Approximate optimal control of the compass gait on rough terrain

Robotics: Science and Systems IV

2008

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Abstract-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.

Section: A Rimless Wheelmentioning

confidence: 99%

“…Note that the dynamic evolution of angular velocity over time does not depend on the choice of a particular magnitude of the point mass, and we will use spokes of unit length, l = 1 meter, throughout. 2 To avoid simulating pathological cases, the distribution is always truncated to remain within ±10 • , or roughly 6σ, of the mean.…”

Section: A Rimless Wheelmentioning

confidence: 99%

Metastable Walking on Stochastically Rough Terrain

Byl

Robotics: Science and Systems IV

2008

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“…In some cases, the combinatorial problem of solving for a mode schedule have been addressed by combinatorial planners; a variant of the Rapidly-Exploring Random Tree (RRT) algorithm was used in [15] to produce bounding trajectories for a quadruped over terrain. Methods for optimal control which approximate the global optimal, such as brute force methods based on dynamic programming, have also been applied [3], but are so far limited to low dimensional problems.…”

Section: The Pitfalls Of Mode Schedulesmentioning

confidence: 99%

Direct Trajectory Optimization of Rigid Body Dynamical Systems through Contact

Posa

Springer Tracts in Advanced Robotics

2013

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Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Most state-of-the-art techniques treat the discontinuous dynamics of contact as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning through contact that eliminates the requirement for an a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem (LCP) for forward simulation, the proposed algorithm leverages Sequential Quadratic Programming (SQP) to naturally resolve contact constraint forces while simultaneously optimizing a trajectory and satisfying nonlinear complementarity constraints. The method scales well to high dimensional systems with large numbers of possible modes. We demonstrate the approach using three increasingly complex systems: rotating a pinned object with a finger, planar walking with the Spring Flamingo robot, and high speed bipedal running on the FastRunner platform.

“…A wide variety of legged robots capable of overcoming rough terrain have been built to examine diverse locomotion strategies. Usually, the control strategy for these robots have been tailored to the specific robot model [20], [18], [2], [6]. This work presents a new control strategy which applicable to a more general robot model, with simulation validation on two canonical robot models.…”

Section: Introductionmentioning

confidence: 99%

Optimizing robust limit cycles for legged locomotion on unknown terrain

Dai

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

2012

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Abstract-While legged animals are adept at traversing rough landscapes, it remains a very challenging task for a legged robot to negotiate unknown terrain. Control systems for legged robots are plagued by dynamic constraints from underactuation, actuator power limits, and frictional ground contact; rather than relying purely on disturbance rejection, considerable advantage can be obtained by planning nominal trajectories which are more easily stabilized. In this paper, we present an approach for designing nominal periodic trajectories for legged robots that maximize a measure of robustness against uncertainty in the geometry of the terrain. We propose a direct collocation method which solves simultaneously for a nominal periodic control input, for many possible one-step solution trajectories (using ground profiles drawn from a distribution over terrain), and for the periodic solution to a jump Riccati equation which provides an expected infinite-horizon cost-to-go for each of these samples. We demonstrate that this trajectory optimization scheme can recover the known deadbeat openloop control solution for the Spring Loaded Inverted Pendulum (SLIP) on unknown terrain. Moreover, we demonstrate that it generalizes to other models like the bipedal compass gait walker, resulting in a dramatic increase in the number of steps taken over moderate terrain when compared against a limit cycle optimized for efficiency only.