Safe Planning And Control Of Autonomous Systems: Robust Predictive Algorithms

Safe autonomous operation of dynamical systems has become one of the most important research problems. Algorithms for planning and control of such systems are now nding place on production vehicles, and are fast becoming ubiquitous on the roads and air-spaces. However most algorithms for such operations, that provide guarantees, either do not scale well or rely on over-simplifying abstractions that make them impractical for real world implementations. On the other hand, the algorithms that are computationally tractable and amenable to implementation generally lack any guarantees on their behavior. In this work, we aim to bridge the gap between provable and scalable planning and control for dynamical systems. The research covered herein can be broadly categorized into: i) multi-agent planning with temporal logic specications, and ii) robust predictive control that takes into account the performance of the perception algorithms used to process information for control. In the rst part, we focus on multi-robot systems with complicated mission requirements, and develop a planning algorithm that can take into account a) spatial, b) temporal and c) reactive mission requirements across multiple robots. The algorithm not only guarantees continuous time satisfaction of the mission requirements, but also that the generated trajectories can be followed by the robot. The other part develops a robust, predictive control algorithm to control the the dynamical system to follow the trajectories generated by the rst part, within some desired bounds. This relies on a contract-based framework wherein the control algorithm controls the dynamical system as well as a resource/quality trade-o in a perception-based state estimation algorithm. We show that this predictive algorithm remains feasible with respect to constraints while following a desired trajectory, and also stabilizes the dynamical system under control. Through simulations, as well as experiments on actual robotic systems, we show that the planning method is computationally ecient as well as scales better than other state-of-the art algorithms that use similar formal specications. We also show that the robust control algorithm provides better control performance, and is also computationally more ecient than similar algorithms that do not leverage the resource/ quality trade-o of the perception-based state estimato

Robust Model Predictive Control for Non-Linear Systems with Input and State Constraints Via Feedback Linearization

Robust predictive control of non-linear systems under state estimation errors and input and state constraints is a challenging problem, and solutions to it have generally involved solving computationally hard non-linear optimizations. Feedback linearization has reduced the computational burden, but has not yet been solved for robust model predictive control under estimation errors and constraints. In this paper, we solve this problem of robust control of a non-linear system under bounded state estimation errors and input and state constraints using feedback linearization. We do so by developing robust constraints on the feedback linearized system such that the non-linear system respects its constraints. These constraints are computed at run-time using online reachability, and are linear in the optimization variables, resulting in a Quadratic Program with linear constraints. We also provide robust feasibility, recursive feasibility and stability results for our control algorithm. We evaluate our approach on two systems to show its applicability and performance

Gaussian Process Learning-Based Model Predictive Control for Safe Interactions of a Platoon of Autonomous and Human-Driven Vehicles

With the continued integration of autonomous vehicles (AVs) into public roads, a mixed traffic environment with large-scale human-driven vehicles (HVs) and AVs interactions is imminent. In challenging traffic scenarios, such as emergency braking, it is crucial to account for the reactive and uncertain behavior of HVs when developing control strategies for AVs. This paper studies the safe control of a platoon of AVs interacting with a human-driven vehicle in longitudinal car-following scenarios. We first propose the use of a model that combines a first-principles model (nominal model) with a Gaussian process (GP) learning-based component for predicting behaviors of the human-driven vehicle when it interacts with AVs. The modeling accuracy of the proposed method shows a $9\%$ reduction in root mean square error (RMSE) in predicting a HV's velocity compared to the nominal model. Exploiting the properties of this model, we design a model predictive control (MPC) strategy for a platoon of AVs to ensure a safe distance between each vehicle, as well as a (probabilistic) safety of the human-driven car following the platoon. Compared to a baseline MPC that uses only a nominal model for HVs, our method achieves better velocity-tracking performance for the autonomous vehicle platoon and more robust constraint satisfaction control for a platoon of mixed vehicles system. Simulation studies demonstrate a $4.2\%$ decrease in the control cost and an approximate $1m$ increase in the minimum distance between autonomous and human-driven vehicles to better guarantee safety in challenging traffic scenarios

