Linearization in Motion Planning under Uncertainty

Motion planning under uncertainty is essential to autonomous robots. Over the past decade, the scalability of such planners have advanced substantially. Despite these advances, the problem remains difficult for systems with non-linear dynamics. Most successful methods for planning perform forward search that relies heavily on a large number of simulation runs. Each simulation run generally requires more costly integration for systems with non-linear dynamics. Therefore, for such problems, the entire planning process remains relatively slow. Not surprisingly, linearization-based methods for planning under uncertainty have been proposed. However, it is not clear how linearization affects the quality of the generated motion strategy, and more importantly where to and where not to use such a simplification. This paper presents our preliminary work towards answering such questions. In particular, we propose a measure, called Statistical-distance-based Non-linearity Measure (SNM), to identify where linearization can and where it should not be performed. The measure is based on the distance between the distributions that represent the original motion-sensing models and their linearized version. We show that when the planning problem is framed as the Partially Observable Markov Decision Process (POMDP), the difference between the value of the optimal strategy generated if we plan using the original model and if we plan using the linearized model, can be upper bounded by a function linear in SNM. We test the applicability of this measure in simulation via two venues. First, we compare SNM with a negentropy-based Measure of Non-Gaussianity (MoNG) —a measure that has recently been shown to be a suitable measure of non-linearity for stochastic systems [1]. We compare their performance in measuring the difference between a general POMDP solver [2] that computes motion strategies using the original model and a solver that uses the linearized model (adapted from [3]) on various scenarios. Our results indicate that SNM is more suitable in taking into account the effect that obstacles have on the effectiveness of linearization. In the second set of tests, we use a local estimate of SNM to develop a simple on-line planner that switches between using the original and the linearized model. Simulation results on a car-like robot with second order dynamics and a 4-DOFs and 6-DOFs manipulator with torque control indicate that our simple planner appropriately decides if and when linearization should be use

Sampling-based Motion Planning for Active Multirotor System Identification

This paper reports on an algorithm for planning trajectories that allow a multirotor micro aerial vehicle (MAV) to quickly identify a set of unknown parameters. In many problems like self calibration or model parameter identification some states are only observable under a specific motion. These motions are often hard to find, especially for inexperienced users. Therefore, we consider system model identification in an active setting, where the vehicle autonomously decides what actions to take in order to quickly identify the model. Our algorithm approximates the belief dynamics of the system around a candidate trajectory using an extended Kalman filter (EKF). It uses sampling-based motion planning to explore the space of possible beliefs and find a maximally informative trajectory within a user-defined budget. We validate our method in simulation and on a real system showing the feasibility and repeatability of the proposed approach. Our planner creates trajectories which reduce model parameter convergence time and uncertainty by a factor of four.Comment: Published at ICRA 2017. Video available at https://www.youtube.com/watch?v=xtqrWbgep5

Realtime State Estimation with Tactile and Visual sensing. Application to Planar Manipulation

Accurate and robust object state estimation enables successful object manipulation. Visual sensing is widely used to estimate object poses. However, in a cluttered scene or in a tight workspace, the robot's end-effector often occludes the object from the visual sensor. The robot then loses visual feedback and must fall back on open-loop execution. In this paper, we integrate both tactile and visual input using a framework for solving the SLAM problem, incremental smoothing and mapping (iSAM), to provide a fast and flexible solution. Visual sensing provides global pose information but is noisy in general, whereas contact sensing is local, but its measurements are more accurate relative to the end-effector. By combining them, we aim to exploit their advantages and overcome their limitations. We explore the technique in the context of a pusher-slider system. We adapt iSAM's measurement cost and motion cost to the pushing scenario, and use an instrumented setup to evaluate the estimation quality with different object shapes, on different surface materials, and under different contact modes

Finite Time Robust Control of the Sit-to-Stand Movement for Powered Lower Limb Orthoses

This study presents a technique to safely control the Sit-to-Stand movement of powered lower limb orthoses in the presence of parameter uncertainty. The weight matrices used to calculate the finite time horizon linear-quadratic regulator (LQR) gain in the feedback loop are chosen from a pool of candidates as to minimize a robust performance metric involving induced gains that measure the deviation of variables of interest in a linear time-varying (LTV) system, at specific times within a finite horizon, caused by a perturbation signal modeling the variation of the parameters. Two relevant Sit-to-Stand movements are simulated for drawing comparisons with the results documented in a previous work.Comment: 8 pages, 14 figures, ACC 2018 Submissio