Shankar Sastry

Robust Face Recognition via Sparse Representation

We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by C1-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.

Nonholonomic motion planning: steering using sinusoids

Methods for steering systems with nonholonomic c.onstraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given. >

Adaptive control of mechanical manipulators

When an accurate dynamic model of a mechanical manipu lator is available, it may be used in a nonlinear, model-based scheme to control the manipulator. Such a control formula tion yields a controller that suppresses disturbances and tracks desired trajectories uniformly in all configurations of the manipulator. Use of a poor dynamic model with this kind of model-based decoupling and linearizing scheme, however, may result in performance that is inferior to a much simpler, fixed-gain scheme. In this paper, we develop a parameter-adaptive control scheme in a set of adaptive laws that can be added to the nonlinear, model-based controller. The scheme is unique be cause it is designed specifically for the nonlinear, model- based controller and has been proven stable in a full, nonlin ear setting. After adaptation, the error dynamics of the joints are decoupled with uniform disturbance rejection in all ma nipulator configurations. The issues of sufficient excitation and the effect of disturbances are also discussed. The theory is demonstrated with simulation results and also with data from an implementation for an industrial robot, the Adept One.

Adaptive control of linearizable systems

The authors give some initial results on the adaptive control of minimum-phase nonlinear systems which are exactly input-output linearizable by state feedback. Parameter adaptation is used as a technique to make robust the exact cancellation of nonlinear terms, which is called for in the linearization technique. The application of the adaptive technique to control of robot manipulators is discussed. Only the continuous-time case is considered; extensions to the discrete-time and sampled-data cases are not obvious. >

Foundations of Control and Estimation Over Lossy Networks

This paper considers control and estimation problems where the sensor signals and the actuator signals are transmitted to various subsystems over a network. In contrast to traditional control and estimation problems, here the observation and control packets may be lost or delayed. The unreliability of the underlying communication network is modeled stochastically by assigning probabilities to the successful transmission of packets. This requires a novel theory which generalizes classical control/estimation paradigms. The paper offers the foundations of such a novel theory. The central contribution is to characterize the impact of the network reliability on the performance of the feedback loop. Specifically, it is shown that for network protocols where successful transmissions of packets is acknowledged at the receiver (e.g., TCP-like protocols), there exists a critical threshold of network reliability (i.e., critical probabilities for the successful delivery of packets), below which the optimal controller fails to stabilize the system. Further, for these protocols, the separation principle holds and the optimal LQG controller is a linear function of the estimated state. In stark contrast, it is shown that when there is no acknowledgement of successful delivery of control packets (e.g., UDP-like protocols), the LQG optimal controller is in general nonlinear. Consequently, the separation principle does not hold in this circumstance

Conflict resolution for air traffic management: a study in multiagent hybrid systems

Air traffic management (ATM) of the future allows for the possibility of free flight, in which aircraft choose their own optimal routes, altitudes, and velocities. The safe resolution of trajectory conflicts between aircraft is necessary to the success of such a distributed control system. In this paper, we present a method to synthesize provably safe conflict resolution manoeuvres. The method models the aircraft and the manoeuvre as a hybrid control system and calculates the maximal set of safe initial conditions for each aircraft so that separation is assured in the presence of uncertainties in the actions of the other aircraft. Examples of manoeuvres using both speed and heading changes are worked out in detail.

Nonlinear control design for slightly non-minimum phase systems: application to V/STOL aircraft

Abstract There has been a great deal of excitement recently over the development of a theory for explicitly linearizing the input-output response of a nonlinear system using state feedback. One shortcoming of this theory is the inability to deal with non-minimum phase nonlinear systems. Highly maneuverable jet aircraft, such as the V/STOL Harrier, belong to an important class of a slightly non-minimum phase nonlinear systems. The non-minimum phase character of aircraft is a result of the small body forces that are produced in the process of generating body moments. In this paper, we show that, while straightforward application of the linearization theory to a non-minimum phase system results in a system with a linear input-output response but unstable internal dynamics, designing a feedback control based on a minimum phase approximation to the true system results in a system with desirable properties such as bounded tracking and asymptotic stability.

Controllers for reachability specifications for hybrid systems

The problem of systematically synthesizing hybrid controllers which satisfy multiple control objectives is considered. We present a technique, based on the principles of optimal control, for determining the class of least restrictive controllers that satisfies the most important objective (which we refer to as safety). The system performance with respect to lower priority objectives (which we refer to as efficiency) can then be optimized within this class. We motivate our approach by showing how the proposed synthesis technique simplifies to well-known results from supervisory control and pursuit evasion games when restricted to purely discrete and purely continuous systems respectively. We then illustrate the application of this technique to two examples, one hybrid (the steam boiler benchmark problem), and one primarily continuous (a flight vehicle management system with discrete flight modes).

Probabilistic pursuit-evasion games: theory, implementation, and experimental evaluation

We consider the problem of having a team of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) pursue a second team of evaders while concurrently building a map in an unknown environment. We cast the problem in a probabilistic game theoretical framework, and consider two computationally feasible greedy pursuit policies: local-mar and global-max. To implement this scenario on real UAVs and UGVs, we propose a distributed hierarchical hybrid system architecture which emphasizes the autonomy of each agent, yet allows for coordinated team efforts. We describe the implementation of the architecture on a fleet of UAVs and UGVs, detailing components such as high-level pursuit policy computation, map building and interagent communication, and low-level navigation, sensing, and control. We present both simulation and experimental results of real pursuit-evasion games involving our fleet of UAVs and UGVs, and evaluate the pursuit policies relating expected capture times to the speed and intelligence of the evaders and the sensing capabilities of the pursuers.

Output tracking control design of a helicopter model based on approximate linearization

Output tracking control of a helicopter model is investigated. The model is derived from Newton-Euler equations by assuming that the helicopter body is rigid. First, we show that for several choices of output variables exact input-output linearization fails to linearize the whole state space and results in having unstable zero dynamics. By neglecting the couplings between moments and forces, we show that the approximated system with dynamic decoupling is full state linearizable by choosing positions and heading as outputs. We prove that bounded tracking is achieved by applying the approximate control. Next, we derive a diffeomorphism showing that an approximation of the system is differentially flat, thus state trajectory and nominal inputs can be generated from a given output trajectory. Simulation results using both output tracking controllers based on exact and approximate input-output linearization are presented for comparison.