Brian Paden

A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles

Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efficiency, and convenience of automotive transportation. Safety-critical tasks that must be executed by a self-driving vehicle include planning of motions through a dynamic environment shared with other vehicles and pedestrians, and their robust executions via feedback control. The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting. A selection of proposed techniques is reviewed along with a discussion of their effectiveness. The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements. The side by side comparison presented in this survey helps to gain insight into the strengths and limitations of the reviewed approaches and assists with system level design choices.

Modeling and Control of an Electromagnetic Variable Valve Actuation System

A novel electromechanical valve actuation system comprised of a linear actuator, valve, and energy storing cam/spring mechanism is presented. The system dynamics are modeled using Lagrangian mechanics, and a minimum-energy point-to-point optimal control problem is solved to find an optimal trajectory and input. The optimal input is used as a feedforward component in a transition controller to move the valve between the open and closed positions. Between transitions, a simple linear controller stabilizes the valve in the open and closed positions. A high-order model capturing the distributed nature of valve springs is used to validate state constraints related to positive cam/follower forces and a nonslip condition on the cam/follower. Finally, a prototype system is fabricated and tested with promising results.

Point-to-point control near heteroclinic orbits: Plant and controller optimality conditions

In this paper we consider the simultaneous optimization of the controller and plant in a one degree-of-freedom system. In particular we are interested in optimal trajectories between fixed points connected by heteroclinic orbits. We find that designing the plant dynamics to have a heteroclinic connection between target states enables a low energy transfer between the states. We use a nested optimization strategy to find the optimal plant dynamics and control effort for the transition. Additionally, we uncover plant optimality conditions which reduce the complexity of the optimization.

Computational methods for MIMO flat linear systems: Flat output characterization, test and tracking control

This paper is concerned with the study of flat outputs for multiple-input-multiple-output (MIMO) controllable linear time-invariant discrete- and continuous-time systems in state-space representation. Leveraging the equivalence of flatness to an estimation-theoretic system property known as strong observability, a quick computational test is developed for ascertaining if an output candidate is flat and the subspace of flat outputs can be constructively characterized. Moreover, we propose a computational method to find differentially (continuous-time), as well as non-causal and causal difference (discrete-time) flat outputs via a system transformation into a special control canonical form. Finally, design principles for flatness-based trajectory planning and tracking control for discrete-time systems are presented, which to our best knowledge, have yet to be successfully demonstrated.

Asymptotically reachable states and related symmetry in systems theory

In executing state-to-state maneuvers, end states which are stabilizable states provide for robust maneuver control. In the normal circumstance that a maneuver only takes the system to a neighborhood of a stabilizable state, feedback control can be used to regulate to a neighborhood of the desired end state. In contrast, if the end state is not a stabilizable state, large try-again maneuvers which cannot be bounded by the terminal tracking error of the prior maneuver are often required in the event of a near miss. In this paper it is shown that the subspace of stabilizable states for a linear stabilizable system is the intersection of the reachable subspace and a particular controlled invariant subspace we call the constant state subspace. The stabilizable states are also the states which can be approached asymptotically with appropriate choice of control, and we use this characterization as our definition of stabilizable states.

Selection of input primitives for the generalized label correcting method

The generalized label correcting method is an efficient search-based approach to trajectory optimization. It relies on a finite set of piecewise constant control primitives that are concatenated into candidate control signals. This paper investigates the principled selection of this set of control primitives. Emphasis is placed on a particularly challenging input space geometry, the n-dimensional sphere. We propose using controls which minimize a generalized energy function and discuss the optimization technique used to obtain these control primitives. A numerical experiment is presented showing a factor of two improvement in running time when using the optimized control primitives over a random sampling strategy.