Justin Teo

Real-Time Motion Planning With Applications to Autonomous Urban Driving

This paper describes a real-time motion planning algorithm, based on the rapidly-exploring random tree (RRT) approach, applicable to autonomous vehicles operating in an urban environment. Extensions to the standard RRT are predominantly motivated by: 1) the need to generate dynamically feasible plans in real-time; 2) safety requirements; 3) the constraints dictated by the uncertain operating (urban) environment. The primary novelty is in the use of closed-loop prediction in the framework of RRT. The proposed algorithm was at the core of the planning and control software for Team MITs entry for the 2007 DARPA Urban Challenge, where the vehicle demonstrated the ability to complete a 60 mile simulated military supply mission, while safely interacting with other autonomous and human driven vehicles.

Motion planning for urban driving using RRT

This paper provides a detailed analysis of the motion planning subsystem for the MIT DARPA Urban Challenge vehicle. The approach is based on the Rapidly-exploring Random Trees (RRT) algorithm. The purpose of this paper is to present the numerous extensions made to the standard RRT algorithm that enable the on-line use of RRT on robotic vehicles with complex, unstable dynamics and significant drift, while preserving safety in the face of uncertainty and limited sensing. The paper includes numerous simulation and race results that clearly demonstrate the effectiveness of the planning system.

Motion Planning in Complex Environments using Closed-loop Prediction

This paper describes the motion planning and control subsystems of Team MIT’s entry in the 2007 DARPA Grand Challenge. The novelty is in the use of closed-loop prediction in the framework of Rapidly-exploring Random Tree (RRT). Unlike the standard RRT, an input to the controller is sampled, followed by the forward simulation using the vehicle model and the controller to compute the predicted trajectory. This enables the planner to generate smooth trajectories much more efficiently, while the randomization allows the planner to explore cluttered environment. The controller consists of a Proportional-Integral speed controller and a nonlinear pure-pursuit steering controller, which are used both in execution and in the simulation-based prediction. The main advantages of the forward simulation are that it can easily incorporate any nonlinear control law and nonlinear vehicle dynamics, and the resulting trajectory is dynamically feasible. By using a stabilizing controller, it can handle vehicles with unstable dynamics. Several results obtained using MIT’s race vehicle demonstrate these features of the approach.

Proportional-Integral Controllers for Minimum-Phase Nonaffine-in-Control Systems

We show that stabilizing tracking proportional-integral (PI) controllers can be constructed for minimum-phase nonaffine-in-control systems. The constructed PI controller is an equivalent realization of an approximate dynamic inversion controller. This equivalence holds only for the time response when applied to the unperturbed system. Even when restricted to unperturbed minimum-phase linear time invariant systems, their closed loop robustness properties differ. This shows that in general, properties that do not define the equivalence relation for systems/controllers are not preserved under such equivalence transformations.

Anti-windup compensation for nonlinear systems via gradient projection: Application to adaptive control

Control saturation is an important limitation in practical control systems and it is well known that performance degradation or instability may result if this limitation is not effectively addressed. Using ideas from the gradient projection method in nonlinear programming, we propose a new anti-windup scheme for multi-input, multi-output nonlinear dynamic controllers. The key idea is to project the controller state update law onto the tangent plane of the active saturation constraints. To do this, we first extend the gradient projection method to the continuous-time case that can accommodate multiple nonlinear constraints. This is then used for anti-windup compensation, resulting in a hybrid controller that switches its state update law over arbitrary combinations of saturating controls. Simulations on a nonlinear two-link robot driven by an adaptive sliding mode controller illustrates its effectiveness and limitations.

On Approximate Dynamic Inversion and Proportional-Integral control

Approximate Dynamic Inversion (ADI) has been established as a method to control minimum-phase, nonaffine-in-control systems. Previous results have shown that for single-input nonaffine-in-control systems, every ADI controller admits a linear Proportional-Integral (PI) realization that is largely independent of the nonlinear function that defines the system. This paper extends these previous results in three ways. First, we present an extension of ADI that renders the closed loop error dynamics independent of the reference model dynamics. It is then shown that the equivalence between the ADI and PI controllers only holds for the time response when applied to the exact system. Finally, key robustness properties of the two control approaches are compared using linear system techniques. These results indicate that the PI realization is preferable when accurate knowledge of the nonlinear system dynamics is not available, and that the ADI realization would be preferred if time delays are the major limitations in the system.

Equivalence between Approximate Dynamic Inversion and Proportional-Integral control

Approximate dynamic inversion is a method applicable to control of minimum phase, nonaffine-in-control systems. We show that if all the system states are available for feedback, the approximate dynamic Inversion controller can be realized as a linear Proportional-Integral model reference controller without knowledge of the nonlinear system beyond the sign of the control effectiveness, and without any approximations. Similarities with earlier work on high-gain feedback and variable structure control of affine-in-control nonlinear systems are highlighted, which suggests a possible link between approximate dynamic Inversion and variable structure control for nonaffine-in-control systems.

Region of attraction comparison for gradient projection anti-windup compensated systems

The gradient projection anti-windup (GPAW) scheme was recently proposed for saturated multi-input-multi-output (MIMO) nonlinear systems driven by MIMO nonlinear controllers, a topic recognized as an open problem in a recent survey paper. Thus far, stability results for GPAW compensated systems are restricted to the simple case of a saturated first order linear time invariant (LTI) plant driven by a first order LTI controller. Here, we present a region of attraction (ROA) comparison result for general GPAW compensated regulatory systems. The ROA comparison result is demonstrated on a simple planar nonlinear system, which also highlights the limitations of existing state-of-the-art anti-windup results.