Related papers: Complexity of control-affine motion planning
We present complexity results regarding a matching-type problem related to structural controllability of dynamical systems modelled on graphs. Controllability of a dynamical system is the ability to choose certain inputs in order to drive…
Approximate simulation, an extension of simulation relations from formal methods to continuous systems, is a powerful tool for hierarchical control of complex systems. Finding an approximate simulation relation between the full "concrete"…
Reliable real-time planning for robots is essential in today's rapidly expanding automated ecosystem. In such environments, traditional methods that plan by relaxing constraints become unreliable or slow-down for kinematically constrained…
Virtual constraints are relations imposed in a control system that become invariant via feedback, instead of real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…
We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
Farber and Rudyak introduced topological complexity $\mathbf{TC}(X)$ of motion planning and its higher analogs $\mathbf{TC}_n(X)$ to measure the complexity of assigning paths to point tuples. Motivated by motion planning where a robotic…
We compute the higher topological complexity of ordered configuration spaces of orientable surfaces, thus extending Cohen-Farber's description of the ordinary topological complexity of those spaces.
This paper explores general multi-robot task and motion planning, where multiple robots in close proximity manipulate objects while satisfying constraints and a given goal. In particular, we formulate the plan refinement problem--which,…
The topological complexity TC(X) is a homotopy invariant which reflects the complexity of the problem of constructing a motion planning algorithm in the space X, viewed as configuration space of a mechanical system. In this paper we…
In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost…
The early classifications of the computational complexity of planning under various restrictions in STRIPS (Bylander) and SAS+ (Baeckstroem and Nebel) have influenced following research in planning in many ways. We go back and reanalyse…
This work explores the trade-off between the number of samples required to accurately build models of dynamical systems and the degradation of performance in various control objectives due to a coarse approximation. In particular, we show…
This paper considers the problem of robot motion planning in a workspace with obstacles for systems with uncertain 2nd-order dynamics. In particular, we combine closed form potential-based feedback controllers with adaptive control…
In this paper we generalize the discrete r-homotopy to the discrete (s, r)-homotopy. Then by this notion, we introduce the discrete motion planning for robots which can move discreetly. Moreover, in this case the number of motion planning,…
The motion planning problem is a fundamental problem in robotics, so that every autonomous robot should be able to deal with it. A number of solutions have been proposed and a probabilistic one seems to be quite reasonable. However, here we…
This article addresses the obstacle avoidance problem for setpoint stabilization and path-following tasks in complex dynamic 2D environments that go beyond conventional scenes with isolated convex obstacles. A combined motion planner and…
The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…