Motion planning under bounded uncertainty using ensemble control

Abstract

Abstract-This paper considers the problem of motion planning for a nonholonomic unicycle despite uncertainty that scales both the forward speed and the turning rate by an unknown but bounded constant. We model the unicycle as an ensemble control system, show that the position of this ensemble is controllable, and derive motion planning algorithms to steer this position between a given start and goal. We apply our work to a differential-drive robot with unknown but bounded wheel radius, and validate our approach with hardware experiments.

Feedback synthesis for underactuated systems using sequential second-order needle variations

“…Various approaches to nonlinear control range from steering methods using sinusoid controls (Murray and Sastry, 1993), sequential actions of Lie bracket sequences (Murray et al, 1994) and backstepping (Kokotovic, 1992; Seto and Baillieul, 1994) to perturbation methods (Junkins and Thompson, 1986), sliding mode control (SMC) (Perruquetti and Barbot, 2002; Utkin, 1992; Xu and zgüner, 2008), intelligent control (Brown and Passino, 1997; Harris et al, 1993) or hybrid control (Fierro et al, 1999), and nonlinear model predictive control (NMPC) methods (Allgöwer et al, 2004). These schemes have been successful in well-studied examples including, but not limited to, the rolling disk, the kinematic car, wheeling mobile robots, the Snakeboard, surface vessels, quadrotors, and cranes (Becker and Bretl, 2010; Boskovic et al, 1999; Bouadi et al, 2007a,b; Bullo et al, 2000; Chen et al, 2013; Escareo et al, 2013; Fang et al, 2003; Kolmanovsky and McClamroch, 1995; Lin et al, 2014; Morbidi and Prattichizzo, 2007; Nakazono et al, 2008; Reyhanoglu et al, 1996; Roy and Asada, 2007; Shammas and de Oliveira, 2012; Toussaint et al, 2000).…”

Model-Based Generalization Under Parameter Uncertainty Using Path Integral Control

“…Our approach mirrors model-based optimal control method (in particular ensemble model-based control [13], [14], [15], [16]) which have existed for some time. Specifically, we use an ensemble [17], [18] of physics simulators in receding horizon to generate an optimal control sequence which we apply to the robot. Prior work uses motion primitives and policies [17], [16], or standard trajectory optimization with PD control feedback to handle the ensemble models [18].…”

“…Specifically, we use an ensemble [17], [18] of physics simulators in receding horizon to generate an optimal control sequence which we apply to the robot. Prior work uses motion primitives and policies [17], [16], or standard trajectory optimization with PD control feedback to handle the ensemble models [18]. The main difference is that we utilize the free energy formulation for a stochastic control problem to directly incorporate the uncertainty in the ensemble into synthesis of the control.…”