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Unified Multi-Rate Control: from Low Level Actuation to High Level Planning.

TL;DR: The proposed hierarchical multi-rate control architecture maximizes the probability of satisfying the high-level specifications while guaranteeing state and input constraint satisfaction and is tested in simulations and experiments on examples inspired by the Mars exploration mission.
Abstract: In this paper we present a hierarchical multi-rate control architecture for nonlinear autonomous systems operating in partially observable environments. Control objectives are expressed using syntactically co-safe Linear Temporal Logic (LTL) specifications and the nonlinear system is subject to state and input constraints. At the highest level of abstraction, we model the system-environment interaction using a discrete Mixed Observable Markov Decision Problem (MOMDP), where the environment states are partially observed. The high level control policy is used to update the constraint sets and cost function of a Model Predictive Controller (MPC) which plans a reference trajectory. Afterwards, the MPC planned trajectory is fed to a low-level high-frequency tracking controller, which leverages Control Barrier Functions (CBFs) to guarantee bounded tracking errors. Our strategy is based on model abstractions of increasing complexity and layers running at different frequencies. We show that the proposed hierarchical multi-rate control architecture maximizes the probability of satisfying the high-level specifications while guaranteeing state and input constraint satisfaction. Finally, we tested the proposed strategy in simulations and experiments on examples inspired by the Mars exploration mission, where only partial environment observations are available.
Citations
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Posted Content
22 Jul 2020
TL;DR: This work presents a safety-critical model predictive control strategy utilizing discrete-time control barrier functions (CBFs), which guarantees system safety and accomplishes optimal performance via model predictivecontrol.
Abstract: The optimal performance of robotic systems is usually achieved near the limit of state and input bounds. Model predictive control (MPC) is a prevalent strategy to handle these operational constraints, however, safety still remains an open challenge for MPC as it needs to guarantee that the system stays within an invariant set. In order to obtain safe optimal performance in the context of set invariance, we present a safety-critical model predictive control strategy utilizing discrete-time control barrier functions (CBFs), which guarantees system safety and accomplishes optimal performance via model predictive control. We analyze the stability and the feasibility properties of our control design. We verify the properties of our method on a 2D double integrator model for obstacle avoidance. We also validate the algorithm numerically using a competitive car racing example, where the ego car is able to overtake other racing cars.

86 citations

Posted Content
TL;DR: In this article, the authors propose a principled approach to formulate and solve complex embodied intelligence co-design problems, leveraging a monotone codesign theory. And they illustrate through a case study how, given a set of desired behaviors, their framework is able to compute Pareto efficient solutions for the entire hardware and software stack of a self-driving vehicle.
Abstract: We consider the problem of co-designing embodied intelligence as a whole in a structured way, from hardware components such as propulsion systems and sensors to software modules such as control and perception pipelines. We propose a principled approach to formulate and solve complex embodied intelligence co-design problems, leveraging a monotone co-design theory. The methods we propose are intuitive and integrate heterogeneous engineering disciplines, allowing analytical and simulation-based modeling techniques and enabling interdisciplinarity. We illustrate through a case study how, given a set of desired behaviors, our framework is able to compute Pareto efficient solutions for the entire hardware and software stack of a self-driving vehicle.

9 citations

Journal ArticleDOI
TL;DR: In this article , the authors present a controller synthesis method that does not rely on any explicit representation of the noise distributions and provides probabilistic guarantees on safely reaching a target, while also avoiding unsafe regions of the state space.
Abstract: Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel controller synthesis method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target, while also avoiding unsafe regions of the state space. First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is, with a user-specified confidence probability, robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP and compute a controller for which these guarantees carry over to the original control system. In addition, we develop a tailored computational scheme that reduces the complexity of the synthesis of these guarantees on the iMDP. Benchmarks on realistic control systems show the practical applicability of our method, even when the iMDP has hundreds of millions of transitions.

6 citations

Proceedings ArticleDOI
01 Apr 2022
TL;DR: This work seeks to address the stabilization of constrained nonlinear systems through a multi-rate control architecture by connecting these two levels of control design in a way that ensures constraint satisfaction is achieved through the use of Bézier curves.
Abstract: Modern control systems must operate in increasingly complex environments subject to safety constraints and input limits, and are often implemented in a hierarchical fashion with different controllers running at multiple time scales. Yet traditional constructive methods for nonlinear controller synthesis typically "flatten" this hierarchy, focusing on a single time scale, and thereby limited the ability to make rigorous guarantees on constraint satisfaction that hold for the entire system. In this work we seek to address the stabilization of constrained nonlinear systems through a multi-rate control architecture. This is accomplished by iteratively planning continuous reference trajectories for a nonlinear system using a linearized model and Model Predictive Control (MPC), and tracking said trajectories using the full-order nonlinear model and Control Lyapunov Functions (CLFs). Connecting these two levels of control design in a way that ensures constraint satisfaction is achieved through the use of Bézier curves, which enable planning continuous trajectories respecting constraints by planning a sequence of discrete points. Our framework is encoded via convex optimization problems which may be efficiently solved, as demonstrated in simulation.

