Matthew Zucker

CHOMP: Gradient optimization techniques for efficient motion planning

Existing high-dimensional motion planning algorithms are simultaneously overpowered and underpowered. In domains sparsely populated by obstacles, the heuristics used by sampling-based planners to navigate “narrow passages” can be needlessly complex; furthermore, additional post-processing is required to remove the jerky or extraneous motions from the paths that such planners generate. In this paper, we present CHOMP, a novel method for continuous path refinement that uses covariant gradient techniques to improve the quality of sampled trajectories. Our optimization technique both optimizes higher-order dynamics and is able to converge over a wider range of input paths relative to previous path optimization strategies. In particular, we relax the collision-free feasibility prerequisite on input paths required by those strategies. As a result, CHOMP can be used as a standalone motion planner in many real-world planning queries. We demonstrate the effectiveness of our proposed method in manipulation planning for a 6-DOF robotic arm as well as in trajectory generation for a walking quadruped robot.

CHOMP: Covariant Hamiltonian optimization for motion planning

In this paper, we present CHOMP (covariant Hamiltonian optimization for motion planning), a method for trajectory optimization invariant to reparametrization. CHOMP uses functional gradient techniques to iteratively improve the quality of an initial trajectory, optimizing a functional that trades off between a smoothness and an obstacle avoidance component. CHOMP can be used to locally optimize feasible trajectories, as well as to solve motion planning queries, converging to low-cost trajectories even when initialized with infeasible ones. It uses Hamiltonian Monte Carlo to alleviate the problem of convergence to high-cost local minima (and for probabilistic completeness), and is capable of respecting hard constraints along the trajectory. We present extensive experiments with CHOMP on manipulation and locomotion tasks, using seven-degree-of-freedom manipulators and a rough-terrain quadruped robot.

Multipartite RRTs for Rapid Replanning in Dynamic Environments

The rapidly-exploring random tree (RRT) algorithm has found widespread use in the field of robot motion planning because it provides a single-shot, probabilistically complete planning method which generalizes well to a variety of problem domains. We present the multipartite RRT (MP-RRT), an RRT variant which supports planning in unknown or dynamic environments. By purposefully biasing the sampling distribution and re-using branches from previous planning iterations, MP-RRT combines the strengths of existing adaptations of RRT for dynamic motion planning. Experimental results show MP-RRT to be very effective for planning in dynamic environments with unknown moving obstacles, replanning in high-dimensional configuration spaces, and replanning for systems with space time constraints.

Optimization and learning for rough terrain legged locomotion

We present a novel approach to legged locomotion over rough terrain that is thoroughly rooted in optimization. This approach relies on a hierarchy of fast, anytime algorithms to plan a set of footholds, along with the dynamic body motions required to execute them. Components within the planning framework coordinate to exchange plans, cost-to-go estimates, and ‘certificates’ that ensure the output of an abstract high-level planner can be realized by lower layers of the hierarchy. The burden of careful engineering of cost functions to achieve desired performance is substantially mitigated by a simple inverse optimal control technique. Robustness is achieved by real-time re-planning of the full trajectory, augmented by reflexes and feedback control. We demonstrate the successful application of our approach in guiding the LittleDog quadruped robot over a variety of types of rough terrain. Other novel aspects of our past research efforts include a variety of pioneering inverse optimal control techniques as well as a system for planning using arbitrary pre-recorded robot behavior.

An optimization approach to rough terrain locomotion

We present a novel approach to legged locomotion over rough terrain that is thoroughly rooted in optimization. This approach relies on a hierarchy of fast, anytime algorithms to plan a set of footholds, along with the dynamic body motions required to execute them. Components within the planning framework coordinate to exchange plans, cost-to-go estimates, and “certificates” that ensure the output of an abstract high-level planner can be realized by deeper layers of the hierarchy. The burden of careful engineering of cost functions to achieve desired performance is substantially mitigated by a simple inverse optimal control technique. Robustness is achieved by real-time re-planning of the full trajectory, augmented by reflexes and feedback control. We demonstrate the successful application of our approach in guiding the LittleDog quadruped robot over a variety of rough terrains.

