Guaranteeing safety in human-centric applications is critical in robot learning as the learned policies may demonstrate unsafe behaviors in formerly unseen scenarios. We present a framework to locally repair an erroneous policy network to satisfy a set of formal safety constraints using Mixed Integer Quadratic Programming (MIQP). Our MIQP formulation explicitly imposes the safety constraints to the learned policy while minimizing the original loss function. The policy network is then verified to be locally safe. We demonstrate the application of our framework to derive safe policies for a robotic lower-leg prosthesis.

Assistive robotic devices are a particularly promising field of application for neural networks (NN) due to the need for personalization and hard-to-model human-machine interaction dynamics. However, NN based estimators and controllers may produce potentially unsafe outputs over previously unseen data points. In this paper, we introduce an algorithm for updating NN control policies to satisfy a given set of formal safety constraints, while also optimizing the original loss function. Given a set of mixed-integer linear constraints, we define the NN repair problem as a Mixed Integer Quadratic Program (MIQP). In extensive experiments, we demonstrate the efficacy of our repair method in generating safe policies for a lower-leg prosthesis.

The increasing deployment of robots in co-working scenarios with humans has revealed complex safety and efficiency challenges in the computation of the robot behavior. Movement among humans is one of the most fundamental —and yet critical— problems in this frontier. While several approaches have addressed this problem from a purely navigational point of view, the absence of a unified paradigm for communicating with humans limits their ability to prevent deadlocks and compute feasible solutions. This paper presents a joint communication and motion planning framework that selects from an arbitrary input set of robot's communication signals while computing robot motion plans. It models a human co-worker's imperfect perception of these communications using a noisy sensor model and facilitates the specification of a variety of social/workplace compliance priorities with a flexible cost function. Theoretical results and simulator-based empirical evaluations show that our approach efficiently computes motion plans and communication strategies that reduce conflicts between agents and resolve potential deadlocks.

Sampling-based methods such as Rapidly-exploring Random Trees (RRTs) have been widely used for generating motion paths for autonomous mobile systems. In this work, we extend time-based RRTs with Control Barrier Functions (CBFs) to generate, safe motion plans in dynamic environments with many pedestrians. Our framework is based upon a human motion prediction model which is well suited for indoor narrow environments. We demonstrate our approach on a high-fidelity model of the Toyota Human Support Robot navigating in narrow corridors. We show in three scenarios that our proposed online method can navigate safely in the presence of moving agents with unknown dynamics.

In this paper, we design real-time controllers that react to uncertainties with stochastic characteristics and bound the probability of a failure in finite-time to a given desired value. Stochastic control barrier functions are used to derive sufficient conditions on the control input that bound the probability that the states of the system enter an unsafe region within a finite time. These conditions are combined with reachability conditions and used in an optimization problem to find the required control actions that lead the system to a goal set. We illustrate our theoretical development using a simulation of a lane-changing scenario in a highway with dense traffic.

In this paper, the car-like robot kinematic model trajectory tracking and control problem is revisited by exploring an optimal analytical solution which guarantees the global exponential stability of the tracking error. The problem is formulated in the form of tracking error optimization in which the quadratic errors of the position, velocity, and acceleration are minimized subject to the rear-wheel car-like robot kinematic model. The input-output linearization technique is employed to transform the nonlinear problem into a linear formulation. By using the variational approach, the analytical solution is obtained, which is guaranteed to be globally exponentially stable and is also appropriate for real-time applications. The simulation results demonstrate the validity of the proposed mechanism in generating an optimal trajectory and control inputs by evaluating the proposed method in an eight-shape tracking scenario.

In this paper, a novel kinematic-based optimal trajectory planning formulation for an autonomous vehicle is presented. In this new formulation, the quadratic errors of position, velocity, and acceleration are minimized subject to the rear wheel car-like vehicle nonlinear kinematic model. Minimizing the error of velocity and acceleration in addition to the error of position, allows us to obtain both optimal vehicle trajectory and control law. The Variational approach is used to minimize the cost function. Then, optimal trajectory and control inputs are numerically calculated by solving a set of two-point boundary value (TPBV) nonlinear differential equations. Finally, the proposed method is evaluated in two scenarios of lane changing and multi-curvature road which verifies the success of the proposed method in generating an optimal trajectory and control inputs.

In this paper, we propose a framework to repair a pre-trained feed-forward neural network (NN) to satisfy a set of properties. We formulate the properties as a set of predicates that impose constraints on the output of NN over the target input domain. We define the NN repair problem as a Mixed Integer Quadratic Program (MIQP) to adjust the weights of a single layer subject to the given predicates while minimizing the original loss function over the original training domain. We demonstrate the application of our framework in bounding an affine transformation, correcting an erroneous NN in classification, and bounding the inputs of a NN controller.