Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot

This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3D (spatial) bipedal robot consisting of a torso, two legs, and passive (unactuated) point feet. The contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and 6 actuators. The interest of studying robots with point feet is that the robot's natural dynamics must be explicitly taken into account to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit. This method allows the computations to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincar\'e map of the hybrid zero dynamics. Three strategies are explored. The first strategy consists of imposing a stability condition during the search of a periodic gait by optimization. The second strategy uses an event-based controller. In the third approach, the effect of output selection is discussed and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller

Trajectory Optimization and Machine Learning to Design Feedback Controllers for Bipedal Robots with Provable Stability

This thesis combines recent advances in trajectory optimization of hybrid dynamical systems with machine learning and geometric control theory to achieve unprecedented performance in bipedal robot locomotion. The work greatly expands the class of robot models for which feedback controllers can be designed with provable stability. The methods are widely applicable beyond bipedal robots, including exoskeletons, and prostheses, and eventually, drones, ADAS, and other highly automated machines. One main idea of this thesis is to greatly expand the use of multiple trajectories in the design of a stabilizing controller. The computation of many trajectories is now feasible due to new optimization tools. The computations are not fast enough to apply in the real-time, however, so they are not feasible for model predictive control (MPC). The offline “library” approach will encounter the curse of dimensionality for the high-dimensional models common in bipedal robots. To overcome these obstructions, we embed a stable walking motion in an attractive low-dimensional surface of the system's state space. The periodic orbit is now an attractor of the low-dimensional state-variable model but is not attractive in the full-order system. We then use the special structure of mechanical models associated with bipedal robots to embed the low-dimensional model in the original model in such a manner that the desired walking motions are locally exponentially stable. The ultimate solution in this thesis will generate model-based feedback controllers for bipedal robots, in such a way that the closed-loop system has a large stability basin, exhibits highly agile, dynamic behavior, and can deal with significant perturbations coming from the environment. In the case of bipeds: “model-based” means that the controller will be designed on the basis of the full floating-base dynamic model of the robot, and not a simplified model, such as the LIP (Linear Inverted Pendulum). By “agile and dynamic” is meant that the robot moves at the speed of a normal human or faster while walking off a curb. By “significant perturbation” is meant a human tripping, and while falling, throwing his/her full weight into the back of the robot.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145992/1/xda_1.pd

Fast biped walking with a neuronal controller and physical computation

Biped walking remains a difficult problem and robot models can greatly {facilitate} our understanding of the underlying biomechanical principles as well as their neuronal control. The goal of this study is to specifically demonstrate that stable biped walking can be achieved by combining the physical properties of the walking robot with a small, reflex-based neuronal network, which is governed mainly by local sensor signals. This study shows that human-like gaits emerge without {specific} position or trajectory control and that the walker is able to compensate small disturbances through its own dynamical properties. The reflexive controller used here has the following characteristics, which are different from earlier approaches: (1) Control is mainly local. Hence, it uses only two signals (AEA=Anterior Extreme Angle and GC=Ground Contact) which operate at the inter-joint level. All other signals operate only at single joints. (2) Neither position control nor trajectory tracking control is used. Instead, the approximate nature of the local reflexes on each joint allows the robot mechanics itself (e.g., its passive dynamics) to contribute substantially to the overall gait trajectory computation. (3) The motor control scheme used in the local reflexes of our robot is more straightforward and has more biological plausibility than that of other robots, because the outputs of the motorneurons in our reflexive controller are directly driving the motors of the joints, rather than working as references for position or velocity control. As a consequence, the neural controller and the robot mechanics are closely coupled as a neuro-mechanical system and this study emphasises that dynamically stable biped walking gaits emerge from the coupling between neural computation and physical computation. This is demonstrated by different walking experiments using two real robot as well as by a Poincar\'{e} map analysis applied on a model of the robot in order to assess its stability. In addition, this neuronal control structure allows the use of a policy gradient reinforcement learning algorithm to tune the parameters of the neurons in real-time, during walking. This way the robot can reach a record-breaking walking speed of 3.5 leg-lengths per second after only a few minutes of online learning, which is even comparable to the fastest relative speed of human walking