Forward Dynamics of Variable Topology Mechanisms - The Case of Constraint Activation

This paper presents an object manipulation strategy for the Variable Topology Truss (VTT) system, a truss robot that comprises actuated truss members connected by passive spherical joints. Although truss robots were originally proposed as rapidly deployable manipulators, manipulation strategy has not been studied thoroughly. To enable manipulation, we introduce a hybrid control framework that regulates position and force concurrently without explicit decoupling. At the actuator level, each member employs a sensor-based force feedback controller to generate the desired axial forces despite high actuator friction. At the task level, the forces applied at the end-effector nodes are produced by computing the required member forces using a static model of the VTT. We evaluate force-tracking performance through experiments on both a single member module and the full VTT system. Finally, we demonstrate object manipulation using two representative configurations and quantitatively assess combined position and force tracking performance. Experimental results confirm that the proposed approach enables consistent and reliable object manipulation with the VTT system.

We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the constrained state space. To achieve this, we introduce ``constraint manifolds with corners" to represent the state space satisfying mixed nonlinear equality and inequality constraints. We further extend manifold optimization algorithms to operate on this new topological structure. We demonstrate the power and robustness of our framework in the context of a large-scale kinodynamic planning problem, successfully generating dynamically feasible trajectories where standard methods fail.

Planar path synthesis requires mechanisms whose coupler curves match a prescribed trajectory; the mapping from curve to linkage is inherently one-to-many across four-, six-, and eight-bar topologies. We address this design problem with simulation-grounded evaluation on a curated corpus of over one million mechanisms, reporting Chamfer distance and dynamic time warping after forward kinematics and geometric alignment. We formulate synthesis as conditional autoregressive sequence modeling: joint coordinates are uniformly quantized to tokens and generated by a decoder-only transformer with a variational-autoencoder (VAE) latent of the target curve and an explicit mechanism-type token. Training combines token cross-entropy with a Gaussian-smoothed bin auxiliary loss that respects ordinal structure among bins. At inference, a bounded latent-noise schedule decodes all mechanism types at each noise level; we retain the top five candidates by geometric error, yielding diverse accurate families without dataset lookup. On held-out tests, aggregate mean Chamfer distance is $0.0132$ and mean dynamic time warping is $0.153$; a latent $k$-nearest-neighbor baseline that conditions on training-set neighbor latents in VAE space achieves matched-topology mean Chamfer distance $0.0071$ and mean dynamic time warping $0.117$ using the same decoder.