Katie Byl

Dominant sources of variability in passive walking

This paper investigates possible sources of variability in the dynamics of legged locomotion, even in its most idealized form. The rimless wheel model is a seemingly deterministic legged dynamic system, popular within the legged locomotion community for understanding basic collision dynamics and energetics during passive phases of walking. Despite the simplicity of this legged model, however, experimental motion capture data recording the passive step-to-step dynamics of a rimless wheel down a constant-slope terrain actually demonstrate significant variability, providing strong evidence that stochasticity is an intrinsic-and thus unavoidable-property of legged locomotion that should be modeled with care when designing reliable walking machines. We present numerical comparisons of several hypotheses as to the dominant source(s) of this variability: 1) the initial distribution of the angular velocity, 2) the uneven profile of the leg lengths and 3) the distribution of the coefficients of friction and restitution across collisions. Our analysis shows that the 3rd hypothesis most accurately predicts the noise characteristics observed in our experimental data while the 1st hypothesis is also valid for certain contexts of terrain friction. These findings suggest that variability due to ground contact dynamics, and not simply due to geometric variations more typically modeled in terrain, is important in determining the stochasticity and resulting stability of walking robots. Although such ground contact variability might be an expected result in field robotics on significantly rough terrain, we again note our experimental data applies seemingly deterministic-looking terrains: our results suggest that stochastic ground collision models should play an important role in the analysis and optimization of dynamic performance and stability in robot walking.

Metastable Walking Machines

Legged robots that operate in the real world are inherently subject to stochasticity in their dynamics and uncertainty about the terrain. Owing to limited energy budgets and limited control authority, these “disturbances” cannot always be canceled out with high-gain feedback. Minimally actuated walking machines subject to stochastic disturbances no longer satisfy strict conditions for limit-cycle stability; however, they can still demonstrate impressively long-living periods of continuous walking. Here, we employ tools from stochastic processes to examine the “stochastic stability” of idealized rimless-wheel and compass-gait walking on randomly generated uneven terrain. Furthermore, we employ tools from numerical stochastic optimal control to design a controller for an actuated compass gait model which maximizes a measure of stochastic stability—the mean first-passage time—and compare its performance with a deterministic counterpart. Our results demonstrate that walking is well characterized as a metastable process, and that the stochastic dynamics of walking should be accounted for during control design in order to improve the stability of our machines.

Approximate optimal control of the compass gait on rough terrain

In this paper, we explore the capabilities of actuated models of the compass gait walker on rough terrain. We solve for the optimal high-level feedback policy to negotiate a perfectly known but qualitatively complex terrain, using a fixed low-level controller which selects a high-level action once- per-step. We also demonstrate that a one-step time horizon control strategy using the same low-level controller can provide performance which is surprisingly comparable to that of the infinite time horizon optimal policy. The model presented here uses a torque at the hip and an axially-directed impulsive toe-off applied just before each ground collision. Our results provide compelling evidence that actuated robots based on passive dynamic principles (e.g. no ankle torque) should inherently be capable of walking on significantly rough terrain.

Reliable Dynamic Motions for a Stiff Quadruped

We present a kinodynamic planning methodology for a high-impedance quadruped robot to negotiate a wide variety of terrain types with high reliability. We achieve motion types ranging from dynamic, double-support lunges for efficient locomotion over extreme obstacles to careful, deliberate foothold and body pose selections which allow for precise foothold placement on rough or intermittent terrain.

Mobile Manipulation and Mobility as Manipulation-Design and Algorithms of RoboSimian

This article presents the hardware design and software algorithms of RoboSimian, a statically stable quadrupedal robot capable of both dexterous manipulation and versatile mobility in difficult terrain. The robot has generalized limbs and hands capable of mobility and manipulation, along with almost fully hemispherical three-dimensional sensing with passive stereo cameras. The system is semiautonomous, enabling low-bandwidth, high latency control operated from a standard laptop. Because limbs are used for mobility and manipulation, a single unified mobile manipulation planner is used to generate autonomous behaviors, including walking, sitting, climbing, grasping, and manipulating. The remote operator interface is optimized to designate, parametrize, sequence, and preview behaviors, which are then executed by the robot. RoboSimian placed fifth in the DARPA Robotics Challenge Trials, demonstrating its ability to perform disaster recovery tasks in degraded human environments.

