Dorsa Sadigh

Reactive synthesis from signal temporal logic specifications

We present a counterexample-guided inductive synthesis approach to controller synthesis for cyber-physical systems subject to signal temporal logic (STL) specifications, operating in potentially adversarial nondeterministic environments. We encode STL specifications as mixed integer-linear constraints on the variables of a discrete-time model of the system and environment dynamics, and solve a series of optimization problems to yield a satisfying control sequence. We demonstrate how the scheme can be used in a receding horizon fashion to fulfill properties over unbounded horizons, and present experimental results for reactive controller synthesis for case studies in building climate control and autonomous driving.

Automating exercise generation: a step towards meeting the MOOC challenge for embedded systems

The advent of massively open online courses (MOOCs) poses several technical challenges for educators. One of these challenges is the need to automate, as much as possible, the generation of problems, creation of solutions, and grading, in order to deal with the huge number of students. We collectively refer to this challenge as automated exercise generation. In this paper, we present a step towards tackling this challenge for an embedded systems course. We present a template-based approach to classifying problems in a recent textbook by Lee and Seshia, and outline approaches to problem and solution generation based on mutation and satisfiability solving. Several directions for future work are also outlined.

Synthesis for Human-in-the-Loop Control Systems

Several control systems in safety-critical applications involve the interaction of an autonomous controller with one or more human operators. Examples include pilots interacting with an autopilot system in an aircraft, and a driver interacting with automated driver-assistance features in an automobile. The correctness of such systems depends not only on the autonomous controller, but also on the actions of the human controller. In this paper, we present a formalism for human-in-the-loop (HuIL) control systems. Particularly, we focus on the problem of synthesizing a semi-autonomous controller from high-level temporal specifications that expect occasional human intervention for correct operation. We present an algorithm for this problem, and demonstrate its operation on problems related to driver assistance in automobiles.

Planning for Autonomous Cars that Leverage Effects on Human Actions

Traditionally, autonomous cars make predictions about other drivers’ future trajectories, and plan to stay out of their way. This tends to result in defensive and opaque behaviors. Our key insight is that an autonomous car’s actions will actually affect what other cars will do in response, whether the car is aware of it or not. Our thesis is that we can leverage these responses to plan more efficient and communicative behaviors. We model the interaction between an autonomous car and a human driver as a dynamical system, in which the robot’s actions have immediate consequences on the state of the car, but also on human actions. We model these consequences by approximating the human as an optimal planner, with a reward function that we acquire through Inverse Reinforcement Learning. When the robot plans with this reward function in this dynamical system, it comes up with actions that purposefully change human state: it merges in front of a human to get them to slow down or to reach its own goal faster; it blocks two lanes to get them to switch to a third lane; or it backs up slightly at an intersection to get them to proceed first. Such behaviors arise from the optimization, without relying on hand-coded signaling strategies and without ever explicitly modeling communication. Our user study results suggest that the robot is indeed capable of eliciting desired changes in human state by planning using this dynamical system.

Information gathering actions over human internal state

Much of estimation of human internal state (goal, intentions, activities, preferences, etc.) is passive: an algorithm observes human actions and updates its estimate of human state. In this work, we embrace the fact that robot actions affect what humans do, and leverage it to improve state estimation. We enable robots to do active information gathering, by planning actions that probe the user in order to clarify their internal state. For instance, an autonomous car will plan to nudge into a human drivers lane to test their driving style. Results in simulation and in a user study suggest that active information gathering significantly outperforms passive state estimation.

A learning based approach to control synthesis of Markov decision processes for linear temporal logic specifications

We propose to synthesize a control policy for a Markov decision process (MDP) such that the resulting traces of the MDP satisfy a linear temporal logic (LTL) property. We construct a product MDP that incorporates a deterministic Rabin automaton generated from the desired LTL property. The reward function of the product MDP is defined from the acceptance condition of the Rabin automaton. This construction allows us to apply techniques from learning theory to the problem of synthesis for LTL specifications even when the transition probabilities are not known a priori. We prove that our method is guaranteed to find a controller that satisfies the LTL property with probability one if such a policy exists, and we suggest empirically that our method produces reasonable control strategies even when the LTL property cannot be satisfied with probability one.

Safe Control under Uncertainty with Probabilistic Signal Temporal Logic

Safe control of dynamical systems that satisfy temporal invariants expressing various safety properties is a challenging problem that has drawn the attention of many researchers. However, making the assumption that such temporal properties are deterministic is far from the reality. For example, a robotic system might employ a camera sensor and a machine learned system to identify obstacles. Consequently, the safety properties the controller has to satisfy, will be a function of the sensor data and the associated classifier. We propose a framework for achieving safe control. At the heart of our approach is the new Probabilistic Signal Temporal Logic (PrSTL), an expressive language to define stochastic properties, and enforce probabilistic guarantees on them. We also present an efficient algorithm to reason about safe controllers given the constraints derived from the PrSTL specification. One of the key distinguishing features of PrSTL is that the encoded logic is adaptive and changes as the system encounters additional data and updates its beliefs about the latent random variables that define the safety properties. We demonstrate our approach by deriving safe control of quadrotors and autonomous vehicles in dynamic environments.

Safety envelope for security

We present an approach for detecting sensor spoofing attacks on a cyber-physical system. Our approach consists of two steps. In the first step, we construct a safety envelope of the system. Under nominal conditions (that is, when there are no attacks), the system always stays inside its safety envelope. In the second step, we build an attack detector: a monitor that executes synchronously with the system and raises an alarm whenever the system state falls outside the safety envelope. We synthesize safety envelopes using a modifed machine learning procedure applied on data collected from the system when it is not under attack. We present experimental results that show effectiveness of our approach, and also validate the several novel features that we introduced in our learning procedure.

Formal methods for semi-autonomous driving

We give an overview of the main challenges in the specification, design, and verification of human cyber-physical systems, with a special focus on semi-autonomous vehicles. We identify unique characteristics of formal modeling, specification, verification and synthesis in this domain. Some initial results and design principles are presented along with directions for future work.

Robust subspace system identification via weighted nuclear norm optimization

Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework to handle outliers. The proposed framework takes the form of a convex optimization problem with an objective that trades off fit, rank and sparsity. As in robust PCA, it can be problematic to find a suitable regularization parameter. We show how the space in which a suitable parameter should be sought can be limited to a bounded open set of the two dimensional parameter space. In practice, this is very useful since it restricts the parameter space that is needed to be surveyed.