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.Comment: Conference submissio

Nonlinear control methods for planar carangiform robot fish locomotion

Considers the design of motion control algorithms for robot fish. We present modeling, control design, and experimental trajectory tracking results for an experimental planar robotic fish system that is propelled using carangiform-like locomotion. Our model for the fish's propulsion is based on quasi-steady fluid flow. Using this model, we propose gaits for forward and turning trajectories and analyze system response under such control strategies. Our models and predictions are verified by experiment

Characterization of Local Configuration Controllability for a Class of Mechanical Systems

We investigate local configuration controllability for mechanical control systems within the affine connection formalism. Extending the work by Lewis for the single-input case, we are able to characterize local configuration controllability for systems with $n$ degrees of freedom and $n-1$ input forces.Comment: 20 pages, no figure

New developments on the Geometric Nonholonomic Integrator

In this paper, we will discuss new developments regarding the Geometric Nonholonomic Integrator (GNI) [23, 24]. GNI is a discretization scheme adapted to nonholonomic mechanical systems through a discrete geometric approach. This method was designed to account for some of the special geometric structures associated to a nonholonomic motion, like preservation of energy, preservation of constraints or the nonholonomic momentum equation. First, we study the GNI versions of the symplectic-Euler methods, paying special attention to their convergence behavior. Then, we construct an extension of the GNI in the case of affine constraints. Finally, we generalize the proposed method to nonholonomic reduced systems, an important subclass of examples in nonholonomic dynamics. We illustrate the behavior of the proposed method with the example of the Chaplygin sphere, which accounts for the last two features, namely it is both a reduced and an affine system.Comment: 28 pages. v2: Added references and the example of the Chaplygin spher

Flat systems, equivalence and trajectory generation

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft

The Signals and Systems Approach to Animation

Animation is ubiquitous in visualization systems, and a common technique for creating these animations is the transition. In the transition approach, animations are created by smoothly interpolating a visual attribute between a start and end value, reaching the end value after a specified duration. This approach works well when each transition for an attribute is allowed to finish before the next is triggered, but performs poorly when a new transition is triggered before the current transition has finished. In particular, interruptions introduce velocity discontinuities, and frequent interruptions can slow down the resulting animation. To solve these problems, we model the problem of animation as a signal processing problem. In our technique, animations are produced by transformations of signals, or functions over time. In particular, an animation is produced by transforming an input signal, a function from time to target attribute value, into an output signal, a function from time to displayed attribute value. We show that well-known signal-processing techniques can be applied to produce animations that are free from velocity discontinuities even when interrupted

On stabilization of nonlinear systems with drift by time-varying feedback laws

This paper deals with the stabilization problem for nonlinear control-affine systems with the use of oscillating feedback controls. We assume that the local controllability around the origin is guaranteed by the rank condition with Lie brackets of length up to 3. This class of systems includes, in particular, mathematical models of rotating rigid bodies. We propose an explicit control design scheme with time-varying trigonometric polynomials whose coefficients depend on the state of the system. The above coefficients are computed in terms of the inversion of the matrix appearing in the controllability condition. It is shown that the proposed controllers can be used to solve the stabilization problem by exploiting the Chen-Fliess expansion of solutions of the closed-loop system. We also present results of numerical simulations for controlled Euler's equations and a mathematical model of underwater vehicle to illustrate the efficiency of the obtained controllers.Comment: This is the author's version of the manuscript accepted for publication in the Proceedings of the 12th International Workshop on Robot Motion Control (RoMoCo'19

Learning How to Autonomously Race a Car: a Predictive Control Approach

In this paper we present a Learning Model Predictive Controller (LMPC) for autonomous racing. We model the autonomous racing problem as a minimum time iterative control task, where an iteration corresponds to a lap. In the proposed approach at each lap the race time does not increase compared to the previous lap. The system trajectory and input sequence of each lap are stored and used to systematically update the controller for the next lap. The first contribution of the paper is to propose a LMPC strategy which reduces the computational burden associated with existing LMPC strategies. In particular, we show how to construct a safe set and an approximation to the value function, using a subset of the stored data. The second contribution is to present a system identification strategy for the autonomous racing iterative control task. We use data from previous iterations and the vehicle's kinematics equations to build an affine time-varying prediction model. The effectiveness of the proposed strategy is demonstrated by experimental results on the Berkeley Autonomous Race Car (BARC) platform

Singular trajectories in multi-input time-optimal problems: Application to controlled mechanical systems

This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain special properties. These properties are explored and are used in conjunction with the Pontryagin maximum principle to determine the structure of singular extremals and, in particular, time-optimal trajectories. The theory is illustrated with an application to a time-optimal problem for a class of underwater vehiclesComment: See http://www.math.rutgers.edu/~sontag for related wor

A Polyhedral Bound on the Indeterminate Contact Forces in Planar Quasi-Rigid Fixturing and Grasping Arrangements

This paper considers multiple-contact arrangements where several bodies grasp, fixture, or support an object via frictional point contacts. Within a strictly rigid-body modeling paradigm, when an external wrench (i.e., force and torque) acts on the object, the reaction forces at the contacts are typically indeterminate and span an unbounded linear space. This paper analyzes the contact reaction forces within a generalized quasi-rigid-body framework that keeps the desirable geometric properties of rigid-body modeling, while also including more realistic physical effects. We describe two basic principles that govern the contact mechanics of quasi-rigid bodies. The main result is that for any given external wrench acting on a quasi-rigid object, the statically feasible contact reaction forces lie in a bounded polyhedral set that depends on the external wrench, the grasp's geometry, and the preload forces. Moreover, the bound does not depend upon any detailed knowledge of the contact mechanics parameters. When some knowledge of the parameters is available, the bound can be sharpened. The polyhedral bound is useful for “robust” grasp and fixture synthesis. Given a set of external wrenches that may act upon an object, the grasp's geometry and preload forces can be chosen such that all of these external wrenches would be automatically supported by the contacts