Frank Noble Permenter

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.

An efficiently solvable quadratic program for stabilizing dynamic locomotion

We describe a whole-body dynamic walking controller implemented as a convex quadratic program. The controller solves an optimal control problem using an approximate value function derived from a simple walking model while respecting the dynamic, input, and contact constraints of the full robot dynamics. By exploiting sparsity and temporal structure in the optimization with a custom active-set algorithm, we surpass the performance of the best available off-the-shelf solvers and achieve 1kHz control rates for a 34-DOF humanoid. We describe applications to balancing and walking tasks using the simulated Atlas robot in the DARPA Virtual Robotics Challenge.

Using Bayesian Filtering to Localize Flexible Materials During Manipulation

Localization and manipulation of features such as buttons, snaps, or grommets embedded in fabrics and other flexible materials is a difficult robotics problem. Approaches that rely too much on sensing and localization that occurs before touching the material are likely to fail because the flexible material can move when the robot actually makes contact. This paper experimentally explores the possibility to use proprioceptive and load-based tactile information to localize features embedded in flexible materials during robot manipulation. In our experiments, Robonaut 2, a robot with human-like hands and arms, uses particle filtering to localize features based on proprioceptive and tactile measurements. Our main contribution is to propose a method to interact with flexible materials that reduces the state space of the interaction by forcing the material to comply in repeatable ways. Measurements are matched to a “haptic map,” which is created during a training phase, that describes expected measurements as a low-dimensional function of state. We evaluate localization performance when using proprioceptive information alone and when tactile data are also available. The two types of measurements are shown to contain complementary information. We find that the tactile measurement model is critical to localization performance and propose a series of models that offer increasingly better accuracy. Finally, this paper explores the localization approach in the context of two flexible material insertion tasks that are relevant to manufacturing applications.

Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone

We develop a practical semidefinite programming (SDP) facial reduction procedure that utilizes computationally efficient approximations of the positive semidefinite cone. The proposed method simplifies SDPs with no strictly feasible solution (a frequent output of parsers) by solving a sequence of easier optimization problems and could be a useful pre-processing technique for SDP solvers. We demonstrate effectiveness of the method on SDPs arising in practice, and describe our publicly-available software implementation. We also show how to find maximum rank matrices in our PSD cone approximations (which helps us find maximal simplifications), and we give a post-processing procedure for dual solution recovery that generally applies to facial-reduction-based pre-processing techniques. Finally, we show how approximations can be chosen to preserve problem sparsity.

Basis selection for SOS programs via facial reduction and polyhedral approximations

We develop a monomial basis selection procedure for sum-of-squares (SOS) programs based on facial reduction. Using linear programming and polyhedral approximations, the proposed technique finds a face of the SOS cone containing the feasible set of a given SOS program. The identified face in turn identifies a set of monomials that can be used to convert the SOS program into a semidefinite program (SDP). The technique can be viewed as a generalization of standard parsing algorithms for monomial basis selection. As we illustrate with examples, the proposed method can lead to smaller SDPs that are simpler to solve.

Solving Conic Optimization Problems via Self-Dual Embedding and Facial Reduction: A Unified Approach

We establish connections between the facial reduction algorithm of Borwein and Wolkowicz and the self-dual homogeneous model of Goldman and Tucker when applied to conic optimization problems. Specifically, we show that the self-dual homogeneous model returns facial reduction certificates when it fails to return a primal-dual optimal solution or a certificate of infeasibility. Using this observation, we give an algorithm based on facial reduction for solving the primal problem that, in principle, always succeeds. (An analogous algorithm is easily stated for the dual problem.) This algorithm has the appealing property that it only performs facial reduction when it is required, not when it is possible; e.g., if a primal-dual optimal solution exists, it will be found in lieu of a facial reduction certificate even if Slaters condition fails. For the case of linear, second-order, and semidefinite optimization, we show that the algorithm can be implemented by assuming oracle access to the central-path limit poi...

Selecting a monomial basis for sums of squares programming over a quotient ring

In this paper we describe a method for choosing a “good” monomial basis for a sums of squares (SOS) program formulated over a quotient ring. It is known that the monomial basis need only include standard monomials with respect to a Groebner basis. We show that in many cases it is possible to use a reduced subset of standard monomials by combining Groebner basis techniques with the well-known Newton polytope reduction. This reduced subset of standard monomials yields a smaller semidefinite program for obtaining a certificate of non-negativity of a polynomial on an algebraic variety.

A miniature load cell suitable for mounting on the phalanges of human-sized robot fingers

It is frequently accepted that tactile sensing must play a key role in robust manipulation and assembly. The potential exists to complement the gross shape information that vision or range sensors can provide with fine-scale information about the texture, stiffness, and shape of the object grasped. Nevertheless, no widely accepted tactile sensing technology currently exists for robot hands. Furthermore, while several proposals exist in the robotics literature regarding how to use tactile sensors to improve manipulation, there is little consensus. This paper describes the electro-mechanical design of the Robonaut 2 phalange load cell. This is a miniature load cell suitable for mounting on the phalanges of humanoid robot fingers. The important design characteristics of these load cells are the shape of the load cell spring element and the routing of small-gauge wires from the sensor onto a circuit board. The paper reports results from a stress analysis of the spring element and establishes the theoretical sensitivity of the device to loads in different directions. The paper also compares calibrated load cell data to ground truth load measurements for four different manufactured sensors. Finally, the paper analyzes the response of the load cells in the context of a flexible materials localization task.

Position control of tendon-driven fingers with position controlled actuators

Conventionally, tendon-driven manipulators implement some force-based controller using either tension feedback or dynamic models of the actuator. The force control allows the system to maintain proper tensions on the tendons. In some cases, whether it is due to the lack of tension feedback or actuator torque control, a purely position-based controller is needed. This work compares three position controllers for tendon-driven manipulators that implement a nested actuator position controller. A new controller is introduced that achieves the best overall performance with regards to speed, accuracy, and transient behavior. To compensate for the lack of tension control, the controller nominally maintains the internal tension on the tendons through a range-space constraint on the actuator positions. These control laws are validated experimentally on the Robonaut-2 humanoid hand.

A numerical algebraic geometry approach to regional stability analysis of polynomial systems

We explore region of attraction (ROA) estimation for polynomial systems via the numerical solution of polynomial equations. Computing an optimal, stable sub-level set of a Lyapunov function is first posed as a polynomial optimization problem. Solutions to this optimization problem are found by solving a polynomial system of equations using techniques from numerical algebraic geometry. This system describes KKT points and singular points not satisfying a regularity condition. Though this system has exponentially many solutions, the proposed method trivially parallelizes and is practical for problems of moderate dimension and degree. In suitably generic settings, the method can solve the underlying optimization problem to arbitrary precision, which could make it a useful tool for studying popular semidefinite programming based relaxations used in ROA analysis.