-- Humanoid robots have great potential for real-world applications due to their ability to operate in environments built for humans, but their deployment is hindered by the challenge of controlling their underlying high-dimensional nonlinear hybrid dynamics. While reduced-order models like the Hybrid Linear Inverted Pendulum (HLIP) are simple and computationally efficient, they lose whole-body expressiveness. Meanwhile, recent advances in Contact-Implicit Model Predictive Control (CI-MPC) enable robots to plan through multiple hybrid contact modes, but remain vulnerable to local minima and require significant tuning. We propose a control framework that combines the strengths of HLIP and CI-MPC. The reduced-order model generates a nominal gait, while CI-MPC manages the whole-body dynamics and modifies the contact schedule as needed. We demonstrate the effectiveness of this approach in simulation with a novel 24 degree-of-freedom humanoid robot: Achilles. Our proposed framework achieves rough terrain walking, disturbance recovery, robustness under model and state uncertainty, and allows the robot to interact with obstacles in the environment, all while running online in real-time at 50 Hz. Humanoid robots, due to their anthropomorphic structure, are well suited to perform tasks in environments built for humans.

We show that contact-rich motion planning is also sparsity-rich when viewed as polynomial optimization (POP). We can exploit not only the correlative and term sparsity patterns that are general to all POPs, but also specialized sparsity patterns from the robot kinematic structure and the separability of contact modes. Such sparsity enables the design of high-order but sparse semidefinite programming (SDPs) relaxations--building upon Lasserre's moment and sums of squares hierarchy--that (i) can be solved in seconds by off-the-shelf SDP solvers, and (ii) compute near globally optimal solutions to the nonconvex contact-rich planning problems with small certified suboptimality. Through extensive experiments both in simulation (Push Bot, Push Box, Push Box with Obstacles, and Planar Hand) and real world (Push T), we demonstrate the power of using convex SDP relaxations to generate global contact-rich motion plans. As a contribution of independent interest, we release the Sparse Polynomial Optimization Toolbox (SPOT)--implemented in C++ with interfaces to both Python and Matlab--that automates sparsity exploitation for robotics and beyond.

As bipedal robots become more and more popular in commercial and industrial settings, the ability to control them with a high degree of reliability is critical. To that end, this paper considers how to accurately estimate which feet are currently in contact with the ground so as to avoid improper control actions that could jeopardize the stability of the robot. Additionally, modern algorithms for estimating the position and orientation of a robot's base frame rely heavily on such contact mode estimates. Dedicated contact sensors on the feet can be used to estimate this contact mode, but these sensors are prone to noise, time delays, damage/yielding from repeated impacts with the ground, and are not available on every robot. To overcome these limitations, we propose a momentum observer based method for contact mode estimation that does not rely on such contact sensors. Often, momentum observers assume that the robot's base frame can be treated as an inertial frame. However, since many humanoids' legs represent a significant portion of the overall mass, the proposed method instead utilizes multiple simultaneous dynamic models. Each of these models assumes a different contact condition. A given contact assumption is then used to constrain the full dynamics in order to avoid assuming that either the body is an inertial frame or that a fully accurate estimate of body velocity is known. The (dis)agreement between each model's estimates and measurements is used to determine which contact mode is most likely using a Markov-style fusion method. The proposed method produces contact detection accuracy of up to 98.44% with a low noise simulation and 77.12% when utilizing data collect on the Sarcos Guardian XO robot (a hybrid humanoid/exoskeleton).

Planning contact-rich interactions for multi-finger manipulation is challenging due to the high-dimensionality and hybrid nature of dynamics. Recent advances in data-driven methods have shown promise, but are sensitive to the quality of training data. Combining learning with classical methods like trajectory optimization and search adds additional structure to the problem and domain knowledge in the form of constraints, which can lead to outperforming the data on which models are trained. We present Diffusion-Informed Probabilistic Contact Search (DIPS), which uses an A* search to plan a sequence of contact modes informed by a diffusion model. We train the diffusion model on a dataset of demonstrations consisting of contact modes and trajectories generated by a trajectory optimizer given those modes. In addition, we use a particle filter-inspired method to reason about variability in diffusion sampling arising from model error, estimating likelihoods of trajectories using a learned discriminator. We show that our method outperforms ablations that do not reason about variability and can plan contact sequences that outperform those found in training data across multiple tasks. We evaluate on simulated tabletop card sliding and screwdriver turning tasks, as well as the screwdriver task in hardware to show that our combined learning and planning approach transfers to the real world.

Parameterizing finger rolling and finger-object contacts in a differentiable manner is important for formulating dexterous manipulation as a trajectory optimization problem. In contrast to previous methods which often assume simplified geometries of the robot and object or do not explicitly model finger rolling, we propose a method to further extend the capabilities of dexterous manipulation by accounting for non-trivial geometries of both the robot and the object. By integrating the object's Signed Distance Field (SDF) with a sampling method, our method estimates contact and rolling-related variables and includes those in a trajectory optimization framework. This formulation naturally allows for the emergence of finger-rolling behaviors, enabling the robot to locally adjust the contact points. Our method is tested in a peg alignment task and a screwdriver turning task, where it outperforms the baselines in terms of achieving desired object configurations and avoiding dropping the object. We also successfully apply our method to a real-world screwdriver turning task, demonstrating its robustness to the sim2real gap.

