Munther A. Dahleh

Real-Time Motion Planning for Agile Autonomous Vehicles

Planning the path of an autonomous, agile vehicle in a dynamic environment is a very complex problem, especially when the vehicle is required to use its full maneuvering capabilities. Recent efforts aimed at using randomized algorithms for planning the path of kinematic and dynamic vehicles have demonstrated considerable potential for implementation on future autonomous platforms. This paper builds upon these efforts by proposing a randomized path planning architecture for dynamical systems in the presence of fixed and moving obstacles. This architecture addresses the dynamic constraints on the vehicles motion, and it provides at the same time a consistent decoupling between low-level control and motion planning. The path planning algorithm retains the convergence properties of its kinematic counterparts. System safety is also addressed in the face of finite computation times by analyzing the behavior of the algorithm when the available onboard computation resources are limited, and the planning must be performed in real time. The proposed algorithm can be applied to vehicles whose dynamics are described either by ordinary differential equations or by higher-level, hybrid representations. Simulation examples involving a ground robot and a small autonomous helicopter are presented and discussed.

Distributed control of spatially invariant systems

We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are spatially distributed. These systems arise in many applications such as the control of vehicular platoons, flow control, microelectromechanical systems (MEMS), smart structures, and systems described by partial differential equations with constant coefficients and distributed controls and measurements. For fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator (LQR), H/sub 2/ and H/sub /spl infin//, optimal controllers can be obtained by solving a parameterized family of standard finite-dimensional problems. We show that optimal controllers have an inherent degree of decentralization, and this provides a practical distributed controller architecture. We also prove a general result that applies to partially distributed control and a variety of performance criteria, stating that optimal controllers inherit the spatial invariance structure of the plant. Connections of this work to that on systems over rings, and systems with dynamical symmetries are discussed.

Maneuver-based motion planning for nonlinear systems with symmetries

In this paper, we introduce an approach for the efficient solution of motion-planning problems for time-invariant dynamical control systems with symmetries, such as mobile robots and autonomous vehicles, under a variety of differential and algebraic constraints on the state and on the control inputs. Motion plans are described as the concatenation of a number of well-defined motion primitives, selected from a finite library. Rules for the concatenation of primitives are given in the form of a regular language, defined through a finite-state machine called a Maneuver Automaton. We analyze the reachability properties of the language, and present algorithms for the solution of a class of motion-planning problems. In particular, it is shown that the solution of steering problems for nonlinear dynamical systems with symmetries and invariant constraints can be reduced to the solution of a sequence of kinematic inversion problems. A detailed example of the application of the proposed approach to motion planning for a small aerobatic helicopter is presented.

Robust hybrid control for autonomous vehicle motion planning

The operation of an autonomous vehicle in an unknown, dynamic environment is a very complex problem, especially when the vehicle is required to use its full maneuvering capabilities, and to react in real time to changes in the operational environment. A possible approach to reduce the computational complexity of the motion planning problem for a nonlinear, high dimensional system, is based on a quantization of the system dynamics, leading to a control architecture based on a hybrid automaton, the states of which represent feasible trajectory primitives for the vehicle. The paper focuses on the feasibility of this approach, in the presence of disturbances and uncertainties in the plant and/or in the environment: the structure of a robust hybrid automaton is defined and its properties are analyzed. In particular, we address the issues of well-posedness, consistency and reachability. For the case of autonomous vehicles, we provide sufficient conditions to guarantee reachability of the automaton.

Trajectory tracking control design for autonomous helicopters using a backstepping algorithm

In this paper we present a tracking controller for a class of underactuated mechanical systems, based on a backstepping procedure. This class includes an approximation of small helicopter dynamics. The need to avoid artificial singularities due to the attitude representation is the main driver behind the control design presented in this paper: to achieve this goal, we will operate directly in the configuration manifold of the vehicle. The control design provides asymptotic tracking for an approximate model of small helicopters, and bounded tracking when more complete models are considered. Simulation examples, including both point stabilization and aggressive maneuver tracking, are presented and discussed.

L^{1} -optimal compensators for continuous-time systems

Previous work has been concerned with minimizing the l^{1}- norm of an error pulse response for discrete-time SISO [1] and MIMO [2] systems. In this paper we study the problem of minimizing the L1-norm of the error impulse response for SISO continuous-time systems. This problem is quite different from the discrete-time problem in that irrational solutions are obtained even when the problem data are rational. Two methods are suggested for the solution of the continuous-time problem; an exact method which leads to a finite-dimensional nonlinear programming problem, and an approximate method which leads to a linear programming problem.

Feedback Control in the Presence of Noisy Channels: “Bode-Like” Fundamental Limitations of Performance

This paper addresses fundamental limitations of feedback using information theoretic conservation laws and flux arguments. The paper has two parts. In the first part, we derive a conservation law dictating that causal feedback cannot reduce the differential entropy inserted in the loop by external sources. An interpretation of this result is that the total randomness induced by disturbances, as measured by differential entropy, cannot be reduced by causal feedback; it can only be re-allocated in time or in frequency (if well defined). Under asymptotic stationarity assumptions, this result has a spectral representation which constitutes an extension of Bodes inequality for arbitrary feedback. Our proofs make clear the role of causality, as well as how stability assumptions impact the final result. In the second part, we derive an inequality unveiling that the feedback loop must be able to convey information originating from two independent sources: 1) initial states of the physical plant; 2) exogenous disturbance signals. By using such principle, we construct a variety of information rate (information flux) inequalities. Furthermore, we derive a universal performance bound which is parameterized solely by the feedback capacity and the parameters of the plant. The latter is a new fundamental limitation, which is different from Bodes classical result, indicating that finite feedback capacity brings a new type of performance bound.

Volatility of Power Grids Under Real-Time Pricing

The paper proposes a framework for modeling and analysis of the dynamics of supply, demand, and clearing prices in power systems with real-time retail pricing and information asymmetry. Characterized by passing on the real-time wholesale electricity prices to the end consumers, real-time pricing creates a closed-loop feedback system between the physical layer and the market layer of the system. In the absence of a carefully designed control law, such direct feedback can increase sensitivity and lower the systems robustness to uncertainty in demand and generation. It is shown that price volatility can be characterized in terms of the systems maximal relative price elasticity, defined as the maximal ratio of the generalized price-elasticity of consumers to that of the producers. As this ratio increases, the system may become more volatile. Since new demand response technologies increase the price-elasticity of demand, and since increased penetration of distributed generation can also increase the uncertainty in price-based demand response, the theoretical findings suggest that the architecture under examination can potentially lead to increased volatility. This study highlights the need for assessing architecture systematically and in advance, in order to optimally strike the trade-offs between volatility/robustness and performance metrics such as economic efficiency and environmental efficiency.

Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization

The problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case. The minimum value of the objective function can be obtained by solving a semi-infinite linear programming problem, and an iterative procedure for obtaining approximate solutions is introduced. Application of the l/sup 1/-optimal problem to robustness is discussed. A mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations. >

Feedback stabilization of uncertain systems in the presence of a direct link

We study the stabilizability of uncertain stochastic systems in the presence of finite capacity feedback. Motivated by the structure of communication networks, we consider a variable rate digital link. Such link is used to transmit state measurements between the plant and the controller. We derive necessary and sufficient conditions for internal and external stabilizability of the feedback loop. In accordance with previous publications, stabilizability of unstable plants is possible if and only if the links average transmission rate is above a positive critical value. In addition, stability in the presence of uncertainty in the plant is analyzed using a small-gain argument. We also show that robustness can be increased at the expense of a higher transmission rate.