Narrow passage path planning is a prevalent problem from industrial to household sites, often facing difficulties in finding feasible paths or requiring excessive computational resources. We propose a Homotopy Optimization Method (HOM) tailored for the narrow passage problem, utilizing a novel collision constraint interpolation method using signed distance functions (SDF). The framework begins by decomposing the environment into convex objects and representing it as a simplicial complex based on their connectivity. This representation enables topological analysis to induce a easy-to-hard sequence of collision constraint interpolation that preserves homotopy equivalence. Using this collision constraint interpolation, the optimization proceeds through a series of subproblems, gradually guiding the path to the final solution. Several examples are presented to demonstrate how the proposed framework addresses narrow passage path planning problems.

Shape abstraction, simplifying shape representation into a set of primitives, is a fundamental topic in computer vision. The choice of primitives shapes the structure of world understanding, yet achieving both high abstraction accuracy and versatility remains challenging. In this paper, we introduce a novel framework for shape abstraction utilizing a differentiable support function (DSF), which offers unique advantages in representing a wide range of convex shapes with fewer parameters, providing smooth surface approximation and enabling differentiable contact features (gap, point, normal) essential for downstream applications involving contact-related problems. To tackle the associated optimization and combinatorial challenges, we introduce two techniques: differentiable shape parameterization and hyperplane-based marching to enhance accuracy and reduce DSF requirements. We validate our method through experiments demonstrating superior accuracy and efficiency, and showcase its applicability in tasks requiring differentiable contact information.

In this paper, we implement the GPU-accelerated subsystem-based Alternating Direction Method of Multipliers (SubADMM) for interactive simulation. The challenging objective for interactive simulations is to deliver realistic results under tight performance, even for large-scale scenarios. We aim to achieve this by exploiting the parallelizable nature of SubADMM to the fullest extent. We introduce a new subsystem division strategy to make SubADMM ‘GPU friendly' along with custom kernel designs and optimization regarding efficient memory access patterns. We successfully implement the GPUaccelerated SubADMM and show the accuracy and speed of the framework for large-scale scenarios, highlighted with an interactive ‘Hand demo’ scenario. We also show improved robustness and accuracy compared to other state-of-the-art interactive simulators with several challenging scenarios that introduce large-scale ill-conditioned dynamics problems.

We propose a novel high-force/high-precision interaction control framework of a dual-arm robot system on a flexible base, with one arm holding, or making contact with, a supporting surface, while the other arm can exert any arbitrary wrench in a certain polytope through a desired pose against environments or objects. Our proposed framework can achieve high-force/precision tasks by utilizing the supporting surface just as we humans do while taking into account various important constraints (e.g., system stability, joint angle/torque limits, friction-cone constraint, etc.) and the passive compliance of the flexible base. We first design the control as a combination of: 1) nominal control; 2) active stiffness control; and 3) feedback wrench control. We then sequentially perform optimizations of the nominal configuration (and its related wrenches) and the active stiffness control gain. We also design the proportional–integral type feedback wrench control to improve the robustness and precision of the control. The key theoretical enabler for our framework is a novel stiffness analysis of the dual-arm system with flexibility, which, when combined with certain constraints, provides some peculiar relations, that can effectively be used to significantly simplify the optimization problem-solving and to facilitate the feedback wrench control design by manifesting the compliance relation at the interaction port. The efficacy of the theory is then validated and demonstrated through simulations and experiments.

The multi-contact nonlinear complementarity problem (NCP) is a naturally arising challenge in robotic simulations. Achieving high performance in terms of both accuracy and efficiency remains a significant challenge, particularly in scenarios involving intensive contacts and stiff interactions. In this article, we introduce a new class of multi-contact NCP solvers based on the theory of the Augmented Lagrangian (AL). We detail how the standard derivation of AL in convex optimization can be adapted to handle multi-contact NCP through the iteration of surrogate problem solutions and the subsequent update of primal-dual variables. Specifically, we present two tailored variations of AL for robotic simulations: the Cascaded Newton-based Augmented Lagrangian (CANAL) and the Subsystem-based Alternating Direction Method of Multipliers (SubADMM). We demonstrate how CANAL can manage multi-contact NCP in an accurate and robust manner, while SubADMM offers superior computational speed, scalability, and parallelizability for high degrees-of-freedom multibody systems with numerous contacts. Our results showcase the effectiveness of the proposed solver framework, illustrating its advantages in various robotic manipulation scenarios.

