arXiv subjects

Charles Dawson

Publications and source records attributed to Charles Dawson.

22 records · Page 2Linked to original sources

arXiv2021

Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions

Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models. We develop a model-based learning approach to synthesize robust feedback controllers with safety and stability guarantees. We take inspiration from robust convex optimization and Lyapunov theory to define robust control Lyapunov barrier functions that generalize despite model uncertainty. We demonstrate our approach in simulation on problems including car trajectory tracking, nonlinear control with obstacle avoidance, satellite rendezvous with safety constraints, and flight control with a learned ground effect model. Simulation results show that our approach yields controllers that match or exceed the capabilities of robust MPC while reducing computational costs by an order of magnitude.

eess.SY↗

arXiv2020

Fast Certification of Collision Probability Bounds with Uncertain Convex Obstacles

To operate reactively in uncertain environments, robots need to be able to quickly estimate the risk that they will collide with their environment. This ability is important for both planning (to ensure that plans maintain acceptable levels of safety) and execution (to provide real-time warnings when risk exceeds some threshold). Existing methods for estimating this risk are often limited to models with simplified geometry (e.g. point robots); others handle complex geometry but are too slow for many applications. In this paper, we present two algorithms for quickly computing upper bounds on the risk of collision between a robot and uncertain obstacles by searching for certificate regions that capture collision probability mass while avoiding the robot. These algorithms come with strong theoretical guarantees that the true risk does not exceed the estimated value, support arbitrary geometry via convex decomposition, and provide fast query times ($<200μ$s) in representative scenarios. We characterize the performance of these algorithms in environments of varying complexity, demonstrating at least an order of magnitude speedup over existing techniques.

cs.RO↗

arXiv2020

Provably Safe Trajectory Optimization in the Presence of Uncertain Convex Obstacles

Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of safety as the robot moves, even when the exact locations of nearby obstacles are not known. In this paper, we solve this chance-constrained motion planning problem using a sequential convex optimization framework. To constrain the risk of collision incurred by planned movements, we employ geometric objects called $ε$-shadows to compute upper bounds on the risk of collision between the robot and uncertain obstacles. We use these $ε$-shadow-based estimates as constraints in a nonlinear trajectory optimization problem, which we then solve by iteratively linearizing the non-convex risk constraints. This sequential optimization approach quickly finds trajectories that accomplish the desired motion while maintaining a user-specified limit on collision risk. Our method can be applied to robots and environments with arbitrary convex geometry; even in complex environments, it runs in less than a second and provides provable guarantees on the safety of planned trajectories, enabling fast, reactive, and safe robot motion in realistic environments.

cs.RO↗

arXiv2019

Magnetic properties of double perovskite $Ln_2$CoIrO$_6$ ($Ln$ = Eu, Tb, Ho): hetero-tri-spin $3d$-$5d$-$4f$ systems

The field of double perovskites is now advancing to three magnetic elements on the A, B and B$'$ sites. A series of iridium-based double perovskite compounds, $Ln_2$CoIrO$_6$ ($Ln$ = Eu, Tb, Ho) with three magnetic elements were synthesized as polycrystalline samples. The compounds crystalize in monoclinic structures with the space group $P2_1/n$. Magnetic properties of these hetero-tri-spin $3d$-$5d$-$4f$ systems were studied by magnetic susceptibility and field dependent magnetization in both DC and pulsed magnetic fields. All these compounds show ferrimagnetic transitions at temperatures $T_C$ above 100 K, which are attributable to antiferromagnetic coupling between Co$^{2+}$ and Ir$^{4+}$ spins. For Eu$_2$CoIrO$_6$, the magnetic properties are similar to those of La$_2$CoIrO$_6$. The Eu$^{3+}$ spins show Van Vleck paramagnetism that don't significantly interact with transition-metal cations. By contrast, Tb$_2$CoIrO$_6$ and Ho$_2$CoIrO$_6$ reveal a second transition to antiferromagnetic order below a lower temperature $T_N$. The temperature-induced ferrimagnetic-to-antiferromagnetic phase transition might be explained by a spin-reorientation transition. Moreover, a magnetic-field-induced spin-flop transition with a small hysteresis was observed below $T_N$ in these two compounds. The magnetic moment of all three compounds do not saturate up to 60 T at low temperatures. Moderate magnetocaloric effect was also observed in all three compounds. Our results should motivate further investigation of the spin configuration on single crystals of these iridium-based double perovskites.

cond-mat.mtrl-sci↗