Feature-based terrain classification for LittleDog

Recent work in terrain classification has relied largely on 3D sensing methods and color based classification. We present an approach that works with a single, compact camera and maintains high classification rates that are robust to changes in illumination. Terrain is classified using a bag of visual words (BOVW) created from speeded up robust features (SURF) with a support vector machine (SVM) classifier. We present several novel techniques to augment this approach. A gradient descent inspired algorithm is used to adjust the SURF Hessian threshold to reach a nominal feature density. A sliding window technique is also used to classify mixed terrain images with high resolution. We demonstrate that our approach is suitable for small legged robots by performing real-time terrain classification on LittleDog. The classifier is used to select between predetermined gaits to traverse terrain of varying difficulty. Results indicate that real-time classification in-the-loop is faster than using a single all-terrain gait.

Robust Policies via Meshing for Metastable Rough Terrain Walking

In this paper, we present and verify methods for developing robust, high-level policies for metastable (i.e., rarely falling) rough-terrain robot walking. We focus on simultaneously addressing the important, real-world challenges of (1) use of a tractable mesh, to avoid the curse of dimensionality and (2) maintaining near-optimal performance that is robust to uncertainties. Toward our first goal, we present an improved meshing technique, which captures the step-to-step dynamics of robot walking as a discrete-time Markov chain with a small number of points. We keep our methods and analysis generic, and illustrate robustness by quantifying the stability of resulting control policies derived through our methods. To demonstrate our approach, we focus on the challenge of optimally switching among a finite set of low-level controllers for underactuated, rough-terrain walking. Via appropriate meshing techniques, we see that even terrain-blind switching between multiple controllers increases the stability of the robot, while lookahead (terrain information) makes this improvement dramatic. We deal with both noise on the lookahead information and on the state of the robot. These two robustness requirements are essential for our methods to be applicable to real high-DOF robots, which is the primary motivation of the authors.

Metastable Walking on Stochastically Rough Terrain

Simplified models of limit-cycle walking on flat terrain have provided important insights into the nature of legged locomotion. Real walking robots (and humans), however, do not exhibit true limit cycle dynamics because terrain, even in a carefully designed laboratory setting, is inevitably non-flat. Walking systems on stochastically rough terrain may not satisfy strict conditions for limit-cycle stability but can still demonstrate impressively long-living periods of continuous walking. Here, we examine the dynamics of rimless-wheel and compass-gait walking on randomly generated rough terrain and employ tools from stochastic processes to describe the ‘stochastic stability’ of these gaits. This analysis generalizes our understanding of walking stability and may provide statistical tools for experimental limit cycle analysis on real walking systems.

Switching policies for metastable walking

In this paper, we study an underactuated five-link biped walking on stochastically rough terrain. We propose a simple and powerful Sliding Mode Control scheme. By taking Poincaré sections just before the impact, we accurately represent ten dimensional system dynamics of metastable walking as a Markov process. By switching between two qualitatively different controllers, we show that the number of steps before failure can be increased by more than 10 million times compared to using either one of the controllers only. To achieve this, only the current state and approximate terrain slope for a one step lookahead on geometrically rough terrain is needed. The analysis techniques in this paper are also designed for future application to a range of other simulated or experimental walkers.

Nonlinear model predictive control for rough-terrain robot hopping

This paper examines and quantifies the theoretical efficacy of a limited look-ahead strategy for hopping robots on rough terrain. Here, a classic spring-loaded inverted pendulum (SLIP) hopper and an actuated, lossy SLIP (ALSLIP) hopper with a more realistic dynamic model that includes an unsprung mass and a series-elastic actuator are each analyzed under conditions where the desired footholds are predetermined according to a stochastic process. We examine the effect of the length of the horizon on the accuracy of foot placement, and we test the robustness of the approach to model uncertainties. Our simulation results show that a model predictive control (MPC) approach is an effective technique for foothold selection, and that a two-step planning horizon for upcoming terrain is theoretically adequate for practical footstep planning in realistically noisy rough terrain running conditions.