Online Discrimination of Nonlinear Dynamics with Switching Differential Equations

How to recognise whether an observed person walks or runs? We consider a dynamic environment where observations (e.g. the posture of a person) are caused by different dynamic processes (walking or running) which are active one at a time and which may transition from one to another at any time. For this setup, switching dynamic models have been suggested previously, mostly, for linear and nonlinear dynamics in discrete time. Motivated by basic principles of computations in the brain (dynamic, internal models) we suggest a model for switching nonlinear differential equations. The switching process in the model is implemented by a Hopfield network and we use parametric dynamic movement primitives to represent arbitrary rhythmic motions. The model generates observed dynamics by linearly interpolating the primitives weighted by the switching variables and it is constructed such that standard filtering algorithms can be applied. In two experiments with synthetic planar motion and a human motion capture data set we show that inference with the unscented Kalman filter can successfully discriminate several dynamic processes online

Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.National Science Foundation (IIS 0308213, IIS 0329009, CNS 0202067

Substructure and Boundary Modeling for Continuous Action Recognition

This paper introduces a probabilistic graphical model for continuous action recognition with two novel components: substructure transition model and discriminative boundary model. The first component encodes the sparse and global temporal transition prior between action primitives in state-space model to handle the large spatial-temporal variations within an action class. The second component enforces the action duration constraint in a discriminative way to locate the transition boundaries between actions more accurately. The two components are integrated into a unified graphical structure to enable effective training and inference. Our comprehensive experimental results on both public and in-house datasets show that, with the capability to incorporate additional information that had not been explicitly or efficiently modeled by previous methods, our proposed algorithm achieved significantly improved performance for continuous action recognition.Comment: Detailed version of the CVPR 2012 paper. 15 pages, 6 figure

Recovering from External Disturbances in Online Manipulation through State-Dependent Revertive Recovery Policies

Robots are increasingly entering uncertain and unstructured environments. Within these, robots are bound to face unexpected external disturbances like accidental human or tool collisions. Robots must develop the capacity to respond to unexpected events. That is not only identifying the sudden anomaly, but also deciding how to handle it. In this work, we contribute a recovery policy that allows a robot to recovery from various anomalous scenarios across different tasks and conditions in a consistent and robust fashion. The system organizes tasks as a sequence of nodes composed of internal modules such as motion generation and introspection. When an introspection module flags an anomaly, the recovery strategy is triggered and reverts the task execution by selecting a target node as a function of a state dependency chart. The new skill allows the robot to overcome the effects of the external disturbance and conclude the task. Our system recovers from accidental human and tool collisions in a number of tasks. Of particular importance is the fact that we test the robustness of the recovery system by triggering anomalies at each node in the task graph showing robust recovery everywhere in the task. We also trigger multiple and repeated anomalies at each of the nodes of the task showing that the recovery system can consistently recover anywhere in the presence of strong and pervasive anomalous conditions. Robust recovery systems will be key enablers for long-term autonomy in robot systems. Supplemental info including code, data, graphs, and result analysis can be found at [1].Comment: 8 pages, 8 figures, 1 tabl