Balance recoverability and control of bipedal robotic walkers with foot slip
Creators: name: Mihalec, Marko
Publisher: name: No Publisher Supplied
Year: 2022

description: Low-friction surfaces present a particular challenge in the field of bipedal walking as they can lead to foot slippage. Human foot slip often leads to falls, which is a major cause of injuries and results in a high societal and economic burden, especially for the elderly population. Since slip cannot always be avoided, it is valuable to understand the dynamics of walking under slip conditions, the likelihood of falling, and the effects of foot-slip on biped walking stability. Furthermore, recovery control strategies can potentially stabilize slipping gait and prevent fall. Such developments would therefore benefit both the robotic and clinical biomechanics walking communities. This dissertation addresses the questions of whether a walker experiencing a foot-slip is in danger of falling or whether it can successfully recover balance and prevent a fall. We present dynamics models which describe the motion of slipping gait and the frameworks to evaluate the stability of gaits with foot-slip. We further present the algorithms which can decide on the appropriate control input to increase stability on multiple levels of control design. The feasibility of the theoretical results is demonstrated both in simulation and by deploying an experimental robotic walker, as well as by comparison with human subject trials.The first part of this dissertation focuses on modeling of walking under foot-slip conditions. Reduced-order models, such as linear inverted pendulum models, are used to represent the key dynamic behavior of a walker without constraining a particular structure. While models exist for normal walking, they need to be adapted to relax the ubiquitous assumption of the stationary, non-slip contact point between the walker's foot and the ground. We introduce two novel models which are based on inverted pendulum but incorporate an angular moment of inertia as well as allow movement in the vertical direction. With those modifications, the new models have the ability to accurately capture slipping dynamics. Building upon those models, the stability of slipping gaits is assessed using the concept of capturability. We demonstrate how varying the variables such as step duration and ground friction changes the capture regions and influences reliable foot positioning.Next, a variation of a linear inverted pendulum model is presented which allows for explicit modeling of foot-slip conditions while also retaining the linearity and dimensionality of its dynamics. We analytically solve the dynamics motion equations and present solutions in the form of time-invariant manifolds for both normal walking and foot-slip conditions. By utilizing the solution manifolds, predictions of walker's motion no longer rely on solving differential equations but rather on simplified algebraic equations which define the geometry of hyperbolic solution manifolds. Based on the geometry of solution manifolds, we introduce the concept of slip recoverability. Recoverability partitions the phase portrait space into three distinct regions such that every state can be classified as safe, recoverable with adequate input, and non-recoverable. Based on the results of the recoverability analysis, we introduce a novel optimal control framework that ensures robustness when slip is imminent, and reduces the within-step control effort when fall is not likely. In addition to the within-step control, the proposed controller also prescribes step location for single- or multi-step recovery. The performance of the controller is verified via extensive simulation. To further verify the proposed abstract model, we analyze human walking data including subjects' responses to unexpected slips. An example of successful and unsuccessful slip recovery is used to compare the pose evolution to the prediction of the proposed model.In order to realize the high-level recovery strategy, a whole-body controller is needed to calculate joint torques. To that extent, the second half of this dissertation deals with whole-body operational space (WBOS) based torque controller. We extend the WBOS-based controller to the case of foot slip. The new frictional WBOS (FWBOS) is formulated such that the dynamics remains consistent with both forward and backward slip of the standing foot. We formulate a task to maintain balance and demonstrate the performance of the FWBOS algorithm through extensive simulation. The whole-body controller is then integrated with the reduced-order model proposed in the previous chapters. The current state of the reduced model is calculated from the full model and yields the solution manifolds. Based on the solution manifolds, the controller predicts the appropriate stepping location to maintain the walker's forward progression. The FWBOS algorithm is then used to plan and design the foot placement. In this way, both step planning and joint torque calculation explicitly consider foot slip. Simulation is carried out to demonstrate the improvement of considering slip at both levels of the integrated controller. Finally, the performance of the proposed control algorithms is demonstrated experimentally using a planar 5-link robot with pointy feet. We present the setup, modeling, system identification, friction compensation, and other aspects of a mechanical system. Walking gaits are demonstrated both for normal walking, as well as on slippery surfaces where foot-slip is present. We implement the FWBOS-based controller and experimentally demonstrate the successful robot walking on a slippery surface.