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1. Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling

   Djeumou, Franck. ; Neary, Cyrus. ; Goubault, Eric. ; Putot, Sylvie. ; Topcu, Ufuk. ( January 2022 , 4th Annual Conference on Learning for Dynamics and Control)

   Firoozi, R. ; Mehr, N. ; Yel, E. ; Antonova, R. ; Bohg, J. ; Schwager, M. ; Kochenderfer, M. (Ed.)

   Effective inclusion of physics-based knowledge into deep neural network models of dynamical sys- tems can greatly improve data efficiency and generalization. Such a priori knowledge might arise from physical principles (e.g., conservation laws) or from the system’s design (e.g., the Jacobian matrix of a robot), even if large portions of the system dynamics remain unknown. We develop a framework to learn dynamics models from trajectory data while incorporating a priori system knowledge as inductive bias. More specifically, the proposed framework uses physics-based side information to inform the structure of the neural network itself, and to place constraints on the values of the outputs and the internal states of the model. It represents the system’s vector field as a composition of known and unknown functions, the latter of which are parametrized by neural networks. The physics-informed constraints are enforced via the augmented Lagrangian method during the model’s training. We experimentally demonstrate the benefits of the proposed approach on a variety of dynamical systems – including a benchmark suite of robotics environments featur- ing large state spaces, non-linear dynamics, external forces, contact forces, and control inputs. By exploiting a priori system knowledge during training, the proposed approach learns to predict the system dynamics two orders of magnitude more accurately than a baseline approach that does not include prior knowledge, given the same training dataset. 

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2. Limit Cycle Minimization by Time-Invariant Extremum Seeking Control

   https://doi.org/10.23919/ACC.2019.8815344  

   Kumar, Saurav ; Mohammadi, Alireza ; Gregg, Robert D. ; Gans, Nicholas ( July 2019 , Proceedings of the ... American Control Conference)

   Conventional perturbation-based extremum seeking control (ESC) employs a slow time-dependent periodic signal to find an optimum of an unknown plant. To ensure stability of the overall system, the ESC parameters are selected such that there is sufficient time-scale separation between the plant and the ESC dynamics. This approach is suitable when the plant operates at a fixed time-scale. In case the plant slows down during operation, the time-scale separation can be violated. As a result, the stability and performance of the overall system can no longer be guaranteed. In this paper, we propose an ESC for periodic systems, where the external time-dependent dither signal in conventional ESC is replaced with the periodic signals present in the plant, thereby making ESC time-invariant in nature. The advantage of using a state-based dither is that it inherently contains the information about the rate of the rhythmic task under control. Thus, in addition to maintaining time-scale separation at different plant speeds, the adaptation speed of a time-invariant ESC automatically changes, without changing the ESC parameters. We illustrate the effectiveness of the proposed time-invariant ESC with a Van der Pol oscillator example and present a stability analysis using averaging and singular perturbation theory. 

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3. Predicting 3-D Lower Back Joint Load in Lifting: A Deep Pose Estimation Approach

   https://doi.org/10.1109/THMS.2018.2884811  

   Mehrizi, Rahil ; Peng, Xi ; Metaxas, Dimitris N. ; Xu, Xu ; Zhang, Shaoting ; Li, Kang ( January 2019 , IEEE Transactions on Human-Machine Systems)

