The theory of affordances

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.

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

To plan dynamic, whole-body motions for robots, one conventionally faces the choice between a complex, full-body dynamic model containing every link and actuator of the robot, or a highly simplified model of the robot as a point mass. In this paper we explore a powerful middle ground between these extremes. We exploit the fact that while the full dynamics of humanoid robots are complicated, their centroidal dynamics (the evolution of the angular momentum and the center of mass (COM) position) are much simpler. By treating the dynamics of the robot in centroidal form and directly optimizing the joint trajectories for the actuated degrees of freedom, we arrive at a method that enjoys simpler dynamics, while still having the expressiveness required to handle kinematic constraints such as collision avoidance or reaching to a target. We further require that the robot's COM and angular momentum as computed from the joint trajectories match those given by the centroidal dynamics. This ensures that the dynamics considered by our optimization are equivalent to the full dynamics of the robot, provided that the robot's actuators can supply sufficient torque. We demonstrate that this algorithm is capable of generating highly-dynamic motion plans with examples of a humanoid robot negotiating obstacle course elements and gait optimization for a quadrupedal robot. Additionally, we show that we can plan without pre-specifying the contact sequence by exploiting the complementarity conditions between contact forces and contact distance.

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Whole-body motion planning with centroidal dynamics and full kinematics

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 robot's 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 robot's 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].

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Footstep planning on uneven terrain with mixed-integer convex optimization

The Inverse Kinematics (IK) algorithms implemented in the open-source Orocos Kinematics and Dynamics Library (KDL) are arguably the most widely-used generic IK solvers worldwide. However, KDL's only joint-limit-constrained IK implementation, a pseudoinverse Jacobian IK solver, repeatedly exhibits false-negative failures on various humanoid platforms. In order to find a better IK solver for generic manipulator chains, a variety of open-source, drop-in alternatives have been implemented and evaluated for this paper. This article provides quantitative comparisons, using multiple humanoid platforms, between an improved implementation of the KDL inverse Jacobian algorithm, a set of sequential quadratic programming (SQP) IK algorithms that use a variety of quadratic error metrics, and a combined algorithm that concurrently runs the best performing SQP algorithm and the improved inverse Jacobian implementation. The best alternative IK implementation finds solutions much more often than KDL, is faster on average than KDL for typical manipulation chains, and (when desired) allows tolerances on each Cartesian dimension, further improving speed and convergence when an exact Cartesian pose is not possible and/or necessary.

TRAC-IK: An open-source library for improved solving of generic inverse kinematics

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 robot's 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.

/pdf/an-architecture-for-online-affordance-based-perception-and-gc6fyaftsd.pdf

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

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.

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

Interest in human-robot coexistence, in which humans and robots share a common work volume, is increasing in manufacturing environments. Efficient work coordination requires both awareness of the human pose and a plan of action for both human and robot agents in order to compute robot motion trajectories that synchronize naturally with human motion. In this paper, we present a data-driven approach that synthesizes anticipatory knowledge of both human motions and subsequent action steps in order to predict in real-time the intended target of a human performing a reaching motion. Motion-level anticipatory models are constructed using multiple demonstrations of human reaching motions. We produce a library of motions from human demonstrations, based on a statistical representation of the degrees of freedom of the human arm, using time series analysis, wherein each time step is encoded as a multivariate Gaussian distribution. We demonstrate the benefits of this approach through offline statistical analysis of human motion data. The results indicate a considerable improvement over prior techniques in early prediction, achieving 70% or higher correct classification on average for the first third of the trajectory (<; 500msec). We also indicate proof-of-concept through the demonstration of a human-robot cooperative manipulation task performed with a PR2 robot. Finally, we analyze the quality of task-level anticipatory knowledge required to improve prediction performance early in the human motion trajectory.

Claudia Pérez D'Arpino

Papers

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

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

Fast target prediction of human reaching motion for cooperative human-robot manipulation tasks using time series classification