AUTOPLUG: An Architecture for Remote Electronic Controller Unit Diagnostics in Automotive Systems

In 2010, over 20.3 million vehicles were recalled. Software issues related to automotive controls such as cruise control, anti-lock braking system, traction control and stability control, account for an increasingly large percentage of the overall vehicles recalled. There is a need for new and scalable methods to evaluate automotive controls in a realistic and open setting. We have developed AutoPlug, an automotive Electronic Controller Unit (ECU) architecture between the vehicle and a Remote Diagnostics Center to diagnose, test, update and verify controls software. Within the vehicle, we evaluate observerbased runtime diagnostic schemes and introduce a framework for remote management of vehicle recalls. The diagnostics scheme deals with both real-time and non-real time faults, and we introduce a decision function to detect and isolate faults in a system with modeling uncertainties. We also evaluate the applicability of “Opportunistic Diagnostics”, where the observerbased diagnostics are scheduled in the ECU’s RTOS only when there is slack available in the system. This aperiodic diagnostics scheme performs similar to the standard, periodic diagnostics scheme under reasonable assumptions. This approach works on existing ECUs and does not interfere with current task sets. The overall framework integrates in-vehicle and remote diagnostics and serves to make vehicle recalls management a less reactive and cost-intensive procedure

Technical Report: Control Using the Smooth Robustness of Temporal Logic

Cyber-Physical Systems must withstand a wide range of errors, from bugs in their software to attacks on their physical sensors. Given a formal specification of their desired behavior in Metric Temporal Logic (MTL), the robust semantics of the specification provides a notion of system robustness that can be calculated directly on the output behavior of the system, without explicit reference to the various sources or models of the errors. The robustness of the MTL specification has been used both to verify the system offline (via robustness minimization) and to control the system online (to maximize its robustness over some horizon). Unfortunately, the robustness objective function is difficult to work with: it is recursively defined, non-convex and non-differentiable. In this paper, we propose smooth approximations of the robustness. Such approximations are differentiable, thus enabling us to use powerful off-the- shelf gradient descent algorithms for optimizing it. By using them we can also offer guarantees on the performance of the optimization in terms of convergence to minima. We show that the approximation error is bounded to any desired level, and that the approximation can be tuned to the specification. We demonstrate the use of the smooth robustness to control two quad-rotors in an autonomous air traffic control scenario, and for temperature control of a building for comfort

Smooth Operator: Control using the Smooth Robustness of Temporal Logic

Modern control systems, like controllers for swarms of quadrotors, must satisfy complex control objectives while withstanding a wide range of disturbances, from bugs in their software to attacks on their sensors and changes in their environments. These requirements go beyond stability and tracking, and involve temporal and sequencing constraints on system response to various events. This work formalizes the requirements as formulas in Metric Temporal Logic (MTL), and designs a controller that maximizes the robustness of the MTL formula. Formally, if the system satisfies the formula with robustness r, then any disturbance of size less than r cannot cause it to violate the formula. Because robustness is not differentiable, this work provides arbitrarily precise, infinitely differentiable, approximations of it, thus enabling the use of powerful gradient descent optimizers. Experiments on a temperature control example and a two-quadrotor system demonstrate that this approach to controller design outper- forms existing approaches to robustness maximization based on Mixed Integer Linear Programming and stochastic heuristics. Moreover, it is not constrained to linear systems

Peak Power Control of Battery and Super-capacitor Energy Systems in Electric Vehicles