   Goal: Lifting is a common manual material handling task performed in the workplaces. It is considered as one of the main risk factors for work-related musculoskeletal disorders. An important criterion to identify the unsafe lifting task is the values of the net force and moment at L5/S1 joint. These values are mainly calculated in a laboratory environment, which utilizes marker-based sensors to collect three-dimensional (3-D) information and force plates to measure the external forces and moments. However, this method is usually expensive to set up, time-consuming in process, and sensitive to the surrounding environment. In this study, we propose a deep neural network (DNN)-based framework for 3-D pose estimation, which addresses the aforementioned limitations, and we employ the results for L5/S1 moment and force calculation. Methods: At the first step of the proposed framework, full body 3-D pose is captured using a DNN, then at the second step, estimated 3-D body pose along with the subject's anthropometric information is utilized to calculate L5/S1 join's kinetic by a top-down inverse dynamic algorithm. Results: To fully evaluate our approach, we conducted experiments using a lifting dataset consisting of 12 subjects performing various types of lifting tasks. The results are validated against a marker-based motion capture system as a reference. The grand mean ± SD of the total moment/force absolute errors across all the dataset was 9.06 ± 7.60 N·m/4.85 ± 4.85 N. Conclusion: The proposed method provides a reliable tool for assessment of the lower back kinetics during lifting and can be an alternative when the use of marker-based motion capture systems is not possible. 

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4. Mapping and coverage with a particle swarm controlled by uniform inputs

   https://doi.org/10.1109/IROS.2017.8202280  

   Mahadev, Arun ; Krupke, Dominik ; Fekete, Sandor P. ; Becker, Aaron T. ( September 2017 , Intelligent Robots and Systems (IROS), 2017 IEEE/RSJ International Conference on)

   We propose an approach to mapping tissue and vascular systems without the use of contrast agents, based on moving and measuring magnetic particles. To this end, we consider a swarm of particles in a 1D or 2D grid that can be tracked and controlled by an external agent. Control inputs are applied uniformly so that each particle experiences the same applied forces. We present algorithms for three tasks: (1) Mapping, i.e., building a representation of the free and obstacle regions of the workspace; (2) Subset Coverage, i.e., ensuring that at least one particle reaches each of a set of desired locations; and (3) Coverage, i.e., ensuring that every free region on the map is visited by at least one particle. These tasks relate to a large body of previous work from robot navigation, both from theory and practice, which is based on individual control. We provide theoretical insights that have potential relevance for fast MRI scans with magnetically controlled contrast media. In particular, we develop a fundamentally new approach for searching for an object at an unknown distance D, where the search is subject to two different and independent cost parameters for moving and for measuring. We show that regardless of the relative cost of these two operations, there is a simple O(log D/log log D)-competitive strategy, which is the best possible. Also, we provide practically useful and computationally efficient strategies for higher-dimensional settings. These algorithms extend to any number of particles and show that additional particles tend to reduce the mean and the standard deviation of the time required for each task. 

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5. Finger stability in precision grips

   https://doi.org/10.1073/pnas.2122903119  

   Sharma, Neelima ; Venkadesan, Madhusudhan ( March 2022 , Proceedings of the National Academy of Sciences)

   Stable precision grips using the fingertips are a cornerstone of human hand dexterity. However, our fingers become unstable sometimes and snap into a hyperextended posture. This is because multilink mechanisms like our fingers can buckle under tip forces. Suppressing this instability is crucial for hand dexterity, but how the neuromuscular system does so is unknown. Here we show that people rely on the stiffness from muscle contraction for finger stability. We measured buckling time constants of 50 ms or less during maximal force application with the index finger—quicker than feedback latencies—which suggests that muscle-induced stiffness may underlie stability. However, a biomechanical model of the finger predicts that muscle-induced stiffness cannot stabilize at maximal force unless we add springs to stiffen the joints or people reduce their force to enable cocontraction. We tested this prediction in 38 volunteers. Upon adding stiffness, maximal force increased by 34 ± 3%, and muscle electromyography readings were 21 ± 3% higher for the finger flexors (mean ± SE). Muscle recordings and mathematical modeling show that adding stiffness offloads the demand for muscle cocontraction, thus freeing up muscle capacity for fingertip force. Hence, people refrain from applying truly maximal force unless an external stabilizing stiffness allows their muscles to apply higher force without losing stability. But more stiffness is not always better. Stiff fingers would affect the ability to adapt passively to complex object geometries and precisely regulate force. Thus, our results show how hand function arises from neurally tuned muscle stiffness that balances finger stability with compliance. 

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