To explore safely in such environments, it is critical for robots to generate quick, yet smooth responses to any changes in the obstacles, map, and environment. In this paper, we propose a means to design and compose control barrier functions (CBFs) for multiple non-overlapping obstacles and evaluate the system on a 20-degree-of-freedom (DoF) bipedal robot. In an autonomous system, the task of avoiding obstacles is usually handled by a planning algorithm because it has access to the map of an entire environment. Given the map, the planning algorithm is then able to design a collision-free path from the robot's current position to a goal. If the map is updated due to a change in the environment, the planner then needs to update the planned path, so-called replanning, to accommodate the new environment. Such maps are typically large and contain rich information such as semantics, terrain characteristics, and uncertainty, and thus are slow to update. This raises a concern when obstacles either move into the planned path but the map has not been updated or a robot's new pose allows the detection of previously unseen obstacles. The slow update rate of the map leads to either collision or abrupt maneuvers to avoid collisions. The non-smooth aspects arising from the map updates or changes in the perceived environment can be detrimental to the stability of the overall system.

Uneven terrain necessarily transforms periodic walking into a non-periodic motion. As such, traditional stability analysis tools no longer adequately capture the ability of a bipedal robot to locomote in the presence of such disturbances. This motivates the need for analytical tools aimed at generalized notions of stability -- robustness. Towards this, we propose a novel definition of robustness, termed \emph{$\delta$-robustness}, to characterize the domain on which a nominal periodic orbit remains stable despite uncertain terrain. This definition is derived by treating perturbations in ground height as disturbances in the context of the input-to-state-stability (ISS) of the extended Poincar\'{e} map associated with a periodic orbit. The main theoretic result is the formulation of robust Lyapunov functions that certify $\delta$-robustness of periodic orbits. This yields an optimization framework for verifying $\delta$-robustness, which is demonstrated in simulation with a bipedal robot walking on uneven terrain.

This paper presents a gait controller for bipedal robots to achieve highly agile walking over various terrains given local slope and friction cone information. Without these considerations, untimely impacts can cause a robot to trip and inadequate tangential reaction forces at the stance foot can cause slippages. We address these challenges by combining, in a novel manner, a model based on an Angular Momentum Linear Inverted Pendulum (ALIP) and a Model Predictive Control (MPC) foot placement planner that is executed by the method of virtual constraints. The process starts with abstracting from the full dynamics of a Cassie 3D bipedal robot, an exact low-dimensional representation of its center of mass dynamics, parameterized by angular momentum. Under a piecewise planar terrain assumption and the elimination of terms for the angular momentum about the robot's center of mass, the centroidal dynamics about the contact point become linear and have dimension four. Importantly, we include the intra-step dynamics at uniformly-spaced intervals in the MPC formulation so that realistic workspace constraints on the robot's evolution can be imposed from step-to-step. The output of the low-dimensional MPC controller is directly implemented on a high-dimensional Cassie robot through the method of virtual constraints. In experiments, we validate the performance of our control strategy for the robot on a variety of surfaces with varied inclinations and textures.

This is not a story about how the polar vortex is bad--bad for the human body, bad for public transportation, bad for virtually everything in its path. This is a story about how one being among us is actually taking advantage of the historic cold snap: Cassie the bipedal robot. While humans suffer through the chill, this trunkless pair of ostrich-like legs is braving the frozen grounds of the University of Michigan, for the good of science. "When we saw the announcement for the polar vortex, we started making plans to see how long we could operate in that kind of weather," says roboticist Jessy Grizzle. "We were going to tie a scarf on her just so it looked cute, but we decided people would think that was keeping her warm and affecting the experiment, so we didn't." Scarves aside, this is vital research for a future in which robots tackle not just polar vortices but any number of other brutal environments.

They can walk through (controlled) conflagrations on college campuses. At least, that is, the robots in and around roboticist Jessy Grizzle's lab at the University of Michigan. Specifically, Grizzle is working with a remote-controlled biped called Cassie, a research platform that roboticists are using to master bipedal locomotion. So Grizzle isn't just making Cassie walk through fire: He's experimenting with other extreme use cases, like riding a Segway. Are those experiments a bit silly?

Every chance we get, we post videos highlighting the adventures of MARLO, the University of Michigan's blissfully unaware bipedal robot. MARLO is totally "blind," without cameras, lidar, or anything else to show it where it's going. But the robot is still able to walk dynamically over a range of terrain that I think would be appropriate to call staggering. Varied terrain does indeed stagger MARLO on a regular basis, and it's probably fallen over more times on video than any robot we've ever seen. Professor Jessy Grizzle and his students have been challenging MARLO with increasingly difficult terrain, most recently at a location on the beautiful Ann Arbor campus called the "Wave Field," an "earth sculpture" created by artist Maya Lin.

MARLO, the 3D bipedal robot that belongs to electrical engineering professor Jessy Grizzle and his team of students, is starting to really figure out this walking thing. Here, robotics PhD student Ross Hartley watches as MARLO demonstrate's her ability to conquer tough terrain. Image credit: Evan Dougherty, Michigan EngineeringANN ARBOR--An unsupported bipedal robot at the University of Michigan can now walk down steep slopes, through a thin layer of snow, and over uneven and unstable ground. The robot's feedback control algorithms should be able to help other two-legged robots as well as powered prosthetic legs gain similar capabilities. "The robot has no feeling in her tiny feet, but she senses the angles of her joints--for instance, her knee angles, hip angles and the rotation angle of her torso," said Jessy Grizzle, professor of electrical engineering and computer science and of mechanical engineering.