Hybrid energy systems consist of a load powered by a source and a form of energy storage. Systems with mixed energy supply find applications in the electric grid with renewable and non-renewable sources, in mission critical systems such as Mars rovers with rechargeable and non-rechargeable batteries and low-power monitoring systems with energy harvesting. A general problem for hybrid energy systems is the reduction of peak power consumption to ensure cost-efficient operation as peak power draws require additional resources, adversely affect the system reliability and storage lifetime. Furthermore, in some cases such as electric vehicles, the load dynamics are fast, not perfectly known a priori and the computation power available is often limited, making the implementation of traditional optimal control difficult. This paper aims to develop a control scheme to reduce the peak power drawn from the source for hybrid energy systems with limited computation power and limited load forecasts. We propose a scheme with two control levels and provide a sufficient condition for control of the different energy storage/generation components to meet the instantaneous load while satisfying a peak power threshold. The scheme provides performance comparable to Model Predictive Control, while requiring less computation power and only coarse-grained load predictions. As a case study we implement the scheme for a battery-supercapacitor system in an electric vehicle with real world drive cycles to demonstrate the low execution time and effective reduction of the battery power (hence temperature), which is crucial to the lifetime of the battery

Peak Power Reduction in Hybrid Energy Systems with Limited Load Forecasts

Hybrid energy systems, which consist of a load powered by a source and a form of energy storage, find applications in many systems, e.g., the electric grid and electric vehicles. A key problem for hybrid energy systems is the reduction of peak power consumption to ensure cost-efficient operation as peak power draws require additional resources and adversely affect the system reliability and lifetime. Furthermore, in some cases such as electric vehicles, the load dynamics are fast, not perfectly known in advance and the on-board computation power is often limited, making the implementation of traditional optimal control difficult. We aim to develop a control scheme to reduce the peak power drawn from the source for hybrid energy systems with limited computation power and limited load forecasts. We propose a scheme with two control levels and provide a sufficient condition for control of the different energy storage/generation components to meet the instantaneous load while satisfying a peak power threshold. The scheme provides performance comparable to Model Predictive Control, while requiring less computation power and only coarse-grained load predictions. For a case study, we implement the scheme for a battery-supercapacitor-powered electric vehicle with real world drive cycles to demonstrate the low execution time and effective reduction of the battery power (hence temperature), which is crucial to the lifetime of the battery

Robust Model Predictive Control with Anytime Estimation

With an increasing autonomy in modern control systems comes an increasing amount of sensor data to be processed, leading to overloaded computation and communication in the systems. For example, a vision-based robot controller processes large image data from cameras at high frequency to observe the robot’s state in the surrounding environment, which is used to compute control commands. In real-time control systems where large volume of data is processed for feedback control, the data-dependent state estimation can become a computation and communication bottleneck, resulting in potentially degraded control performance. Anytime algorithms, which offer a trade-off between execution time and accuracy of computation, can be leveraged in such systems. We present a Robust Model Predictive Control approach with an Anytime State Estimation Algorithm, which computes both the optimal control signal for the plant and the (time-varying) deadline/accuracy constraint for the anytime estimator. Our approach improves the system’s performance (concerning both the control performance and the estimation cost) over conventional controllers, which are designed for and operate at a fixed computation time/accuracy setting. We numerically evaluate our approach in an idealized motion model for navigation with both state and control constraints

Fly-by-Logic: Control of Multi-Drone Fleets with Temporal Logic Objectives

The problem of safe planning and control for multi- drone systems across a variety of missions is of critical impor- tance, as the scope of tasks assigned to such systems increases. In this paper, we present an approach to solve this problem for multi-quadrotor missions. Given a mission expressed in Signal Temporal Logic (STL), our controller maximizes robustness to generate trajectories for the quadrotors that satisfy the STL spec- ification in continuous-time. We also show that the constraints on our optimization guarantees that these trajectories can be tracked nearly perfectly by lower level off-the-shelf position and attitude controllers. Our approach avoids the oversimplifying abstractions found in many planning methods, while retaining the expressiveness of missions encoded in STL allowing us to handle complex spatial, temporal and reactive requirements. Through experiments, both in simulation and on actual quadrotors, we show the performance, scalability and real-time applicability of our method