Tobias Kunz

Time-Optimal Trajectory Generation for Path Following with Bounded Acceleration and Velocity

Presented at the 2012 Robotics: Science and Systems Conference VIII (RSS), 09-13 July 2012, Sydney, Australia.

Real-time path planning for a robot arm in changing environments

We present a practical strategy for real-time path planning for articulated robot arms in changing environments by integrating PRM for Changing Environments with 3D sensor data. Our implementation on Care-O-Bot 3 identifies bottlenecks in the algorithm and introduces new methods that solve the overall task of detecting obstacles and planning a path around them in under 100 ms. A fast planner is necessary to enable the robot to react to quickly changing human environments. We have tested our implementation in real-world experiments where a human subject enters the manipulation area, is detected and safely avoided by the robot. This capability is critical for future applications in automation and service robotics where humans will work closely with robots to jointly perform tasks.

Probabilistically complete kinodynamic planning for robot manipulators with acceleration limits

We introduce acceleration-limited planning for manipulators as a middle ground between pure geometric planning and planning with full robot dynamics. It is more powerful than geometric planning and can be solved more efficiently than planning with full robot dynamics. We present a probabilistically complete RRT motion planner that considers joint acceleration limits and potentially non-zero start and goal velocities. It uses a fast, non-iterative steering method. We demonstrate both the power and efficiency of our planner using the problem of hitting a nail with a hammer, which requires the robot to reach a given goal velocity while avoiding obstacles. Our planner is able to solve this problem in less than 100 ms. In contrast, a purely geometric planner is unable to hit the nail at the desired velocity, whereas a standard kinodynamic RRT is multiple orders of magnitude slower.

Robot limbo: Optimized planning and control for dynamically stable robots under vertical obstacles

We present successful control strategies for dynamically stable robots that avoid low ceilings and other vertical obstacles in a manner similar to limbo dances. Given the parameters of the mission, including the goal and obstacle dimensions, our method uses a sequential composition of IO-linearized controllers and applies stochastic optimization to automatically compute the best controller gains and references, as well as the times for switching between the different controllers. We demonstrate this system through numerical simulations, validation in a physics-based simulation environment, as well as on a novel two-wheeled platform. The results show that the generated control strategies are successful in mission planning for this challenging problem domain and offer significant advantages over hand-tuned alternatives.

Kinodynamic RRTs with Fixed Time Step and Best-Input Extension Are Not Probabilistically Complete

RRTs are a popular method for kinodynamic planning that many consider to be probabilistically complete. However, different variations of the RRT algorithm exist and not all of them are probabilistically complete. The tree can be extended using a fixed or variable time step. The input can be chosen randomly or the best input can be chosen such that the new child node is as close as possible to the sampled state according to the used distance metric. It has been shown that for finite input sets an RRT using a fixed step size with a randomly selected input is probabilistically complete. However, this variant is uncommon since it is less efficient. We prove that the most common variant of choosing the best input in combination with a fixed time step is not probabilistically complete.

DART: Dynamic Animation and Robotics Toolkit

DART (Dynamic Animation and Robotics Toolkit) is a collaborative, cross-platform, open source library created by the Graphics Lab and Humanoid Robotics Lab at Georgia Institute of Technology with ongoing contributions from the Personal Robotics Lab at University of Washington and Open Source Robotics Foundation. The library provides data structures and algorithms for kinematic and dynamic applications in robotics and computer animation. DART is distinguished by its accuracy and stability due to its use of generalized coordinates to represent articulated rigid body systems in the geometric notations (Park, Bobrow, and Ploen 1995) and Featherstone’s Articulated Body Algorithm (Featherstone 2008) using a Lie group formulation to compute forward dynamics (Ploen and Park 1999) and hybrid dynamics (Sohl and Bobrow 2001). For developers, in contrast to many popular physics engines which view the simulator as a black box, DART gives full access to internal kinematic and dynamic quantities, such as the mass matrix, Coriolis and centrifugal forces, transformation matrices and their derivatives. DART also provides an efficient computation of Jacobian matrices for arbitrary body points and coordinate frames. The frame semantics of DART allows users to define arbitrary reference frames (both inertial and non-inertial) and use those frames to specify or request data. For air-tight code safety, forward kinematics and dynamics values are updated automatically through lazy evaluation, making DART suitable for real-time controllers. In addition, DART provides flexibility to extend the API for embedding user-provided classes into DART data structures. Contacts and collisions are handled using an implicit time-stepping, velocity-based LCP (linear complementarity problem) to guarantee non-penetration, directional friction, and approximated Coulomb friction cone conditions (Stewart and Trinkle 1996). DART has applications in robotics and computer animation because it features a multibody dynamic simulator and various kinematic tools for control and motion planning.

Manipulation planning with soft task constraints

We present a randomized configuration space planner that enforces soft workspace task constraints. A soft task constraint allows an interval of feasible values while favoring a given exact value. Previous work only allows for enforcing an exact value or an interval without a specific preference. Soft task constraints are a useful concept in everyday life. For example when carrying a container of liquid we want to keep it as close to the upright position as possible but want to be able to tilt it slightly in order to avoid obstacles. This paper introduces the necessary algorithms for handling such constraints, including projection methods and useful representations of everyday constraints. Our algorithms are evaluated on a series of simulated benchmark problems and shown to yield significant improvement in constraint satisfaction.

Dynamic chess: Strategic planning for robot motion

We introduce and experimentally validate a novel algorithmic model for physical human-robot interaction with hybrid dynamics. Our computational solutions are complementary to passive and compliant hardware. We focus on the case where human motion can be predicted. In these cases, the robot can select optimal motions in response to human actions and maximize safety. By representing the domain as a Markov Game, we enable the robot to not only react to the human but also to construct an infinite horizon optimal policy of actions and responses. Experimentally, we apply our model to simulated robot sword defense. Our approach enables a simulated 7-DOF robot arm to block known attacks in any sequence. We generate optimized blocks and apply game theoretic tools to choose the best action for the defender in the presence of an intelligent adversary.

Hierarchical rejection sampling for informed kinodynamic planning in high-dimensional spaces

We present hierarchical rejection sampling (HRS) to improve the efficiency of asymptotically optimal sampling-based planners for high-dimensional problems with differential constraints. Pruning nodes and rejecting samples that cannot improve the currently best solution have been shown to improve performance for certain problems. We show that in high-dimensional domains this improvement can be so large that rejecting samples becomes the bottleneck of the algorithm because almost all samples are rejected. This contradicts general wisdom that collision checking is always the bottleneck of sampling-based planners. Only samples in the informed subset of the state space can potentially improve the current solution. For systems without differential constraints the informed subset forms an ellipsoid, which can be parameterized and sampled directly. For systems with differential constraints the informed subset is more complicated and no such direct sampling methods exist. HRS improves the efficiency of finding samples within the informed subset without parameterizing it explicitly. Thus, it can also be applied to systems with differential constraints for which a steering method is available. In our experiments we demonstrate efficiency improvements of an RRT* planner of up to two orders of magnitude.

Generation of diverse paths in 3D environments

In this paper we propose a deterministic algorithm to produce a set of diverse paths between a given start and goal configuration in 3D environments. These diverse paths have the following properties: 1) They are bounded in length and 2) They are non-visibility-deformable into one another. Maintaining multiple path alternatives is important in practical applications such as planning in dynamic environments, in which a path may unexpectedly become infeasible due to unforeseen environmental changes. We present our approach, the distance cost considered (based on the path deformability concept previously introduced in [11]) and finally show results of simulated experiments that exemplify the effectiveness of our algorithm.