An official website of the United States government
The popular approach of assuming a control policy and then finding the largest region of attraction (ROA) (e.g., sum-of-squares optimization) may lead to conservative estimates of the ROA, especially for highly nonlinear systems. We present a sampling-based approach that starts by assuming a ROA and then fi nds the necessary control policy by performing trajectory optimization on sampled initial conditions. Our method works with black-box models, produces a relatively large ROA, and ensures exponential convergence of the initial conditions to the periodic motion. We demonstrate the approach on a model of hopping and include extensive verification and robustness checks.
more »
« less
Feedback motion planning of legged robots by composing orbital Lyapunov functions using rapidly-exploring random trees
We present a sampling-based framework for feed- back motion planning of legged robots. Our framework is based on switching between limit cycles at a fixed instance of motion, the Poincare ́section(e.g.,apex or touchdown),by finding overlaps between the regions of attraction (ROA) of two limit cycles. First, we assume a candidate orbital Lyapunov function (OLF) and define a ROA at the Poincare ́ section. Next, we solve multiple trajectory optimization problems, one for each sampled initial condition on the ROA to minimize an energy metric and subject to the exponential convergence of the OLF between two steps. The result is a table of control actions and the corresponding initial conditions at the Poincare ́ section. Then we develop a control policy for each control action as a function of the initial condition using deep learning neural networks. The control policy is validated by testing on initial conditions sampled on ROA of randomly chosen limit cycles. Finally, the rapidly-exploring random tree algorithm is adopted to plan transitions between the limit cycles using the ROAs. The approach is demonstrated on a hopper model to achieve velocity and height transitions between steps.
more »
« less
- Award ID(s):
- 1816925
- PAR ID:
- 10104234
- Date Published:
- Journal Name:
- IEEE Conference on Robotics and Automation
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Vibrational Raman optical activity (ROA) spectra were calculated under off‐resonance, near‐resonance, and at‐resonance conditions for(A) and under off‐resonance conditions for(B) using a new driver software for calculating the ROA intensities from complex (damped) time‐dependent linear response Kohn‐Sham theory. The off‐resonance spectra ofAandBshow many similarities. At an incident laser wavelength of 532 nm, used in commercial ROA spectrometers, the spectrum ofAis enhanced by near‐resonance with the ligand‐field transitions of the complex. The near‐resonance spectrum exhibits many qualitative differences compared with the off‐resonance case, but it remains bi‐signate. Even under full resonance with the ligand‐field electronic transitions, the ROA spectrum ofAremains bi‐signate when the electronic transitions are broadened such as to yield absorption line widths that are comparable with those in the experimental UV‐vis absorption and electronic circular dichroism spectra.more » « less
-
Haptic actuators employing speed reductions display desirable increased force capability but have difficulty producing feelings of free space motion due to friction and inertia magnification implicit to actuator dynamics. This work describes a control topology that enables geared haptic actuators to produce highly transparent free space motion when combined with backlash nonlinearities. While the presence of backlash enables the proposed free space motion control, it is also a source of instability, limit cycles, and to some extent rendering distortion. We introduce a smoothed gain scheduling function to mitigate limit cycling and expand the range of stable impedances that can be rendered. The introduction of a design metric called the free space envelope provides a framework to evaluate the effectiveness of the free space controller. Together these two control approaches enable transparent free space, high-force, and stable haptic interactions in systems with backlash, a characteristic common in many speed reducers.more » « less
-
Applying reinforcement learning (RL) to sparse reward domains is notoriously challenging due to insufficient guiding signals. Common RL techniques for addressing such domains include (1) learning from demonstrations and (2) curriculum learning. While these two approaches have been studied in detail, they have rarely been considered together. This paper aims to do so by introducing a principled task-phasing approach that uses demonstrations to automatically generate a curriculum sequence. Using inverse RL from (suboptimal) demonstrations we define a simple initial task. Our task phasing approach then provides a framework to gradually increase the complexity of the task all the way to the target task, while retuning the RL agent in each phasing iteration. Two approaches for phasing are considered: (1) gradually increasing the proportion of time steps an RL agent is in control, and (2) phasing out a guiding informative reward function. We present conditions that guarantee the convergence of these approaches to an optimal policy. Experimental results on 3 sparse reward domains demonstrate that our task-phasing approaches outperform state-of-the-art approaches with respect to asymptotic performance.more » « less
-
We present Einstein coefficient spectra and a detailed-balance derivation of generalized Einstein relations between them that is based on the connection between spontaneous and stimulated emission. If two broadened levels or bands overlap in energy, transitions between them need not be purely absorptive or emissive. Consequently, spontaneous emission can occur in both transition directions, and four Einstein coefficient spectra replace the three Einstein coefficients for a line. At equilibrium, the four different spectra obey five pairwise relationships and one lineshape generates all four. These relationships are independent of molecular quantum statistics and predict the Stokes’ shift between forward and reverse transitions required by equilibrium with blackbody radiation. For Boltzmann statistics, the relative strengths of forward and reverse transitions depend on the formal chemical potential difference between the initial and final bands, which becomes the standard chemical potential difference for ideal solutes. The formal chemical potential of a band replaces both the energy and degeneracy of a quantum level. Like the energies of quantum levels, the formal chemical potentials of bands obey the Rydberg-Ritz combination principle. Each stimulated Einstein coefficient spectrum gives a frequency-dependent transition cross-section. Transition cross-sections obey causality and a detailed-balance condition with spontaneous emission, but do not directly obey generalized Einstein relations. Even with an energetic width much less than the photon energy, a predominantly absorptive forward transition with an energetic width much greater than the thermal energy can have such an extreme Stokes’ shift that its reverse transition cross-section becomes predominantly absorptive rather than emissive.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
