Robin Deits

Optimization-based locomotion planning, estimation, and control design for the atlas humanoid robot

This paper describes a collection of optimization algorithms for achieving dynamic planning, control, and state estimation for a bipedal robot designed to operate reliably in complex environments. To make challenging locomotion tasks tractable, we describe several novel applications of convex, mixed-integer, and sparse nonlinear optimization to problems ranging from footstep placement to whole-body planning and control. We also present a state estimator formulation that, when combined with our walking controller, permits highly precise execution of extended walking plans over non-flat terrain. We describe our complete system integration and experiments carried out on Atlas, a full-size hydraulic humanoid robot built by Boston Dynamics, Inc.

Footstep planning on uneven terrain with mixed-integer convex optimization

We present a new method for planning footstep placements for a robot walking on uneven terrain with obstacles, using a mixed-integer quadratically-constrained quadratic program (MIQCQP). Our approach is unique in that it handles obstacle avoidance, kinematic reachability, and rotation of footstep placements, which typically have required non-convex constraints, in a single mixed-integer optimization that can be efficiently solved to its global optimum. Reachability is enforced through a convex inner approximation of the reachable space for the robots feet. Rotation of the footsteps is handled by a piecewise linear approximation of sine and cosine, designed to ensure that the approximation never overestimates the robots reachability. Obstacle avoidance is ensured by decomposing the environment into convex regions of obstacle-free configuration space and assigning each footstep to one such safe region. We demonstrate this technique in simple 2D and 3D environments and with real environments sensed by a humanoid robot. We also discuss computational performance of the algorithm, which is currently capable of planning short sequences of a few steps in under one second or longer sequences of 10-30 footsteps in tens of seconds to minutes on common laptop computer hardware. Our implementation is available within the Drake MATLAB toolbox [1].

An Architecture for Online Affordance-based Perception and Whole-body Planning

The DARPA Robotics Challenge Trials held in December 2013 provided a landmark demonstration of dexterous mobile robots executing a variety of tasks aided by a remote human operator using only data from the robots sensor suite transmitted over a constrained, field-realistic communications link. We describe the design considerations, architecture, implementation, and performance of the software that Team MIT developed to command and control an Atlas humanoid robot. Our design emphasized human interaction with an efficient motion planner, where operators expressed desired robot actions in terms of affordances fit using perception and manipulated in a custom user interface. We highlight several important lessons we learned while developing our system on a highly compressed schedule.

Computing Large Convex Regions of Obstacle-Free Space Through Semidefinite Programming

This paper presents iris (Iterative Regional Inflation by Semidefinite programming), a new method for quickly computing large polytopic and ellipsoidal regions of obstacle-free space through a series of convex optimizations . These regions can be used, for example, to efficiently optimize an objective over collision-free positions in space for a robot manipulator. The algorithm alternates between two convex optimizations: (1) a quadratic program that generates a set of hyperplanes to separate a convex region of space from the set of obstacles and (2) a semidefinite program that finds a maximum-volume ellipsoid inside the polytope intersection of the obstacle-free half-spaces defined by those hyperplanes. Both the hyperplanes and the ellipsoid are refined over several iterations to monotonically increase the volume of the inscribed ellipsoid, resulting in a large polytope and ellipsoid of obstacle-free space. Practical applications of the algorithm are presented in 2D and 3D, and extensions to \(N\)-dimensional configuration spaces are discussed. Experiments demonstrate that the algorithm has a computation time which is linear in the number of obstacles, and our matlab [18] implementation converges in seconds for environments with millions of obstacles.

Efficient mixed-integer planning for UAVs in cluttered environments

We present a new approach to the design of smooth trajectories for quadrotor unmanned aerial vehicles (UAVs), which are free of collisions with obstacles along their entire length. To avoid the non-convex constraints normally required for obstacle-avoidance, we perform a mixed-integer optimization in which polynomial trajectories are assigned to convex regions which are known to be obstacle-free. Prior approaches have used the faces of the obstacles themselves to define these convex regions. We instead use IRIS, a recently developed technique for greedy convex segmentation [1], to pre-compute convex regions of safe space. This results in a substantially reduced number of integer variables, which improves the speed with which the optimization can be solved to its global optimum, even for tens or hundreds of obstacle faces. In addition, prior approaches have typically enforced obstacle avoidance at a finite set of sample or knot points. We introduce a technique based on sums-of-squares (SOS) programming that allows us to ensure that the entire piecewise polynomial trajectory is free of collisions using convex constraints. We demonstrate this technique in 2D and in 3D using a dynamical model in the Drake toolbox for Matlab [2].

