, upstairs and downstairs. Specifically, it is shown that certain outputs of the human, independent of locomotion terrain, can be characterized by a single function, termed the extended canonical human function. Optimized functions of this form are tracked via feedback linearization in simulations of a planar robotic biped walking on flat ground, upstairs and downstairs - these three modes of locomotion are termed “motion primitives.” A second optimization is presented, which yields controllers that evolve the robot from one motion primitive to another - these modes of locomotion are termed “motion transitions.” A final simulation is given, which shows the controlled evolution of a robotic biped as it transitions through each mode of locomotion over a pyramidal staircase.