Daniel E. Koditschek

Exact robot navigation using artificial potential functions

A methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design is presented. Complete information about a freespace and goal is encoded in the form of a special artificial potential function, called a navigation function, that connects the kinematic planning problem with the dynamic execution problem in a provably correct fashion. The navigation function automatically gives rise to a bounded-torque feedback controller for the robots actuators that guarantees collision-free motion and convergence to the destination from almost all initial free configurations. A formula for navigation functions that guide a point-mass robot in a generalized sphere world is developed. The simplest member of this family is a space obtained by puncturing a disk by an arbitrary number of smaller disjoint disks representing obstacles. The other spaces are obtained from this model by a suitable coordinate transformation. Simulation results for planar scenarios are provided. >

RHex: A Simple and Highly Mobile Hexapod Robot

In this paper, the authors describe the design and control of RHex, a power autonomous, untethered, compliant-legged hexapod robot. RHex has only six actuators—one motor located at each hip— achieving mechanical simplicity that promotes reliable and robust operation in real-world tasks. Empirically stable and highly maneuverable locomotion arises from a very simple clock-driven, open-loop tripod gait. The legs rotate full circle, thereby preventing the common problem of toe stubbing in the protraction (swing) phase. An extensive suite of experimental results documents the robot’s significant “intrinsic mobility”—the traversal of rugged, broken, and obstacle-ridden ground without any terrain sensing or actively controlled adaptation. RHex achieves fast and robust forward locomotion traveling at speeds up to one body length per second and traversing height variations well exceeding its body clearance.

Hybrid zero dynamics of planar biped walkers

Planar, underactuated, biped walkers form an important domain of applications for hybrid dynamical systems. This paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree-of-freedom greater than the number of available actuators. The within-step control action creates an attracting invariant set - a two-dimensional zero dynamics submanifold of the full hybrid model

Robot navigation functions on manifolds with boundary

whose restriction dynamics admits a scalar linear time-invariant return map. Exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model. A convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions. Parameter optimization is used to tune the hybrid zero dynamics in order to achieve closed-loop, exponentially stable walking with low energy consumption, while meeting natural kinematic and dynamic constraints. The general theory developed in the paper is illustrated on a five link walker, consisting of a torso and two legs with knees.

Sequential composition of dynamically dexterous robot behaviors

This paper concerns the construction of a class of scalar valued analytic maps on analytic manifolds with boundary. These maps, which we term navigation functions, are constructed on an arbitrary sphere world-a compact connected subset of Euclidean n-space whose boundary is formed from the disjoint union of a finite number of (n - l)-spheres. We show that this class is invariant under composition with analytic diffeomorphisms: our sphere world construction immediately generates a navigation function on all manifolds into which a sphere world is deformable. On the other hand, certain well known results of S. Smale guarantee the existence of smooth navigation functions on any smooth manifold. This suggests that analytic navigation functions exist, as well, on more general analytic manifolds than the deformed sphere worlds we presently consider.

Exact robot navigation by means of potential functions: Some topological considerations

We report on our efforts to develop a sequential robot controller-composition technique in the context of dexterous “batting” maneuvers. A robot with a flat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a specified location. The robot’s reachable workspace is blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.

RHex: A Biologically Inspired Hexapod Runner

The limits in global navigation capability of potential function based robot control algorithms are explored. Elementary tools of algebraic and differential topology are used to advance arguments suggesting the existence of potential functions over a bounded planar region with arbitrary fixed obstacles possessed of a unique local minimum. A class of such potential functions is constructed for certain cases of a planar disk region with an arbitrary number of smaller disks removed.

Natural motion for robot arms

RHex is an untethered, compliant leg hexapod robot that travels at better than one body length per second over terrain few other robots can negotiate at all. Inspired by biomechanics insights into arthropod locomotion, RHex uses a clock excited alternating tripod gait to walk and run in a highly maneuverable and robust manner. We present empirical data establishing that RHex exhibits a dynamical (“bouncing”) gait—its mass center moves in a manner well approximated by trajectories from a Spring Loaded Inverted Pendulum (SLIP)—characteristic of a large and diverse group of running animals, when its central clock, body mass, and leg stiffnesses are appropriately tuned. The SLIP template can function as a useful control guide in developing more complex autonomous locomotion behaviors such as registration via visual servoing, local exploration via visual odometry, obstacle avoidance, and, eventually, global mapping and localization.

Comparative experiments with a new adaptive controller for robot arms

This paper describes some initial steps toward the development of more natural control strategies for free motion of robot arms. The standard lumped parameter dynamical model of an open kinematic chain is shown to be stabilizable by linear feedback, after nonlinear gravitational terms have been cancelled. A new control algorithm is proposed and is shown to drive robot joint positions and velocites asymptotically toward arbitrary time-varying reference trajectories.

Quantifying dynamic stability and maneuverability in legged locomotion.

A model-based adaptive controller and proof of its global asymptotic stability with respect to the standard rigid-body model of robot-arm dynamics are presented. Experimental data from a study of one new and several established globally asymptotically stable adaptive controllers on two very different robot arms: (1) demonstrate the superior tracking performance afforded by the model-based algorithms over conventional PD control; (2) demonstrate and compare the superior performance of adaptive model-based algorithms over their nonadaptive counterparts; (3) reconcile several previous contrasting empirical studies; and (4) examine contexts that compromise their advantage. >