23 research outputs found
Controller Synthesis for Discrete-Time Polynomial Systems via Occupation Measures
In this paper, we design nonlinear state feedback controllers for
discrete-time polynomial dynamical systems via the occupation measure approach.
We propose the discrete-time controlled Liouville equation, and use it to
formulate the controller synthesis problem as an infinite-dimensional linear
programming problem on measures, which is then relaxed as finite-dimensional
semidefinite programming problems on moments of measures and their duals on
sums-of-squares polynomials. Nonlinear controllers can be extracted from the
solutions to the relaxed problems. The advantage of the occupation measure
approach is that we solve convex problems instead of generally non-convex
problems, and the computational complexity is polynomial in the state and input
dimensions, and hence the approach is more scalable. In addition, we show that
the approach can be applied to over-approximating the backward reachable set of
discrete-time autonomous polynomial systems and the controllable set of
discrete-time polynomial systems under known state feedback control laws. We
illustrate our approach on several dynamical systems
Optimal Reduced-order Modeling of Bipedal Locomotion
State-of-the-art approaches to legged locomotion are widely dependent on the
use of models like the linear inverted pendulum (LIP) and the spring-loaded
inverted pendulum (SLIP), popular because their simplicity enables a wide array
of tools for planning, control, and analysis. However, they inevitably limit
the ability to execute complex tasks or agile maneuvers. In this work, we aim
to automatically synthesize models that remain low-dimensional but retain the
capabilities of the high-dimensional system. For example, if one were to
restore a small degree of complexity to LIP, SLIP, or a similar model, our
approach discovers the form of that additional complexity which optimizes
performance. In this paper, we define a class of reduced-order models and
provide an algorithm for optimization within this class. To demonstrate our
method, we optimize models for walking at a range of speeds and ground
inclines, for both a five-link model and the Cassie bipedal robot.Comment: Submitted to ICRA 202
Impact-Aware Multi-Contact Balance Criteria
Intentionally applying impacts while maintaining balance is challenging for
legged robots. This study originated from observing experimental data of the
humanoid robot HRP-4 intentionally hitting a wall with its right arm while
standing on two feet. Strangely, violating the usual zero moment point balance
criteria did not systematically result in a fall. To investigate this
phenomenon, we propose the zero-step capture region for non-coplanar contacts,
defined as the center of mass (CoM) velocity area, and validated it with
push-recovery experiments employing the HRP-4 balancing on two non-coplanar
contacts. To further enable on-purpose impacts, we compute the set of candidate
post-impact CoM velocities accounting for frictional-impact dynamics in three
dimensions, and restrict the entire set within the CoM velocity area to
maintain balance with the sustained contacts during and after impacts. We
illustrate the maximum contact velocity for various HRP-4 stances in
simulation, indicating potential for integration into other task-space
whole-body controllers or planners. This study is the first to address the
challenging problem of applying an intentional impact with a
kinematic-controlled humanoid robot on non-coplanar contacts