571 research outputs found
A New Approach to Time-Optimal Path Parameterization based on Reachability Analysis
Time-Optimal Path Parameterization (TOPP) is a well-studied problem in
robotics and has a wide range of applications. There are two main families of
methods to address TOPP: Numerical Integration (NI) and Convex Optimization
(CO). NI-based methods are fast but difficult to implement and suffer from
robustness issues, while CO-based approaches are more robust but at the same
time significantly slower. Here we propose a new approach to TOPP based on
Reachability Analysis (RA). The key insight is to recursively compute reachable
and controllable sets at discretized positions on the path by solving small
Linear Programs (LPs). The resulting algorithm is faster than NI-based methods
and as robust as CO-based ones (100% success rate), as confirmed by extensive
numerical evaluations. Moreover, the proposed approach offers unique additional
benefits: Admissible Velocity Propagation and robustness to parametric
uncertainty can be derived from it in a simple and natural way.Comment: 15 pages, 9 figure
Time-Optimal Path Tracking via Reachability Analysis
Given a geometric path, the Time-Optimal Path Tracking problem consists in
finding the control strategy to traverse the path time-optimally while
regulating tracking errors. A simple yet effective approach to this problem is
to decompose the controller into two components: (i)~a path controller, which
modulates the parameterization of the desired path in an online manner,
yielding a reference trajectory; and (ii)~a tracking controller, which takes
the reference trajectory and outputs joint torques for tracking. However, there
is one major difficulty: the path controller might not find any feasible
reference trajectory that can be tracked by the tracking controller because of
torque bounds. In turn, this results in degraded tracking performances. Here,
we propose a new path controller that is guaranteed to find feasible reference
trajectories by accounting for possible future perturbations. The main
technical tool underlying the proposed controller is Reachability Analysis, a
new method for analyzing path parameterization problems. Simulations show that
the proposed controller outperforms existing methods.Comment: 6 pages, 3 figures, ICRA 201
Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control
This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York
- …