Trajectory generation using sum-of-norms regularization

Abstract-- Many tracking problems are split into two subproblems, first a smooth reference trajectory is generated that meet the control design objectives, and then a closed loop control system is designed to follow this reference trajectory as well as possible. Applications of this kind include (autonomous) vehicle navigation systems and robotics. Typically, a spline model is used for trajectory generation and another physical and dynamical model is used for the control design. Here we propose a direct approach where the dynamical model is used to generate a control signal that takes the state trajectory through the waypoints specified in the design goals. The strength of the proposed formulation is the methodology to obtain a control signal with compact representation and that changes only when needed, something often wanted in tracking. The formulation takes the shape of a constrained least-squares problem with sum-of-norms regularization, a generalization of the 1-regularization. T...

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Henrik Ohlsson, Fredrik Gustafsson, Lennart Ljung, Stephen Boyd
• Keywords: CDC 2010, Control Signal, Control Systems, Reference Trajectory, Trajectory