Localized fluidization burrowing mechanics of Ensis directus

SUMMARY Muscle measurements of Ensis directus, the Atlantic razor clam, indicate that the organism only has sufficient strength to burrow a few centimeters into the soil, yet razor clams burrow to over 70 cm. In this paper, we show that the animal uses the motions of its valves to locally fluidize the surrounding soil and reduce burrowing drag. Substrate deformations were measured using particle image velocimetry (PIV) in a novel visualization system that enabled us to see through the soil and watch E. directus burrow in situ. PIV data, supported by soil and fluid mechanics theory, show that contraction of the valves of E. directus locally fluidizes the surrounding soil. Particle and fluid mixtures can be modeled as a Newtonian fluid with an effective viscosity based on the local void fraction. Using these models, we demonstrate that E. directus is strong enough to reach full burrow depth in fluidized soil, but not in static soil. Furthermore, we show that the method of localized fluidization reduces the amount of energy required to reach burrow depth by an order of magnitude compared with penetrating static soil, and leads to a burrowing energy that scales linearly with depth rather than with depth squared.

Continuous humanoid locomotion over uneven terrain using stereo fusion

For humanoid robots to fulfill their mobility potential they must demonstrate reliable and efficient locomotion over rugged and irregular terrain. In this paper we present the perception and planning algorithms which have allowed a humanoid robot to use only passive stereo imagery (as opposed to actuating a laser range sensor) to safely plan footsteps to continuously walk over rough and uneven surfaces without stopping. The perception system continuously integrates stereo imagery to build a consistent 3D model of the terrain which is then used by our footstep planner which reasons about obstacle avoidance, kinematic reachability and foot rotation through mixed-integer quadratic optimization to plan the required step positions. We illustrate that our stereo imagery fusion approach can measure the walking terrain with sufficient accuracy that it matches the quality of terrain estimates from LIDAR. To our knowledge this is the first such demonstration of the use of computer vision to carry out general purpose terrain estimation on a locomoting robot - and additionally to do so in continuous motion. A particular integration challenge was ensuring that these two computationally intensive systems operate with minimal latency (below 1 second) to allow re-planning while walking. The results of extensive experimentation and quantitative analysis are also presented. Our results indicate that a laser range sensor is not necessary to achieve locomotion in these challenging situations.

Aggressive quadrotor flight through cluttered environments using mixed integer programming

Quadrotor flight has typically been limited to sparse environments due to numerical complications that arise when dealing with large numbers of obstacles. We hypothesized that it would be possible to plan and robustly execute trajectories in obstacle-dense environments using the novel Iterative Regional Inflation by Semidefinite programming algorithm (IRIS), mixed-integer semidefinite programs (MISDP), and model-based control. Unlike sampling-based approaches, the planning algorithm first introduced by Deits theoretically guarantees non-penetration of the trajectories even with small obstacles such as strings. We present experimental validation of this claim by aggressively flying a small quadrotor (34g, 92mm rotor to rotor) in a series of indoor environments including a cubic meter volume containing 20 interwoven strings, and present the control architecture we developed to do so.

Director: A User Interface Designed for Robot Operation with Shared Autonomy

Operating a high degree of freedom mobile manipulator, such as a humanoid, in a field scenario requires constant situational awareness, capable perception modules, and effective mechanisms for interactive motion planning and control. A well-designed operator interface presents the operator with enough context to quickly carry out a mission and the flexibility to handle unforeseen operating scenarios robustly. By contrast, an unintuitive user interface can increase the risk of catastrophic operator error by overwhelming the user with unnecessary information. With these principles in mind, we present the philosophy and design decisions behind Director-the open-source user interface developed by Team MIT to pilot the Atlas robot in the DARPA Robotics Challenge DRC. At the heart of Director is an integrated task execution system that specifies sequences of actions needed to achieve a substantive task, such as drilling a wall or climbing a staircase. These task sequences, developed a priori, make online queries to automated perception and planning algorithms with outputs that can be reviewed by the operator and executed by our whole-body controller. Our use of Director at the DRC resulted in efficient high-level task operation while being fully competitive with approaches focusing on teleoperation by highly trained operators. We discuss the primary interface elements that comprise Director, and we provide an analysis of its successful use at the DRC.

Critical Timescales for Burrowing in Undersea Substrates via Localized Fluidization, Demonstrated by RoboClam: A Robot Inspired by Atlantic Razor Clams

The Atlantic razor clam (Ensis directus) burrows into underwater soil by using motions of its shell to locally fluidize the surrounding substrate. The energy associated with movement through fluidized soil — characterized by a depth-independent density and viscosity — scales linearly with depth. In contrast, moving through static soil requires energy that scales with depth squared. For E. directus, this translates to a 10X reduction in the energy required to reach observed burrow depths. For engineers, localized fluidization offers a mechanically simple and purely kinematic method to dramatically reduce burrowing energy. This concept is demonstrated with RoboClam, an E. directus-inspired robot. Using a genetic algorithm to generate digging kinematics, RoboClam has achieved localized fluidization and burrowing performance comparable to that of the animal, with a linear energy-depth relationship. In this paper, we present the critical timescales and associated kinematics necessary for achieving localized fluidization, which are calculated from soil parameters and validated via RoboClam and E. directus testing.Copyright