Inverse Dynamics vs. Forward Dynamics in Direct Transcription Formulations for Trajectory Optimization

Benchmarks of state-of-the-art rigid-body dynamics libraries report better performance solving the inverse dynamics problem than the forward alternative. Those benchmarks encouraged us to question whether that computational advantage would translate to direct transcription, where calculating rigid-body dynamics and their derivatives accounts for a significant share of computation time. In this work, we implement an optimization framework where both approaches for enforcing the system dynamics are available. We evaluate the performance of each approach for systems of varying complexity, for domains with rigid contacts. Our tests reveal that formulations using inverse dynamics converge faster, require less iterations, and are more robust to coarse problem discretization. These results indicate that inverse dynamics should be preferred to enforce the nonlinear system dynamics in simultaneous methods, such as direct transcription.Comment: Accepted to the 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi'an, China. Supplementary video available in https://youtu.be/pV4s7hzUgjc. Related code in https://github.com/JuliaRobotics/TORA.j

Bipedal Hopping: Reduced-order Model Embedding via Optimization-based Control

This paper presents the design and validation of controlling hopping on the 3D bipedal robot Cassie. A spring-mass model is identified from the kinematics and compliance of the robot. The spring stiffness and damping are encapsulated by the leg length, thus actuating the leg length can create and control hopping behaviors. Trajectory optimization via direct collocation is performed on the spring-mass model to plan jumping and landing motions. The leg length trajectories are utilized as desired outputs to synthesize a control Lyapunov function based quadratic program (CLF-QP). Centroidal angular momentum, taking as an addition output in the CLF-QP, is also stabilized in the jumping phase to prevent whole body rotation in the underactuated flight phase. The solution to the CLF-QP is a nonlinear feedback control law that achieves dynamic jumping behaviors on bipedal robots with compliance. The framework presented in this paper is verified experimentally on the bipedal robot Cassie.Comment: 8 pages, 7 figures, accepted by IROS 201

Lamplighter model of a random copolymer adsorption on a line

We present a model of an AB-diblock random copolymer sequential self-packaging with local quenched interactions on a one-dimensional infinite sticky substrate. It is assumed that the A-A and B-B contacts are favorable, while A-B are not. The position of a newly added monomer is selected in view of the local contact energy minimization. The model demonstrates a self-organization behavior with the nontrivial dependence of the total energy, $E$ (the number of unfavorable contacts), on the number of chain monomers, $N$: $E\sim N^{3/4}$ for quenched random equally probable distribution of A- and B-monomers along the chain. The model is treated by mapping it onto the "lamplighter" random walk and the diffusion-controlled chemical reaction of $X+X\to 0$ type with the subdiffusive motion of reagents.Comment: 8 pages, 5 figure

High-resolution NMR studies of structure and dynamics of human ERp27 indicate extensive interdomain flexibility

ERp27 (endoplasmic reticulum protein 27.7 kDa) is a homologue of PDI (protein disulfide-isomerase) localized to the endoplasmic reticulum. ERp27 is predicted to consist of two thioredoxinfold domains homologous with the non-catalytic b and b domains of PDI. The structure in solution of the N-terminal blike domain of ERp27 was solved using high-resolution NMR data. The structure confirms that it has the thioredoxin fold and that ERp27 is a member of the PDI family. 15N-NMR relaxation data were obtained and ModelFree analysis highlighted limited exchange contributions and slow internal motions, and indicated that the domain has an average order parameter S 2 of 0.79. Comparison of the single-domain structure determined in the present study with the equivalent domain within fulllength ERp27, determined independently by X-ray diffraction, indicated very close agreement. The domain interface inferred from NMR data in solution was much more extensive than that observed in the X-ray structure, suggesting that the domains flex independently and that crystallization selects one specific interdomain orientation. This led us to apply a new rapid method to simulate the flexibility of the full-length protein, establishing that the domains show considerable freedom to flex (tilt and twist) about the interdomain linker, consistent with the NMR data