Collision detection is a fundamental problem across various fields such as robotics, physical simulation, and computer graphics. While numerous studies have provided efficient solutions, based on the well-known Gilbert, Johnson, and Keerthi (GJK) algorithm and Expanding Polytope Algorithm (EPA), existing methods utilizing GJK-EPA often struggle with smooth strictly convex shapes like ellipsoids. This paper proposes a novel approach to the collision detection problem converting it to a problem compatible with an unconstrained Riemannian optimization problem. Moreover, we presents a specific method of solving the problem based on twice differentiable support functions and the Riemannian trust region (RTR) method. The method exhibits fast and robust convergence rate, leveraging the well-established theory of Riemannian optimization. The evaluation studies comparing our method to GJK-EPA method are done with pre-defined primitive shapes. Additionally, a test result with several more complex shapes is demonstrated exhibiting the method’s effectiveness and applicability.

In this paper, we present a new multibody physics simulation framework that utilizes the subsystem-based struc-ture and the Alternating Direction Method of Multiplier (ADMM). The major challenge in simulating complex high degree of freedom systems is a large number of coupled con-straints and large-sized matrices. To address this challenge, we first split the multibody into several subsystems and reformulate the dynamics equation into a subsystem perspective based on the structure of their interconnection. Then we utilize ADMM with our novel subsystem-based variable splitting scheme to solve the equation, which allows parallelizable and modular architecture. The resulting algorithm is fast, scalable, versatile, and converges well while maintaining solution consistency. Sev-eral illustrative examples are implemented with performance evaluation results showing advantages over other state-of-the-art algorithms.

The gradient of typical differentiable simulation is uninformative for two reasons: 1) non-smoothness in contact dynamics not considered properly, and 2) excessive local minima generated from the smoothing procedure. To tackle this issue, we first propose differentiable contact dynamics with an invariant contact set and coordinate differentiation using a signed distance function (SDF). Also, to eliminate the undesirable jittering caused by the smoothing procedure, which induces extra local minima, and to achieve a smooth and informative gradient, we further endow our framework with a novel damped contact model. Various optimization problems are implemented to demonstrate the usefulness and efficacy of our differentiable framework.

In this article, we propose a novel multibody dynamics simulation framework that can efficiently deal with large-dimensionality and complementarity multicontact conditions. Typical contact simulation approaches require performing contact impulse fixed-point iteration, which has high time-complexity from large-size matrix factorization and multiplication, as well as susceptibility to ill-conditioned contact situations. To circumvent this, we propose a novel framework based on velocity fixed-point iteration (V-FPI), which, by utilizing a certain surrogate dynamics and contact nodalization (with virtual nodes), we achieve not only intercontact decoupling but also their interaxes decoupling (i.e., contact diagonalization) at each iteration step. This then enables us to one-shot/parallel-solve the contact problem during each V-FPI iteration-loop, while avoiding large-size/dense matrix inversion/multiplication, thereby, significantly speeding up the simulation time with improved convergence property. We theoretically show that the solution of our framework is consistent with that of the original problem and, further, elucidate mathematical conditions for the convergence of our proposed solver. Performance and properties of our proposed simulation framework are also demonstrated and experimentally validated for various large-dimensional/multicontact scenarios including deformable objects.

We propose a novel real-time physically-accurate simulator for long flexible cable manipulation. We first discretize the cable into multiple rigid link segments, each with complementarity-based contact model and inter-segment compliant coupling; and partition the cable into a number of subsystems, each composed with a number of consecutive links. We then formulate the inter-subsystem consistency constraint as a certain analytical condition among the inter-subsystem coupling and the contact impulses; and solve each subsystem dynamics in parallel with the contact model together with this consistency condition in an iterative manner, achieving both the speed and the accuracy of the simulation. A novel post-regulation scheme is also proposed to further speed up the simulation. Experimental validation/demonstration are also performed to show the theory.

We propose a novel real-time physically-accurate simulation framework for the snap connection process. For this, we first notice the peculiarities of the process, namely, small/smooth deformation, stiff connector and segmented contact. We then design our simulation to fully exploit these peculiarities by adopting the following strategies: 1) the technique of passive midpoint integration (PMI [1]), which allows for stable simulation of arbitrarily light/stiff system by enforcing discrete-time passivity; 2) linear finite element method (FEM [2]) modeling, which is adequate to deal with the small snap connector deformation while providing much faster speed as compared to nonlinear FEM; 3) segmentation of the snap connector FEM model and solving of each segment individually with their coupling analytically eliminated, thereby, further speeding up the simulation; 4) balanced model reduction (BMR [3]) to further reduce the dimension of each segment purely analytically without any prior experiment or simulation; and 5) parallelized data-driven collision detection, which turns out to further significantly speed up our simulation. Experimentally-verified simulations are also performed to show the efficacy of our proposed simulation framework.