4 citations

Journal ArticleDOI
TL;DR: In this paper , a model predictive control (MPC) scheme is proposed to handle disturbances, or process noise, in the state dynamics, the state constraints are tightened in a risk-aware manner to provide a disturbance feedback policy.
Abstract: This paper studies the problem of risk-averse receding horizon motion planning for agents with uncertain dynamics, in the presence of stochastic, dy-namic obstacles. We propose a model predictive control (MPC) scheme that formulates the obstacle avoidance constraint using coherent risk measures. To handle disturbances, or process noise, in the state dynamics, the state constraints are tightened in a risk-aware manner to provide a disturbance feedback policy. We also propose a waypoint following algorithm that uses the proposed MPC scheme for discrete distributions and prove its risk-sensitive recursive feasibility while guaranteeing finite-time task completion. We further investigate some commonly used coherent risk metrics, namely, conditional value-at-risk (CVaR), entropic value-at-risk (EVaR), and g-entropic risk measures, and propose a tractable incorporation within MPC. We illustrate our framework via simulation studies.

4 citations

References
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Proceedings ArticleDOI
30 Sep 1977
TL;DR: A unified approach to program verification is suggested, which applies to both sequential and parallel programs, and the main proof method is that of temporal reasoning in which the time dependence of events is the basic concept.
Abstract: A unified approach to program verification is suggested, which applies to both sequential and parallel programs. The main proof method suggested is that of temporal reasoning in which the time dependence of events is the basic concept. Two formal systems are presented for providing a basis for temporal reasoning. One forms a formalization of the method of intermittent assertions, while the other is an adaptation of the tense logic system Kb, and is particularly suitable for reasoning about concurrent programs.

5,174 citations

Book ChapterDOI
14 Jul 2011
TL;DR: A major new release of the PRISMprobabilistic model checker is described, adding, in particular, quantitative verification of (priced) probabilistic timed automata.
Abstract: This paper describes a major new release of the PRISMprobabilistic model checker, adding, in particular, quantitative verification of (priced) probabilistic timed automata. These model systems exhibiting probabilistic, nondeterministic and real-time characteristics. In many application domains, all three aspects are essential; this includes, for example, embedded controllers in automotive or avionic systems, wireless communication protocols such as Bluetooth or Zigbee, and randomised security protocols. PRISM, which is open-source, also contains several new components that are of independent use. These include: an extensible toolkit for building, verifying and refining abstractions of probabilistic models; an explicit-state probabilistic model checking library; a discrete-event simulation engine for statistical model checking; support for generation of optimal adversaries/strategies; and a benchmark suite.

2,377 citations

Book
30 Mar 1999
TL;DR: In this paper, a unified approach for the study of constrained Markov decision processes with a countable state space and unbounded costs is presented, where a single controller has several objectives; it is desirable to design a controller that minimize one of cost objectives, subject to inequality constraints on other cost objectives.
Abstract: This report presents a unified approach for the study of constrained Markov decision processes with a countable state space and unbounded costs. We consider a single controller having several objectives; it is desirable to design a controller that minimize one of cost objective, subject to inequality constraints on other cost objectives. The objectives that we study are both the expected average cost, as well as the expected total cost (of which the discounted cost is a special case). We provide two frameworks: the case were costs are bounded below, as well as the contracting framework. We characterize the set of achievable expected occupation measures as well as performance vectors. This allows us to reduce the original control dynamic problem into an infinite Linear Programming. We present a Lagrangian approach that enables us to obtain sensitivity analysis. In particular, we obtain asymptotical results for the constrained control problem: convergence of both the value and the policies in the time horizon and in the discount factor. Finally, we present and several state truncation algorithms that enable to approximate the solution of the original control problem via finite linear programs.

1,519 citations


"Unified Multi-Rate Control: from Lo..." refers background in this paper

  • ...(MDPs) and the high-level decision making problem can be solved exactly using dynamic programming, policy iteration and linear programming strategies [21]....

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Journal ArticleDOI
TL;DR: This paper provides a novel solution to the problem of robust model predictive control of constrained, linear, discrete-time systems in the presence of bounded disturbances by solving the optimal control problem that is solved online.

1,357 citations


"Unified Multi-Rate Control: from Lo..." refers methods in this paper

  • ...Compared to our previous work [36], the MPC planner is based on a fixed-tube robust MPC scheme [37], where the initial state of the planned trajectory is an opti-...

    [...]

Proceedings Article
09 Aug 2003
TL;DR: This paper introduces the Point-Based Value Iteration (PBVI) algorithm for POMDP planning, and presents results on a robotic laser tag problem as well as three test domains from the literature.
Abstract: This paper introduces the Point-Based Value Iteration (PBVI) algorithm for POMDP planning. PBVI approximates an exact value iteration solution by selecting a small set of representative belief points and then tracking the value and its derivative for those points only. By using stochastic trajectories to choose belief points, and by maintaining only one value hyper-plane per point, PBVI successfully solves large problems: we present results on a robotic laser tag problem as well as three test domains from the literature.

1,101 citations


"Unified Multi-Rate Control: from Lo..." refers background in this paper

  • ...Computing a control policy in POMDPs settings is NP-hard [22], but approximate solutions can be computed using finite state controllers [23] and performing point-based approximations [24]....

    [...]