We have worked extensively on combining high-level reasoning with low-level motion planning. One of the challenges is to create powerful abstractions that help guide the low-level exploration. Another challenge is to provide feedback from the low-level exploration to the high-level planner that can be used to update a high-level plan. Lately, we have extended this work to policy synthesis.
In kinodynamic planning it is often difficult to find the control inputs that will drive a system from one state to another (even in the absence of obstacles). We have developed several planning algorithms for kinodynamic systems. This includes distributed, asynchronous planning algorithms for multiple car-like systems with second-order dynamics and algorithms for reconfigurable robots with many degrees of freedom (but severe torque limits). The picture above shows a physics simulator used during planning for a reconfigurable robot and the corresponding trajectoruy execution on the actual hardware.
There is a strong emphasis on general algorithms that are not specific to any one particular robot. We have created reference implementations of many of our algrotihms (and many others) that are available as part of the Open Motion Planning Library. The picture above shows an artificial robot with 168 degrees of freedom and many closed chains, which makes it very challenging to plan for. We have recently unified many of the previous approaches to constrained motion planning and generalized it in such a way that almost any sampling-based planner can be used to plan in constrained state space.
There are different types of uncertainty (action uncertainty, sensing uncertainty, modeling uncertainty). A single plan has in general very little chance of success if it does not account for uncertainty. Solving this problem in its full generality with all types of uncertainty is incredibly difficult, especially if the state, observation and action spaces are all continuous. In many cases, some simplifying assumptions can be made and effective policies for robot motion can still be generated in reasonable time. The picture above illustrates the approach we have taken to synthesize a control policy for a kinodynamic system that realizes a high-level task (specified with a temporal logic) in the presence of action uncertainty.
In the early 2000s Simultaneous Localization and Mapping was an extremely active area within robotics. Much of that work relied on expense sensors. We have shown that localization is possible with very simple sensors. For example, in a typical office environment, localization is possible using just WiFi signal strength and the locations of base stations.
We are interested in a broad range of topics, ranging from mathematical knot untangling to manipulation of deformable objects and active perception. We often have visitors from other groups who also help broaden our horizons. The picture above shows a reconstruction of a cave using a Autonomous Underwater Vehicle (AUV). This work was performed at the University of Girona. The motion planning capabilities for the UAV were developed in part during visits of Girona students to our group.
Proteins play a critical role in almost every biological process in the human body. Their function is often mediated by shape changes induced by interactions with other molecules (including drugs). We are working with researchers in the Texas Medical Center to develop methods that allow us to model such conformational changes as well as predict the binding modes of small molecules for a given protein.
Metabolic engineering is the scientific process of manipulating the metabolism of a microorganism to produce valuable compounds. There have been numerous successes of metabolic engineering, including the well publicized biosynthesis of artemisinic acid, a precursor to the antimalarial drug artemisinin, and thebaine, a precursor to hydrocodone and morphine. We have developed pathfinding algorithms that facilitate the discovery of novel pathways using databases of known reactions and compounds.
The function of a protein can often be characterized by a structural motif: a spatial arrangement of a certain number of residues that is unique to that function. We have developed efficient algorithms to search all known protein structures for occurences of a putative motif. We have also shown that families of proteins that share the same function often exhibit subtle patterns of structural variation that, using a careful analysis, can be related to, e.g., phylogenetic distance (as in the figure shown above).
Proteins are not static structures. Accurately simulating the conformational changes in proteins is computationally very expensive. We have developed a variety of methods for generating (ensembles of) biophysically plausible conformations using techniques from robotics and geometric modelling.
Similar to our computational robotics research, we are interested in a broad range of topics in computational biomedicine. We have worked with a broad range of people from the Texas Medical Center and elsewhere. The picture above shows a network of protein-protein interactions, taken from a review written by our group on the computational challenges in systems biology.