4,845 research outputs found
Orbit Characterization, Stabilization and Composition on 3D Underactuated Bipedal Walking via Hybrid Passive Linear Inverted Pendulum Model
A Hybrid passive Linear Inverted Pendulum (H-LIP) model is proposed for characterizing, stabilizing and composing periodic orbits for 3D underactuated bipedal walking. Specifically, Period-l (P1) and Period -2 (P2) orbits are geometrically characterized in the state space of the H-LIP. Stepping controllers are designed for global stabilization of the orbits. Valid ranges of the gains and their optimality are derived. The optimal stepping controller is used to create and stabilize the walking of bipedal robots. An actuated Spring-loaded Inverted Pendulum (aSLIP) model and the underactuated robot Cassie are used for illustration. Both the aSLIP walking with PI or P2 orbits and the Cassie walking with all 3D compositions of the PI and P2 orbits can be smoothly generated and stabilized from a stepping-in-place motion. This approach provides a perspective and a methodology towards continuous gait generation and stabilization for 3D underactuated walking robots
Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds
In this work we present a trajectory Optimization framework for whole-body
motion planning through contacts. We demonstrate how the proposed approach can
be applied to automatically discover different gaits and dynamic motions on a
quadruped robot. In contrast to most previous methods, we do not pre-specify
contact switches, timings, points or gait patterns, but they are a direct
outcome of the optimization. Furthermore, we optimize over the entire dynamics
of the robot, which enables the optimizer to fully leverage the capabilities of
the robot. To illustrate the spectrum of achievable motions, here we show eight
different tasks, which would require very different control structures when
solved with state-of-the-art methods. Using our trajectory Optimization
approach, we are solving each task with a simple, high level cost function and
without any changes in the control structure. Furthermore, we fully integrated
our approach with the robot's control and estimation framework such that
optimization can be run online. By demonstrating a rough manipulation task with
multiple dynamic contact switches, we exemplarily show how optimized
trajectories and control inputs can be directly applied to hardware.Comment: Video: https://youtu.be/sILuqJBsyK
Frequency-Aware Model Predictive Control
Transferring solutions found by trajectory optimization to robotic hardware
remains a challenging task. When the optimization fully exploits the provided
model to perform dynamic tasks, the presence of unmodeled dynamics renders the
motion infeasible on the real system. Model errors can be a result of model
simplifications, but also naturally arise when deploying the robot in
unstructured and nondeterministic environments. Predominantly, compliant
contacts and actuator dynamics lead to bandwidth limitations. While classical
control methods provide tools to synthesize controllers that are robust to a
class of model errors, such a notion is missing in modern trajectory
optimization, which is solved in the time domain. We propose frequency-shaped
cost functions to achieve robust solutions in the context of optimal control
for legged robots. Through simulation and hardware experiments we show that
motion plans can be made compatible with bandwidth limits set by actuators and
contact dynamics. The smoothness of the model predictive solutions can be
continuously tuned without compromising the feasibility of the problem.
Experiments with the quadrupedal robot ANYmal, which is driven by
highly-compliant series elastic actuators, showed significantly improved
tracking performance of the planned motion, torque, and force trajectories and
enabled the machine to walk robustly on terrain with unmodeled compliance
GPU Based Path Integral Control with Learned Dynamics
We present an algorithm which combines recent advances in model based path
integral control with machine learning approaches to learning forward dynamics
models. We take advantage of the parallel computing power of a GPU to quickly
take a massive number of samples from a learned probabilistic dynamics model,
which we use to approximate the path integral form of the optimal control. The
resulting algorithm runs in a receding-horizon fashion in realtime, and is
subject to no restrictive assumptions about costs, constraints, or dynamics. A
simple change to the path integral control formulation allows the algorithm to
take model uncertainty into account during planning, and we demonstrate its
performance on a quadrotor navigation task. In addition to this novel
adaptation of path integral control, this is the first time that a
receding-horizon implementation of iterative path integral control has been run
on a real system.Comment: 6 pages, NIPS 2014 - Autonomously Learning Robots Worksho
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