In this paper, we consider the problem of non-prehensile manipulation using grasped objects. This problem is a superset of many common manipulation skills including instances of tool-use (e.g., grasped spatula flipping a burger) and assembly (e.g., screwdriver tightening a screw). Here, we present an algorithmic approach for non-prehensile manipulation leveraging a gripper with highly compliant and high-resolution tactile sensors. Our approach solves for robot actions that drive object poses and forces to desired values while obeying the complex dynamics induced by the sensors as well as the constraints imposed by static equilibrium, object kinematics, and frictional contact. Our method is able to produce a variety of manipulation skills and is amenable to gradient-based optimization by exploiting differentiability within contact modes (e.g., specifications of sticking or sliding contacts). We evaluate 4 variants of controllers that attempt to realize these plans and demonstrate a number of complex skills including non-prehensile planar sliding and pivoting on a variety of object geometries. The perception and controls capabilities that drive these skills are the building blocks towards dexterous and reactive autonomy in unstructured environments.

There has been significant recent interest in the mechanics community to design structures that can either violate reciprocity, or exhibit elastic asymmetry or odd elasticity. While these properties are highly desirable to enable mechanical metamaterials to exhibit novel wave propagation phenomena, it remains an open question as to how to design passive structures that exhibit both significant non-reciprocity and elastic asymmetry. In this paper, we first define several design spaces for chiral metamaterials leveraging specific design parameters, including the ligament contact angles, the ligament shape, and circle radius. Having defined the design spaces, we then leverage machine learning approaches, and specifically Bayesian optimization, to determine optimally performing designs within each design space satisfying maximal non-reciprocity or stiffness asymmetry. Finally, we perform multi-objective optimization by determining the Pareto optimum and find chiral metamaterials that simultaneously exhibit high non-reciprocity and stiffness asymmetry. Our analysis of the underlying mechanisms reveals that chiral metamaterials that can display multiple different contact states under loading in different directions are able to simultaneously exhibit both high non-reciprocity and stiffness asymmetry. Overall, this work demonstrates the effectiveness of employing ML to bring insights to a novel domain with limited prior information, and more generally will pave the way for metamaterials with unique properties and functionality in directing and guiding mechanical wave energy.

Thus, it is We can make very skillful use of various contacts desirable that a planning algorithm be robust to various (e.g., with the environment, our own body, etc.) to perform uncertainties like grasp center, extrinsic contact location, etc. complex manipulation. In a striking contrast, achieving such We present a method which can incorporate uncertainties in dexterous behavior for robots remains very challenging. Using several of the kinematic constraints to generate robust plans environmental contacts efficiently can provide additional for perform in-hand manipulation. This idea is also illustrated dexterity to robots while performing complex manipulation in Figure 1, where a naïve plan can easily lose contact with the [1]. However, the current generation of robotic systems environment due to uncertainty in the grasp location or the mostly avoid making contacts with their environment.

We present a method for global motion planning of robotic systems that interact with the environment through contacts. Our method directly handles the hybrid nature of such tasks using tools from convex optimization. We formulate the motion-planning problem as a shortest-path problem in a graph of convex sets, where a path in the graph corresponds to a contact sequence and a convex set models the quasi-static dynamics within a fixed contact mode. For each contact mode, we use semidefinite programming to relax the nonconvex dynamics that results from the simultaneous optimization of the object's pose, contact locations, and contact forces. The result is a tight convex relaxation of the overall planning problem, that can be efficiently solved and quickly rounded to find a feasible contact-rich trajectory. As a first application of this technique, we focus on the task of planar pushing. Exhaustive experiments show that our convex-optimization method generates plans that are consistently within a small percentage of the global optimum. We demonstrate the quality of these plans on a real robotic system.

This paper presents a contact-implicit model predictive control (MPC) framework for the real-time discovery of multi-contact motions, without predefined contact mode sequences or foothold positions. This approach utilizes the contact-implicit differential dynamic programming (DDP) framework, merging the hard contact model with a linear complementarity constraint. We propose the analytical gradient of the contact impulse based on relaxed complementarity constraints to further the exploration of a variety of contact modes. By leveraging a hard contact model-based simulation and computation of search direction through a smooth gradient, our methodology identifies dynamically feasible state trajectories, control inputs, and contact forces while simultaneously unveiling new contact mode sequences. However, the broadened scope of contact modes does not always ensure real-world applicability. Recognizing this, we implemented differentiable cost terms to guide foot trajectories and make gait patterns. Furthermore, to address the challenge of unstable initial roll-outs in an MPC setting, we employ the multiple shooting variant of DDP. The efficacy of the proposed framework is validated through simulations and real-world demonstrations using a 45 kg HOUND quadruped robot, performing various tasks in simulation and showcasing actual experiments involving a forward trot and a front-leg rearing motion.