Jarvis A. Schultz

Meso-scale and multicontinuum modeling of a triaxial braided textile composite

Accurately predicting failure in woven composites requires knowledge of the stress states within the meso-scale structure of the fabric reinforcement. Multicontinuum technology provides a computationally efficient way of extracting constituent stresses and strains from a structural-level finite element analysis. This study investigates the value in extending the capabilities of multicontinuum technology to materials with complex heterogeneity that could benefit from the definition of many constituents. To determine the feasibility of this extension, a meso-scale finite element model of a triaxial braid was developed and used as a test case. The model’s predictions of initial matrix failure were in good agreement with the limited experimental data. Also, trends in initial failure predictions for multi-axial load cases are in agreement with physically intuitive expectations. These results show promise for the success of future research in extending multicontinuum technology for application to composites with complex multiscale heterogeneity.

Trajectory generation for underactuated control of a suspended mass

The underactuated system under consideration is a magnetically-suspended, differential drive robot utilizing a winch system to articulate a suspended mass. A dynamic model of the system is first constructed, and then a nonlinear, infinite-dimensional optimization algorithm is presented. The system model uses the principles of kinematic reduction to produce a mixed kinematic-dynamic model that isolates the modeling of the system actuators from the modeling of the rest of the system. In this framework, the inputs become generalized velocities instead of generalized forces facilitating real-world implementation with an embedded system. The optimization algorithm automatically deals with the complexities introduced by the nonlinear dynamics and underactuation to synthesize dynamically feasible system trajectories for a wide array of trajectory generation problems. Applying this algorithm to the mixed kinematic-dynamic model, several example problems are solved and the results are tested experimentally. The experimental results agree quite well with the theoretical showing promise in extending the capabilities of the system to utilize more advanced feedback techniques and to handle more complex, three-dimensional problems.

Structured Linearization of Discrete Mechanical Systems for Analysis and Optimal Control

Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they are not energy-preserving they do exhibit long-time stable energy behavior. However, variational integrators often simulate mechanical system dynamics by solving an implicit difference equation at each time step, one that is moreover expressed purely in terms of configurations at different time steps. This paper formulates the first- and second-order linearizations of a variational integrator in a manner that is amenable to control analysis and synthesis, creating a bridge between existing analysis and optimal control tools for discrete dynamic systems and variational integrators for mechanical systems in generalized coordinates with forcing and holonomic constraints. The forced pendulum is used to illustrate the technique. A second example solves the discrete Linear Quadratic Regulator (LQR) problem to find a locally stabilizing controller for a 40 DOF system with six constraints.

Trajectory Optimization for Well-Conditioned Parameter Estimation

When attempting to estimate parameters in a dynamical system, it is often beneficial to strategically design experimental trajectories that facilitate the estimation process. This paper presents an optimization algorithm which improves conditioning of estimation problems by modifying the experimental trajectory. An objective function which minimizes the condition number of the Hessian of the least-squares identification method is derived and a least-squares method is used to estimate parameters of the nonlinear system. A software-simulated example demonstrates that an arbitrarily designed trajectory can lead to an ill-conditioned least-squares estimation problem, which in turn leads to slower convergence to the best estimate and, in the presence of experimental uncertainties, may lead to no convergence at all. A physical experiment with a robot-controlled suspended mass also shows improved estimation results in practice in the presence of noise and uncertainty using the optimized trajectory.

Trajectory Synthesis for Fisher Information Maximization

Estimation of model parameters in a dynamic system can be significantly improved with the choice of experimental trajectory. For general nonlinear dynamic systems, finding globally “best” trajectories is typically not feasible; however, given an initial estimate of the model parameters and an initial trajectory, we present a continuous-time optimization method that produces a locally optimal trajectory for parameter estimation in the presence of measurement noise. The optimization algorithm is formulated to find system trajectories that improve a norm on the Fisher information matrix (FIM). A double-pendulum cart apparatus is used to numerically and experimentally validate this technique. In simulation, the optimized trajectory increases the minimum eigenvalue of the FIM by three orders of magnitude, compared with the initial trajectory. Experimental results show that this optimized trajectory translates to an order-of-magnitude improvement in the parameter estimate error in practice.

Real-time trajectory synthesis for information maximization using Sequential Action Control and least-squares estimation

This paper presents the details and experimental results from an implementation of real-time trajectory generation and parameter estimation of a dynamic model using the Baxter Research Robot from Rethink Robotics. Trajectory generation is based on the maximization of Fisher information in real-time and closed-loop using a form of Sequential Action Control. On-line estimation is performed with a least-squares estimator employing a nonlinear state observer model computed with trep, a dynamics simulation package. Baxter is tasked with estimating the length of a string connected to a load suspended from the gripper with a load cell providing the single source of feedback to the estimator. Several trials are presented with varying initial estimates showing convergence to the actual length within a 6 second time-frame.

Trust adaptation leads to lower control effort in shared control of crane automation

We present a shared-control framework predicated on a measure of trust in the operator, that is calculated automatically based on the quality of the interactions between a human and autonomous system. This measure of trust is built upon a control-theoretic foundation that rewards stable operation of the system to give more trusted users additional control authority. The level of control authority is used to modify the human input, and as a result, we observe a minimization of the required effort of the controller. We validate this work within a planar crane environment with a receding horizon controller to assist with the regulation of the system dynamics. The human defines the reference trajectory for the controller. In an experimental study users navigate a suspended payload through a set of maze configurations. We find that adaptation of the trust metric over time provides the benefit of substantially (

Model-Based Reactive Control for Hybrid and High-Dimensional Robotic Systems

p <; 0.01

Extending filter performance through structured integration

) improving the automated systems ability to modulate the users input, resulting in stable reference trajectories that require less effort to track. In effect, the human and automation spend less time fighting each other during task execution, suggesting that the automated system and user each have a better understanding of the others ability.

Robotic Puppets and the Engineering of Autonomous Theater

Sequential action control (SAC) is a recently developed algorithm for optimal control of nonlinear systems. Previous work by the authors demonstrates that SAC performs well on several benchmark control problems. This work demonstrates applicability of SAC to a variety of robotic systems; we show that SAC can also be easily applied to hybrid systems without any modification and that its scalability facilitates application to high-dimensional systems. First, SAC is applied to a popular hybrid dynamic running model known as the spring-loaded inverted pendulum (SLIP). The results show that SAC can achieve dynamic hopping without using prescribed touchdown angles/leg stiffness. Moreover no specialized hybrid methods are necessary to handle the contact dynamics, despite the nonsmooth nature of the problem. The same SAC-controlled SLIP model is also implemented in a game for the Android operating system, demonstrating the minimal computational requirements for implementing SAC. Our second example involves successful stabilization and tracking control of a nonlinear, constrained dynamic model of a humanoid marionette with 56 states and 8 inputs. Finally, a discussion that includes best practices on tuning parameters of the SAC algorithm as well as the challenges of hardware implementation is also provided, along with a video that shows the resulting simulations for each example.