Adaptive workspace biasing for sampling-based planners

The widespread success of sampling-based planning algorithms stems from their ability to rapidly discover the connectivity of a configuration space. Past research has found that non-uniform sampling in the configuration space can significantly outperform uniform sampling; one important strategy is to bias the sampling distribution based on features present in the underlying workspace. In this paper, we unite several previous approaches to workspace biasing into a general framework for automatically discovering useful sampling distributions. We present a novel algorithm, based on the REINFORCE family of stochastic policy gradient algorithms, which automatically discovers a locally-optimal weighting of workspace features to produce a distribution which performs well for a given class of sampling-based motion planning queries. We present as well a novel set of workspace features that our adaptive algorithm can leverage for improved configuration space sampling. Experimental results show our algorithm to be effective across a variety of robotic platforms and high- dimensional configuration spaces.

A General-purpose System for Teleoperation of the DRC-HUBO Humanoid Robot

We present a general system with a focus on addressing three events of the 2013 DARPA Robotics Challenge DRC trials: debris clearing, door opening, and wall breaking. Our hardware platform is DRC-HUBO, a redesigned model of the HUBO2+ humanoid robot developed by KAIST and Rainbow, Inc. Our system allowed a trio of operators to coordinate a 32 degree-of-freedom robot on a variety of complex mobile manipulation tasks using a single, unified approach. In addition to descriptions of the hardware and software, and results as deployed on the DRC-HUBO platform, we present some qualitative analysis of lessons learned from this demanding and difficult challenge.

Continuous trajectory optimization for autonomous humanoid door opening

The upcoming DARPA Robotics Challenge (DRC) presents a demanding set of real-world tasks to be accomplished autonomously by robots. In this paper, we describe the development of a system to control an existing humanoid robot to open a door, one of the many tasks of the DRC. Special emphasis is placed upon generating smooth trajectories which minimize unnecessary motion of the robot. We describe methods for generating and optimizing trajectories for the robot, and present preliminary results demonstrated on the physical robotic platform. To the best of our knowledge, we demonstrate the first large scale application of the CHOMP trajectory optimization in a situation with closed kinematic chain constraints.

Reinforcement Planning: RL for optimal planners

Search based planners such as A* and Dijkstras algorithm are proven methods for guiding todays robotic systems. Although such planners are typically based upon a coarse approximation of reality, they are nonetheless valuable due to their ability to reason about the future, and to generalize to previously unseen scenarios. However, encoding the desired behavior of a system into the underlying cost function used by the planner can be a tedious and error-prone task. We introduce Reinforcement Planning, which extends gradient based reinforcement learning algorithms to automatically learn useful surrogate cost functions for optimal planners. Reinforcement Planning presents several advantages over other learning approaches to planning in that it is not limited by the expertise of a human demonstrator, and that it acknowledges the domain of the planner is a simplified model of the world. We demonstrate the effectiveness of our method in learning to solve a noisy physical simulation of the well-known “marble maze” toy.

Multigrid CHOMP with Local Smoothing

The Covariant Hamiltonian Optimization and Motion Planning (CHOMP) algorithm has found many recent applications in robotics research, such as legged locomotion and mobile manipulation. Although integrating kinematic constraints into CHOMP has been investigated, prior work in this area has proven to be slow for trajectories with a large number of constraints. In this paper, we present Multigrid CHOMP with Local Smoothing, an algorithm which improves the runtime of CHOMP under constraints, without significantly reducing optimality. The effectiveness of this algorithm is demonstrated on two simulated problems, and on a physical HUBO+ humanoid robot, in the context of door opening. We demonstrate order-of-magnitude or higher speedups over the original constrained CHOMP algorithm, while achieving within 2% of the performance of the original algorithm on the underlying objective function.