Daniel E. Koditschek

This paper develops a three-degree-of-freedom sagittal-plane hybrid dynamical systems model of a Groucho-style bounding quadrupedal run. Simple within-stance controls using a modular architecture yield a closed-form expression for a family of hybrid limit cycles that represent bounding behavior over a range of user-selected fore-aft speeds as a function of the model’s kinematic and dynamical parameters. Controls acting on the hybrid transitions are structured so as to achieve a cascade composition of in-place bounding driving the fore-aft degree of freedom, thereby decoupling the linearized dynamics of an approximation to the stride map. Careful selection of the feedback channels used to implement these controls affords infinitesimal deadbeat stability, which is relatively robust against parameter mismatch. Experiments with a physical quadruped reasonably closely match the bounding behavior predicted by the hybrid limit cycle and its stable linearized approximation.

Origami processes can generate both rigid and compliant structures from the same homogeneous sheet material. In this article, we advance the origami robotics literature by showing that it is possible to construct an arbitrary rigid kinematic chain with prescribed joint compliance from a single tubular sheet. Our “Kinegami” algorithm converts a Denavit–Hartenberg specification into a single-sheet crease pattern for an equivalent serial robot mechanism by composing origami modules from a catalogue. The algorithm arises from the key observation that tubular origami linkage design reduces to a Dubins path planning problem. The automatically generated structural connections and movable joints that realize the specified design can also be endowed with independent user-specified compliance. We apply the Kinegami algorithm to a number of common robot mechanisms and hand-fold their algorithmically generated single-sheet crease patterns into functioning kinematic chains. We believe this is the first completely automated end-to-end system for converting an abstract manipulator specification into a physically realizable origami design that requires no additional human input.

Brockett's necessary condition yields a test to determine whether a system can be made to stabilize about some operating point via continuous, purely state-dependent feedback. For many real-world systems, however, one wants to stabilize sets which are more general than a single point. One also wants to control such systems to operate safely by making obstacles and other "dangerous" sets repelling. We generalize Brockett's necessary condition to the case of stabilizing general compact subsets having a nonzero Euler characteristic in general ambient state spaces (smooth manifolds). Using this generalization, we also formulate a necessary condition for the existence of "safe" control laws. We illustrate the theory in concrete examples and for some general classes of systems including a broad class of nonholonomically constrained Lagrangian systems. We also show that, for the special case of stabilizing a point, the specialization of our general stabilizability test is stronger than Brockett's.

Translating the center of mass (CoM) while fixing the orientation of a rigid body supported by relatively massless, actuated limbs is a common problem setting in legged robotics. This paper proposes a hierarchical approach to such maneuvers that decouples CoM task planning from body orientation control in sagittal-plane models, thereby exposing a well-studied and computationally effective low dimensional dynamical system that can be used for CoM task planning. The resulting algorithms directly address the control authority (degree of underactuation) available at a given contact mode, enabling a-priori plans with these intuitive, robust pendular dynamics to be formally embedded at the (virtual) CoM of planar floating-torso models, while focusing high gain posture stabilizing feedback upon the body orientation. A series of numerical and empirical examples address single- and multi-legged leaping — transitional maneuvers where only a single brief stance mode is available to load energy into the CoM and guide its direction. We compare our hierarchical method to a model-based model-predictive controller in one of the tasks, demonstrating similar performance with a significantly smaller computational footprint.

Brockett's necessary condition yields a test to determine whether a system can be made to stabilize about some operating point via continuous, purely state-dependent feedback. For many real-world systems, however, one wants to stabilize sets which are more general than a single point. One also wants to control such systems to operate safely by making obstacles and other "dangerous" sets repelling. We generalize Brockett's necessary condition to the case of stabilizing general compact subsets having a nonzero Euler characteristic in general ambient state spaces (smooth manifolds). Using this generalization, we also formulate a necessary condition for the existence of "safe" control laws. We illustrate the theory in concrete examples and for some general classes of systems including a broad class of nonholonomically constrained Lagrangian systems. We also show that, for the special case of stabilizing a point, the specialization of our general stabilizability test is stronger than Brockett's.

This article solves the planar navigation problem by recourse to an online reactive scheme that exploits recent advances in simultaneous localization and mapping (SLAM) and visual object recognition to recast prior geometric knowledge in terms of an offline catalog of familiar objects. The resulting vector field planner guarantees convergence to an arbitrarily specified goal, avoiding collisions along the way with fixed but arbitrarily placed instances from the catalog as well as completely unknown fixed obstacles so long as they are strongly convex and well separated. We illustrate the generic robustness properties of such deterministic reactive planners as well as the relatively modest computational cost of this algorithm by supplementing an extensive numerical study with physical implementation on both a wheeled and legged platform in different settings.

In this article, we physically demonstrate a reactive sensorimotor architecture for mobile robots whose behaviors are generated by motivation dynamics. Motivation dynamics uses a continuous dynamical system to reactively compose low-level control vector fields using valuation functions that capture the potentially competing influences of external stimuli relative to the system’s own internal state. We show that motivation dynamics naturally accommodates external stimuli through standard signal processing tools, and can effectively encode a repetitive higher level task by composing several low-level controllers to achieve a limit cycle in which the robot repeatedly navigates toward two alternatively valuable goal locations in a commensurately alternating order. We show that these behaviors are robust to perturbations, including imperfect models of robot kinematics, sensor noise, and disturbances, resulting from the need to traverse difficult terrain. We argue that motivation dynamics can provide a useful alternative to controllers based on hybrid automata in situations where the control operates at a low level close to the physical hardware.