Marin Kobilarov

People tracking and following with mobile robot using an omnidirectional camera and a laser

The paper presents two different methods for mobile robot tracking and following of a fast-moving person in outdoor unstructured and possibly dynamic environment. The robot is equipped with laser range-finder and omnidirectional camera. The first method is based on visual tracking only and while it works well at slow speeds and controlled conditions, its performance quickly degrades as conditions become more difficult. The second method which uses the laser and the camera in conjunction for tracking performs well in dynamic and cluttered outdoor environments as long as the target occlusions and losses are temporary. Experimental results and analysis are presented for the second approach

Discrete Geometric Optimal Control on Lie Groups

We consider the optimal control of mechanical systems on Lie groups and develop numerical methods that exploit the structure of the state space and preserve the system motion invariants. Our approach is based on a coordinate-free variational discretization of the dynamics that leads to structure-preserving discrete equations of motion. We construct necessary conditions for optimal trajectories that correspond to discrete geodesics of a higher order system and develop numerical methods for their computation. The resulting algorithms are simple to implement and converge to a solution in very few iterations. A general software implementation is provided and applied to two example systems: an underactuated boat and a satellite with thrusters.

Cross-entropy motion planning

This paper is concerned with motion planning for non-linear robotic systems operating in constrained environments. A method for computing high-quality trajectories is proposed building upon recent developments in sampling-based motion planning and stochastic optimization. The idea is to equip sampling-based methods with a probabilistic model that serves as a sampling distribution and to incrementally update the model during planning using data collected by the algorithm. At the core of the approach lies the cross-entropy method for the estimation of rare-event probabilities. The cross-entropy method is combined with recent optimal motion planning methods such as the rapidly exploring random trees (RRT*) in order to handle complex environments. The main goal is to provide a framework for consistent adaptive sampling that correlates the spatial structure of trajectories and their computed costs in order to improve the performance of existing planning methods.

Lie group integrators for animation and control of vehicles

This article is concerned with the animation and control of vehicles with complex dynamics such as helicopters, boats, and cars. Motivated by recent developments in discrete geometric mechanics, we develop a general framework for integrating the dynamics of holonomic and nonholonomic vehicles by preserving their state-space geometry and motion invariants. We demonstrate that the resulting integration schemes are superior to standard methods in numerical robustness and efficiency, and can be applied to many types of vehicles. In addition, we show how to use this framework in an optimal control setting to automatically compute accurate and realistic motions for arbitrary user-specified constraints.

Nonlinear Trajectory Control of Multi-body Aerial Manipulators

This paper studies trajectory control of aerial vehicles equipped with robotic manipulators. The proposed approach employs free-flying multi-body dynamics modeling and backstepping control to develop stabilizing control laws for a class of underactuated aerial systems. Two control methods are developed: coordinate-based and coordinate-free which are both generally applicable to aerial manipulation tasks. A simulated hexrotor vehicle equipped with a simple manipulator is employed to demonstrate the proposed techniques.

Cross-Entropy Randomized Motion Planning

Abstract—This paper is concerned with motion planning for nonlinear robotic systems operating in constrained environments. Motivated by recent developments in sampling-based motion planning and Monte Carlo optimization we propose a general randomized path planning method based on sampling in the space of trajectories. The idea is to construct a probability distribution over the set of feasible paths and to perform the search for an optimal trajectory through importance sampling. At the core of the approach lies the cross-entropy method for estimation of rare-event probabilities. The algorithm recursively approximates the optimal sampling distribution which guides the set of sampled trajectories towards regions of progressively lower cost until converging to a delta distribution at the optimum. Our main goal is to provide a framework for consistent adaptive sampling correlating the spatial structure of trajectories and their computed costs. The approach is illustrated with two simple examples–a point mass vehicle and the Dubins car, and is then applied to a simulated helicopter flying optimally in a 3-D terrain.

Near Time-optimal Constrained Trajectory Planning on Outdoor Terrain

We present an outdoor terrain planner that finds near optimal trajectories under dynamic and kinematic constraints. The planner can find solutions in close to real time by relaxing some of the assumptions associated with costly rigid body simulation and complex terrain surface interactions. Our system is based on control-driven Proba bilistic Roadmaps and can efficiently find and optimize a near time-minimum trajectory. We present simulated results with artificial environments, as well as a real robot experiment using Segway Robotic Mobile Platform.

Trajectory Planning for CubeSat Short-Time-Scale Proximity Operations

This paper considers motion planning for small satellites such as CubeSats performing proximity operations in a several meters range of a target object. The main goal is to develop a principled methodology for handling the coupled effects of orbital dynamics, rotational and translational rigid-body dynamics, underactuation and control bounds, and obstacle avoidance constraints. The proposed approach is based on constructing a reduced-order parameterization of the dynamics through dynamics inversion and differential flatness, and on efficient global optimization over a finite-dimensional reduced representation. Two simulated scenarios, a satellite reconfiguration maneuver and asteroid surface sampling, are developed to illustrate the approach. In addition, a simple two-dimensional experimental testbed consisting of an air-bearing table and two CubeSat engineering models is developed for partial testing and integration of the proposed methods.

Towards model-predictive control for aerial pick-and-place

This paper considers pick-and-place tasks using aerial vehicles equipped with manipulators. The main focus is on the development and experimental validation of a nonlinear model-predictive control methodology to exploit the multi-body system dynamics and achieve optimized performance. At the core of the approach lies a sequential Newton method for unconstrained optimal control and a high-frequency low-level controller tracking the generated optimal reference trajectories. A low cost quadrotor prototype with a simple manipulator extending more than twice the radius of the vehicle is designed and integrated with an on-board vision system for object tracking. Experimental results show the effectiveness of model-predictive control to motivate the future use of real-time optimal control in place of standard ad-hoc gain scheduling techniques.

A Discrete Geometric Optimal Control Framework for Systems with Symmetries

This paper studies the optimal motion control of mechanical systems through a discrete geometric approach. At the core of our formulation is a discrete Lagrange-d’Alembert- Pontryagin variational principle, from which are derived discrete equations of motion that serve as constraints in our optimization framework. We apply this discrete mechanical approach to holonomic systems with symmetries and, as a result, geometric structure and motion invariants are preserved. We illustrate our method by computing optimal trajectories for a simple model of an air vehicle flying through a digital terrain elevation map, and point out some of the numerical benefits that ensue.