In this article, we determine analytical upper bounds on the local Lipschitz constants of feedforward neural networks with rectified linear unit (ReLU) activation functions. We do so by deriving Lipschitz constants and bounds for ReLU, affine-ReLU, and max pooling functions, and combining the results to determine a network-wide bound. Our method uses several insights to obtain tight bounds, such as keeping track of the zero elements of each layer, and analyzing the composition of affine and ReLU functions. Furthermore, we employ a careful computational approach which allows us to apply our method to large networks such as AlexNet and VGG-16. We present several examples using different networks, which show how our local Lipschitz bounds are tighter than the global Lipschitz bounds. We also show how our method can be applied to provide adversarial bounds for classification networks. These results show that our method produces the largest known bounds on minimum adversarial perturbations for large networks such as AlexNet and VGG-16.

The focus of the work in this paper is a systems-theoretic construction, analysis, and evaluation of a deterministic model of human decision making relative to experimental data. In sequential two-alternative forced choice decision tasks, a human subject is presented with two choices at every time step, is given finite time to select one of the choices, and receives a reward after a choice is made (presented as a number on a computer screen). The goal for the human is to obtain the maximal reward while not knowing the underlying reward assignment process. In this work, we present a parameterized deterministic model for human decision making in this context and analyze optimality and stability using a finite state machine approach. This model is then evaluated relative to experimental data from human subjects performing each of six tasks.

This paper is concerned with path planning for an autonomous flight vehicle operating in a steady, uniform flow-field. We model the vehicle as a particle that travels in the horizontal plane at a constant speed relative to the ambient flow. The vehicle may turn in either direction, subject to symmetric constraints on the turn rate and the turn acceleration. The contribution of the paper is a simple method for generating candidate minimum-time paths from a given initial point and heading to a given final point and heading.

We consider the problem of coordinating a group of mobile nodes communicating through a wireless medium. The objective of the network is the alignment of all the nodes towards a common direction through local interactions, without the need for global knowledge such as the network topology or the maximum degree of the network, or even local parameters, such as the number of neighbors. The key feature of our algorithm is that each node state update is done through voting, where the probability of each vote is biased by the state of the node neighbors. We propose two possible physical implementations for our algorithm. The first is based on the explicit exchange of packetized messages, while the second is a cross-layer approach. Our analysis unveils key convergence properties of this simple class of alignment algorithms, via analytical and simulated results.

This paper considers the integration of communication and control with respect to the task of coordinated heading control for a group of N vehicles with the energy efficiency of communications in mind. The heading control employed on each vehicle is a discretization of the well-known Kuramoto model of nonlinearly coupled oscillators over a sequence of logical graphs. Stability for both all-to-all and random one- to-all broadcasts is shown to be dependent on the coupling strength, K, and the time discretization, DeltaT. For desired system performance characteristics, DeltaT imposes a tight deadline by which the state information (M bits) must be propagated through the communication network. Routing optimization with respect to minimizing energy consumption is formulated considering the DeltaT deadline. Due to the tight time deadline, a one-to-all single- hop broadcasting scheme is shown to be more energy efficient for practical choices of M/DeltaT. The proposed modularization is illustrated via a set of simulations where the overall communication energy to reach alignment is optimized.

This paper presents a study which ex- tends previous work on collective motion control of a group of vehicles for target tracking. The approach is to drive the group centroid to follow a moving target while keeping all vehicles near the centroid. The provided analysis shows that the system is sta- ble. However, the tracking performance is sensitive to imperfect communication and steering dynamics. Simulation results show the performance degrades significantly when delays and steering dynamics are present. An analysis is provided to identify a major cause of the performance degradation. An alternative control law is proposed in the paper. Comparisons of the simulation results show the improved performance of the new control law.

In this paper, techniques from geometric mechanics and geometric nonlinear control theory are applied to modeling and construction of trajectory tracking algorithms for a free-swimming underwater vehicle that locomotes and maneuvers using a two-link actuated ldquotailrdquo and independently actuated ldquopectoral finrdquo bow planes. Restricting consideration of fluid forces to the simple effects of added mass and quasi-steady lift and drag, the resulting system model can be expressed in a control-affine structure. With particular choices of oscillatory actuation of the four system joints, maneuvers such as swimming forward, in and out of plane turning, surfacing, and diving can be constructed. Further, the vehicle and model can generate agile maneuvers such as snap turns. Trajectory tracking can then be produced using state error feedback. The methods are demonstrated both in simulation and in experiment using the University of Washington prototype fin-actuated underwater vehicle.

Considers the task of trajectory stabilization for a fish-like robot by means of feedback. We use oscillatory control inputs and apply correction signals at the endpoints of each periodic input signal. Such a strategy can be proven to cause the system to converge to a desired trajectory. We present a specific model of a planar carangiform fish, and verify the stabilization results with simulations and with experiment on a planar robotic fish system that is propelled using carangiform-like movements.

Considers the design of motion control algorithms for robot fish. We present modeling, control design, and experimental trajectory tracking results for an experimental planar robotic fish system that is propelled using carangiform-like locomotion. Our model for the fish's propulsion is based on quasi-steady fluid flow. Using this model, we propose gaits for forward and turning trajectories and analyze system response under such control strategies. Our models and predictions are verified by experiment.

The efficient utilization of the motion capabilities of mobile manipulators, i.e. manipulators mounted on mobile platforms, requires the resolution of the kinematically redundant system formed by the addition of the degrees of freedom (DOF) of the platform to those of the manipulator. At the velocity level, the linearized Jacobian equation for such a redundant system represents an underspecified system of algebraic equations, which can be subject to a set of constraints such as obstacles in the workspace and various limits on the joint motions. A method, which we named the FSP, has been developed to resolve such underspecified systems with constraints that may vary in time and in number during a single trajectory. The application of the method to motion planning problems with obstacle and joint limit avoidance was discussed in some of our previous work. In this paper, we present the treatment in the FSP of a non-holonomic constraint on the platform motion, and give corresponding analytical solutions for resolving the redundancy with a general optimization criterion. Comparative trajectories involving a 10 DOF mobile manipulator testbed moving with and without a non-holonomic constraint for the platform motion, are presented to illustrate the use and efficiency of the FSP approach in motion planning problems for highly kinematically redundant and constrained systems.

A new method for mitigating unexpected impact of a redundant manipulator with an object in its environment is presented. Kinematic constraints are utilized with the recently developed method known as full space parameterization (FSP). System performance criteria and constraints are changed at impact to return the end effector to the point of impact and halt the arm. Since large joint accelerations could occur as the manipulator is halted joint acceleration bounds are imposed to simulate physical actuator limitations. Simulation results are presented for the case of a simple redundant planar manipulator.