Liangjun Zhang

An efficient retraction-based RRT planner

We present a novel optimization-based retraction algorithm to improve the performance of sample-based planners in narrow passages for 3D rigid robots. The retraction step is formulated as an optimization problem using an appropriate distance metric in the configuration space. Our algorithm computes samples near the boundary of C-obstacle using local contact analysis and uses those samples to improve the performance of RRT planners in narrow passages. We analyze the performance of our planner using Voronoi diagrams and show that the tree can grow closely towards any randomly generated sample. Our algorithm is general and applicable to all polygonal models. In practice, we observe significant speedups over prior RRT planners on challenging scenarios with narrow passages.

Collision-free and smooth trajectory computation in cluttered environments

We present a novel trajectory computation algorithm to smooth piecewise linear collision-free trajectories computed by sample-based motion planners. Our approach uses cubic B-splines to generate trajectories that are C2 almost everywhere, except on a few isolated points. The algorithm performs local spline refinement to compute smooth, collision-free trajectories and it works well even in environments with narrow passages. We also present a fast and reliable algorithm for collision checking between a robot and the environment along the B-spline trajectories. We highlight the performance of our algorithm on complex benchmarks, including path computation for rigid and articulated models in cluttered environments.

A hybrid approach for complete motion planning

We present an efficient algorithm for complete motion planning that combines approximate cell decomposition (ACD) with probabilistic roadmaps (PRM). Our approach uses ACD to subdivide the configuration space into cells and computes localized roadmaps by generating samples within these cells. We augment the connectivity graph for adjacent cells in ACD with pseudo-free edges that are computed based on localized roadmaps. These roadmaps are used to capture the connectivity of free space and guide the adaptive subdivision algorithm. At the same time, we use cell decomposition to check for path non-existence and generate samples in narrow passages. Overall, our hybrid algorithm combines the efficiency of PRM methods with the completeness of ACD-based algorithms. We have implemented our algorithm on 3-DOF and 4-DOF robots. We demonstrate its performance on planning scenarios with narrow passages or no collision-free paths. In practice, we observe up to 10 times improvement in performance over prior complete motion planning algorithms.

A Fast and Practical Algorithm for Generalized Penetration Depth Computation.

We present an efficient algorithm to compute the generalized penetration depth (PDg) between rigid models. Given two overlapping objects, our algorithm attempts to compute the minimal translational and rotational motion that separates the two objects. We formulate the PDg computation based on modeldependent distance metrics using displacement vectors. As a result, our formulation is independent of the choice of inertial and body-fixed reference frames, as well as specific representation of the configuration space. Furthermore, we show that the optimum answer lies on the boundary of the contact space and pose the computation as a constrained optimization problem. We use global approaches to find an initial guess and present efficient techniques to compute a local approximation of the contact space for iterative refinement. We highlight the performance of our algorithm on many complex models.

Generalized penetration depth computation

Penetration depth (PD) is a distance metric that is used to describe the extent of overlap between two intersecting objects. Most of the prior work in PD computation has been restricted to translational PD, which is defined as the minimal translational motion that one of the overlapping objects must undergo in order to make the two objects disjoint. In this paper, we extend the notion of PD to take into account both translational and rotational motion to separate the intersecting objects, namely generalized PD. When an object undergoes rigid transformation, some point on the object traces the longest trajectory. The generalized PD between two overlapping objects is defined as the minimum of the longest trajectories of one object under all possible rigid transformations to separate the overlapping objects.We present three new results to compute generalized PD between polyhedral models. First, we show that for two overlapping convex polytopes, the generalized PD is same as the translational PD. Second, when the complement of one of the objects is convex, we pose the generalized PD computation as a variant of the convex containment problem and compute an upper bound using optimization techniques. Finally, when both the objects are non-convex, we treat them as a combination of the above two cases, and present an algorithm that computes a lower and an upper bound on generalized PD. We highlight the performance of our algorithms on different models that undergo rigid motion in the 6-dimensional configuration space. Moreover, we utilize our algorithm for complete motion planning of polygonal robots undergoing translational and rotational motion in a plane. In particular, we use generalized PD computation for checking path non-existence.

