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

An Efficiently Solvable Quadratic Program for Stabilizing Dynamic Locomotion

We describe a whole-body dynamic walking controller implemented as a convex quadratic program. The controller solves an optimal control problem using an approximate value function derived from a simple walking model while respecting the dynamic, input, and contact constraints of the full robot dynamics. By exploiting sparsity and temporal structure in the optimization with a custom active-set algorithm, we surpass the performance of the best available off-the-shelf solvers and achieve 1kHz control rates for a 34-DOF humanoid. We describe applications to balancing and walking tasks using the simulated Atlas robot in the DARPA Virtual Robotics Challenge.Comment: 6 pages, published at ICRA 201

A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control

This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward initialization and a closed-loop forward integration. All algorithms have similar computational complexity, i.e. linear complexity in the time horizon, and can be derived in the same computational framework. We compare the full-step variants of our algorithms and present several simulation examples, including a high-dimensional underactuated robot subject to contact switches. Simulation results show that our multiple-shooting algorithms can achieve faster convergence, better local contraction rates and much shorter runtimes than classical iLQR, which makes them a superior choice for nonlinear model predictive control applications.Comment: 8 page

Graceful Navigation for Mobile Robots in Dynamic and Uncertain Environments.

The ability to navigate in everyday environments is a fundamental and necessary skill for any autonomous mobile agent that is intended to work with human users. The presence of pedestrians and other dynamic objects, however, makes the environment inherently dynamic and uncertain. To navigate in such environments, an agent must reason about the near future and make an optimal decision at each time step so that it can move safely toward the goal. Furthermore, for any application intended to carry passengers, it also must be able to move smoothly and comfortably, and the robot behavior needs to be customizable to match the preference of the individual users. Despite decades of progress in the field of motion planning and control, this remains a difficult challenge with existing methods. In this dissertation, we show that safe, comfortable, and customizable mobile robot navigation in dynamic and uncertain environments can be achieved via stochastic model predictive control. We view the problem of navigation in dynamic and uncertain environments as a continuous decision making process, where an agent with short-term predictive capability reasons about its situation and makes an informed decision at each time step. The problem of robot navigation in dynamic and uncertain environments is formulated as an on-line, finite-horizon policy and trajectory optimization problem under uncertainty. With our formulation, planning and control becomes fully integrated, which allows direct optimization of the performance measure. Furthermore, with our approach the problem becomes easy to solve, which allows our algorithm to run in real time on a single core of a typical laptop with off-the-shelf optimization packages. The work presented in this thesis extends the state-of-the-art in analytic control of mobile robots, sampling-based optimal path planning, and stochastic model predictive control. We believe that our work is a significant step toward safe and reliable autonomous navigation that is acceptable to human users.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120760/1/jongjinp_1.pd

Man-machine cooperation in advanced teleoperation

Teleoperation experiments at JPL have shown that advanced features in a telerobotic system are a necessary condition for good results, but that they are not sufficient to assure consistently good performance by the operators. Two or three operators are normally used during training and experiments to maintain the desired performance. An alternative to this multi-operator control station is a man-machine interface embedding computer programs that can perform some of the operator's functions. In this paper we present our first experiments with these concepts, in which we focused on the areas of real-time task monitoring and interactive path planning. In the first case, when performing a known task, the operator has an automatic aid for setting control parameters and camera views. In the second case, an interactive path planner will rank different path alternatives so that the operator will make the correct control decision. The monitoring function has been implemented with a neural network doing the real-time task segmentation. The interactive path planner was implemented for redundant manipulators to specify arm configurations across the desired path and satisfy geometric, task, and performance constraints

Faster Motion on Cartesian Paths Exploiting Robot Redundancy at the Acceleration Level

The problem of minimizing the transfer time along a given Cartesian path for redundant robots can be approached in two steps, by separating the generation of a joint path associated to the Cartesian path from the exact minimization of motion time under kinematic/dynamic bounds along the obtained parameterized joint path. In this framework, multiple suboptimal solutions can be found, depending on how redundancy is locally resolved in the joint space within the first step. We propose a solution method that works at the acceleration level, by using weighted pseudoinversion, optimizing an inertia-related criterion, and including null-space damping. Several numerical results obtained on different robot systems demonstrate consistently good behaviors and definitely faster motion times in comparison with related methods proposed in the literature. The motion time obtained with our method is reasonably close to the global time-optimal solution along same Cartesian path. Experimental results on a KUKA LWR IV are also reported, showing the tracking control performance on the executed motions