Jack Umenberger

Real-time planning with primitives for dynamic walking over uneven terrain.

We present an algorithm for receding-horizon motion planning using a finite family of motion primitives for underactuated dynamic walking over uneven terrain. The motion primitives are defined as virtual holonomic constraints, and the special structure of underactuated mechanical systems operating subject to virtual constraints is used to construct closed-form solutions and a special binary search tree that dramatically speed up motion planning. We propose a greedy depth-first search and discuss improvement using energy-based heuristics. The resulting algorithm can plan several footsteps ahead in a fraction of a second for both the compass-gait walker and a planar 7-Degree-of-freedom/five-link walker.

System identification and control of a small-scale paramotor

This paper presents a methodology for the system identification of a light weight, small-scale parafoil suspended motorized aircraft, known as a paramotor. The study is concerned with the acquisition of linear models describing both the lateral and longitudinal dynamics of the aircraft, with an emphasis on practical techniques that can be implemented in the real world. The mathematical models developed in this paper are first validated by comparison with real flight data, before being employed in the design of a guidance, navigation and control system, the performance of which is demonstrated by real autonomous flight tests.

Scalable identification of stable positive systems

Positive systems frequently appear in applications, and enjoy substantially simplified analysis and control design compared to the general LTI case. In this paper we construct a polytopic parameterization of all stable positive systems, and a convex upper bound for simulation error (a.k.a. output error) for which the resulting optimization is a linear program. Previous work on analogous methods for both the positive and general LTI case result in semidefinite programs. We exploit the decomposability of the constraints in these linear programs to develop distributed solutions applicable to identification of large-scale networked systems.

Specialized algorithm for identification of stable linear systems using Lagrangian relaxation

Recently Lagrangian relaxation has been used to generate convex approximations of the challenging simulation error minimization problem arising in system identification. In this paper, we present a specialized algorithm to optimize the convex bounds generated by Lagrangian relaxation, applicable to linear state-space models. The algorithm demonstrates superior scalability over general-purpose semidefinite programming solvers. In addition, we show empirically that Lagrangian relaxation is more resilient to a biasing effect commonly observed in other identification methods that guarantee model stability.

Maximum likelihood identification of stable linear dynamical systems

This paper concerns maximum likelihood identification of linear time invariant state space models, subject to model stability constraints. We combine Expectation Maximization (EM) and Lagrangian re ...