A hybrid approach for simulating human motion in constrained environments

Realistic character animation requires elaborate rigging built on top of high quality 3D models. Sophisticated anatomically based rigs are often the choice of visual effect studios where life-like animation of CG characters is the primary objective. However, rigging a character with a muscular-skeletal system is very involving and time-consuming process, even for professionals. Although, there have been recent research efforts to automate either all or some parts of the rigging process, the complexity of anatomically based rigging nonetheless opens up new research challenges. We propose a new method to automate anatomically based rigging that transfers an existing rig of one character to another. The method is based on a data interpolation in the surface and volume domain, where various rigging elements can be transferred between different models. As it only requires a small number of corresponding input feature points, users can produce highly detailed rigs for a variety of desired character with ease. Copyright

Sampling-based exploration of folded state of a protein under kinematic and geometric constraints.

Flexibility is critical for a folded protein to bind to other molecules (ligands) and achieve its functions. The conformational selection theory suggests that a folded protein deforms continuously and its ligand selects the most favorable conformations to bind to. Therefore, one of the best options to study protein‐ligand binding is to sample conformations broadly distributed over the protein‐folded state. This article presents a new sampler, called kino‐geometric sampler (KGS). This sampler encodes dominant energy terms implicitly by simple kinematic and geometric constraints. Two key technical contributions of KGS are (1) a robotics‐inspired Jacobian‐based method to simultaneously deform a large number of interdependent kinematic cycles without any significant break‐up of the closure constraints, and (2) a diffusive strategy to generate conformation distributions that diffuse quickly throughout the protein folded state. Experiments on four very different test proteins demonstrate that KGS can efficiently compute distributions containing conformations close to target (e.g., functional) conformations. These targets are not given to KGS, hence are not used to bias the sampling process. In particular, for a lysine‐binding protein, KGS was able to sample conformations in both the intermediate and functional states without the ligand, while previous work using molecular dynamics simulation had required the ligand to be taken into account in the potential function. Overall, KGS demonstrates that kino‐geometric constraints characterize the folded subset of a protein conformation space and that this subset is small enough to be approximated by a relatively small distribution of conformations. Proteins 2012.

Efficient Cell Labelling and Path Non-existence Computation using C-obstacle Query

We present a simple algorithm to check for path non-existence for a low-degree-of-freedom (DOF) robot among static obstacles. Our algorithm is based on approximate cell decomposition of configuration space or C-space. We use C-obstacle cell query to check whether a cell lies entirely inside the C-obstacle region. This reduces the path non-existence problem to checking whether a path exists through the set of all cells that do not lie entirely inside the C-obstacle region. We present a simple and efficient algorithm to perform C-obstacle cell query using generalized penetration depth computation. Our algorithm is simple to implement and we demonstrate its performance on three-DOF and four-DOF robots.

Retraction-based RRT planner for articulated models

We present a new retraction algorithm for high DOF articulated models and use our algorithm to improve the performance of RRT planners in narrow passages. The retraction step is formulated as a constrained optimization problem and performs iterative refinement on the boundary of C-Obstacle space. We also combine the retraction algorithm with decomposition planners to handle very high DOF articulated models. The performance of our approach is analyzed using Voronoi diagrams and we show that our retraction algorithm provides a good approximation to the ideal RRT-extension in constrained environments. We have implemented our algorithm and tested its performance on robots with more than 40 DOFs in complex environments. In practice, we observe significant performance (2–80X) improvement over prior RRT planners on challenging scenarios with narrow passages.

A Simple Path Non-existence Algorithm Using C-Obstacle Query

We present a simple algorithm to check for path non-existence for a robot among static obstacles. Our algorithm is based on adaptive cell decomposition of configuration space or C-space. We use two basic queries: free cell query, which checks whether a cell in C-space lies entirely inside the free space, and C-obstacle cell query, which checks whether a cell lies entirely inside the C-obstacle region. Our approach reduces the path non-existence problem to checking whether there exists a path through cells that do not belong to the C-obstacle region. We describe simple and efficient algorithms to perform free cell and C-obstacle cell queries using separation distance and generalized penetration depth computations. Our algorithm is simple to implement and we demonstrate its performance on 3 DOF robots.