Multi-legged robots with six or more legs are not in common use, despite designs with superior stability, maneuverability, and a low number of actuators being available for over 20 years. This may be in part due to the difficulty in modeling multi-legged motion with slipping and producing reliable predictions of body velocity. Here we present a detailed measurement of the foot contact forces in a hexapedal robot with multiple sliding contacts, and provide an algorithm for predicting these contact forces and the body velocity. The algorithm relies on the recently published observation that even while slipping, multi-legged robots are principally kinematic, and employ a friction law ansatz that allows us to compute the shape-change to body-velocity connection and the foot contact forces. This results in the ability to simulate motion plans for a large number of contacts, each potentially with slipping. Furthermore, in homogeneous environments, this kind of simulation can run in (parallel) logarithmic time of the planning horizon.

Soft robotic fingers can safely grasp fragile or non-uniform objects, but their force capacity is limited, especially with less contact area: objects which are smaller, not round, or where an enclosing grasp is not feasible. To improve force capacity, this paper considers two types of grip failure, slip and dynamic rotational stability. For slip, a Coulomb model for soft fingers based on total normal and tangential force is validated, identifying the effect of contact area, pressure, and grip position on effective Coulomb coefficient, normal force and transverse stiffness. For rotational stability, bulk stiffness of the fingers is used to develop conditions for dynamic stability about the initial grasp, and a condition for when the rotation leads to slip. Together, these models suggest contact area improves grip by increasing transverse stiffness and normal force. The models are validated in a range of grasp conditions, shown to predict the influence of object radius and finger distance on grip stability limits.

Robotic manipulation and locomotion often entail nearly-simultaneous collisions -- such as heel and toe strikes during a foot step -- with outcomes that are extremely sensitive to the order in which impacts occur. Robotic simulators commonly lack the accuracy to predict this ordering, and instead pick one with a heuristic. This discrepancy degrades performance when model-based controllers and policies learned in simulation are placed on a real robot. We reconcile this issue with a set-valued rigid-body model which generates a broad set of physically reasonable outcomes of simultaneous frictional impacts. We first extend Routh's impact model to multiple impacts by reformulating it as a differential inclusion (DI), and show that any solution will resolve all impacts in finite time. By considering time as a state, we embed this model into another DI which captures the continuous-time evolution of rigid body dynamics, and guarantee existence of solutions. We finally cast simulation of simultaneous impacts as a linear complementarity problem (LCP), and develop an algorithm for tight approximation of the post-impact velocity set with probabilistic guarantees. We demonstrate our approach on several examples drawn from manipulation and legged locomotion.

Contact surfaces in planar motion exhibit a coupling between tangential and rotational friction forces. This paper proposes planar friction models grounded in the LuGre model and limit surface theory. First, distributed planar extended state models are proposed and the Elasto-Plastic model is extended for multi-dimensional friction. Subsequently, we derive a reduced planar friction model, coupled with a pre-calculated limit surface, that offers reduced computational cost. The limit surface approximation through an ellipsoid is discussed. The properties of the planar friction models are assessed in various simulations, demonstrating that the reduced planar friction model achieves comparable performance to the distributed model while exhibiting ~80 times lower computational cost.