Motion planning around obstacles with convex optimization.

From quadrotors delivering packages in urban areas to robot arms moving in confined warehouses, motion planning around obstacles is a core challenge in modern robotics. Planners based on optimization can design trajectories in high-dimensional spaces while satisfying the robot dynamics. However, in the presence of obstacles, these optimization problems become nonconvex and very hard to solve, even just locally. Thus, when facing cluttered environments, roboticists typically fall back to sampling-based planners that do not scale equally well to high dimensions and struggle with continuous differential constraints. Here, we present a framework that enables convex optimization to efficiently and reliably plan trajectories around obstacles. Specifically, we focus on collision-free motion planning with costs and constraints on the shape, the duration, and the velocity of the trajectory. Using recent techniques for finding shortest paths in Graphs of Convex Sets (GCS), we design a practical convex relaxation of the planning problem. We show that this relaxation is typically very tight, to the point that a cheap postprocessing of its solution is almost always sufficient to identify a collision-free trajectory that is globally optimal (within the parameterized class of curves). Through numerical and hardware experiments, we demonstrate that our planner, which we name GCS, can find better trajectories in less time than widely used sampling-based algorithms and can reliably design trajectories in high-dimensional complex environments.

Robust post-stall perching with a simple fixed-wing glider using LQR-Trees.

Birds routinely execute post-stall maneuvers with a speed and precision far beyond the capabilities of our best aircraft control systems. One remarkable example is a bird exploiting post-stall pressure drag in order to rapidly decelerate to land on a perch. Stall is typically associated with a loss of control authority, and it is tempting to attribute this agility of birds to the intricate morphology of the wings and tail, to their precision sensing apparatus, or their ability to perform thrust vectoring. Here we ask whether an extremely simple fixed-wing glider (no propeller) with only a single actuator in the tail is capable of landing precisely on a perch from a large range of initial conditions. To answer this question, we focus on the design of the flight control system; building upon previous work which used linear feedback control design based on quadratic regulators (LQR), we develop nonlinear feedback control based on nonlinear model-predictive control and 'LQR-Trees'. Through simulation using a flat-plate model of the glider, we find that both nonlinear methods are capable of achieving an accurate bird-like perching maneuver from a large range of initial conditions; the 'LQR-Trees' algorithm is particularly useful due to its low computational burden at runtime and its inherent performance guarantees. With this in mind, we then implement the 'LQR-Trees' algorithm on real hardware and demonstrate a 95 percent perching success rate over 147 flights for a wide range of initial speeds. These results suggest that, at least in the absence of significant disturbances like wind gusts, complex wing morphology and sensing are not strictly required to achieve accurate and robust perching even in the post-stall flow regime.

Efficient bipedal robots based on passive-dynamic walkers.

Passive-dynamic walkers are simple mechanical devices, composed of solid parts connected by joints, that walk stably down a slope. They have no motors or controllers, yet can have remarkably humanlike motions. This suggests that these machines are useful models of human locomotion; however, they cannot walk on level ground. Here we present three robots based on passive-dynamics, with small active power sources substituted for gravity, which can walk on level ground. These robots use less control and less energy than other powered robots, yet walk more naturally, further suggesting the importance of passive-dynamics in human locomotion.