Imitation learning is a data-driven approach to learning policies from expert behavior, but it is prone to unreliable outcomes in out-of-sample (OOS) regions. While previous research relying on stable dynamical systems guarantees convergence to a desired state, it often overlooks transient behavior. We propose a framework for learning policies modeled by contractive dynamical systems, ensuring that all policy rollouts converge regardless of perturbations, and in turn, enable efficient OOS recovery. By leveraging recurrent equilibrium networks and coupling layers, the policy structure guarantees contractivity for any parameter choice, which facilitates unconstrained optimization. We also provide theoretical upper bounds for worst-case and expected loss to rigorously establish the reliability of our method in deployment. Empirically, we demonstrate substantial OOS performance improvements for simulated robotic manipulation and navigation tasks. See [sites.google.com/view/contractive-dynamical-policies](https://sites.google.com/view/contractive-dynamical-policies) for our codebase and highlight of the results.

Imitation learning mitigates the resource-intensive nature of learning policies from scratch by mimicking expert behavior. While existing methods can accurately replicate expert demonstrations, they often exhibit unpredictability in unexplored regions of the state space, thereby raising major safety concerns when facing perturbations. We propose SNDS, an imitation learning approach aimed at efficient training of scalable neural policies while formally ensuring global stability. SNDS leverages a neural architecture that enables the joint training of the policy and its associated Lyapunov candidate to ensure global stability throughout the learning process. We validate our approach through extensive simulations and deploy the trained policies on a real-world manipulator arm. The results confirm SNDS’s ability to address instability, accuracy, and computational intensity challenges highlighted in the literature, positioning it as a promising solution for scalable and stable policy learning in complex environments.

The need for rapid and reliable robot deployment is on the rise. Imitation Learning (IL) has become popular for producing motion planning policies from a set of demonstrations. However, many methods in IL are not guaranteed to produce stable policies. The generated policy may not converge to the robot target, reducing reliability, and may collide with its environment, reducing the safety of the system. Stable Estimator of Dynamic Systems (SEDS) produces stable policies by constraining the Lyapunov stability criteria during learning, but the Lyapunov candidate function had to be manually selected. In this work, we propose a novel method for learning a Lyapunov function and a collision-free policy using a single neural network model. The method can be equipped with an obstacle avoidance module for convex object pairs to guarantee no collisions. We demonstrated our method is capable of finding policies in several simulation environments and transfer to a real-world scenario.

Legged robot locomotion requires the planning of stable reference trajectories, especially while traversing uneven terrain. The proposed trajectory optimization framework is capable of generating dynamically stable base and footstep trajectories for multiple steps. The locomotion task can be defined with contact locations, base motion or both, making the algorithm suitable for multiple scenarios (e.g., presence of moving obstacles). The planner uses a simplified momentum-based task space model for the robot dynamics, allowing computation times that are fast enough for online replanning. This fast planning capability also enables the quadruped to accommodate for drift and environmental changes. The algorithm is tested on simulation and a real robot across multiple scenarios, which includes uneven terrain, stairs and moving obstacles. The results show that the planner is capable of generating stable trajectories in the real robot even when a box of 15 cm height is placed in front of its path at the last moment.

Legged systems need to optimize contact force in order to maintain contacts. For this, the controller needs to have the knowledge of the surface geometry and how slippery the terrain is. We can use a vision system to realize the terrain, but the accuracy of the vision system degrades in harsh weather, and it cannot visualize the terrain if it is covered with water or grass. Also, the degree of friction cannot be directly visualized. In this paper, we propose an online method to estimate the surface information via haptic exploration. We also introduce a probabilistic criterion to measure the quality of the estimation. The method is validated on both simulation and a real robot platform.

This paper presents a control framework to teleoperate a quadruped robot's foot for operator-guided haptic exploration of the environment. Since one leg of a quadruped robot typically only has 3 actuated degrees of freedom (DoFs), the torso is employed to assist foot posture control via a hierarchical whole-body controller. The foot and torso postures are controlled by two analytical Cartesian impedance controllers cascaded by a null space projector. The contact forces acting on supporting feet are optimized by quadratic programming (QP). The foot's Cartesian impedance controller may also estimate contact forces from trajectory tracking errors, and relay the force-feedback to the operator. A 7D haptic joystick, Sigma.7, transmits motion commands to the quadruped robot ANYmal, and renders the force feedback. Furthermore, the joystick's motion is bounded by mapping the foot's feasible force polytope constrained by the friction cones and torque limits in order to prevent the operator from driving the robot to slipping or falling over. Experimental results demonstrate the efficiency of the proposed framework.

In this paper, we propose a method for selecting the optimal footholds for legged systems. The goal of the proposed method is to find the best foothold for the swing leg on a local elevation map. First, we evaluate the geometrical characteristics of each cell on the elevation map, checks kinematic constraints and collisions. Then, we apply the Convolutional Neural Network to learn the relationship between the local elevation map and the quality of potential footholds. During execution time, the controller obtains the qualitative measurement of each potential foothold from the neural model. This method evaluates hundreds of potential footholds and checks multiple constraints in a single step which takes 10 ms on a standard computer without GPU. The experiments were carried out on a quadruped robot walking over rough terrain in both simulation and real robotic platforms.

We consider a virtual manipulator in grasping scenarios which allows us to capture the effect of the object dynamics. This modeling approach turns a multi-arm robot into an underactuated system. We observe that controlling floating-base multi-leg robots is fundamentally similar. The Projected Inverse Dynamics Control approach is employed for decoupling contact consistent motion generation and controlling contact wrenches. The proposed framework for underactuated robots has been evaluated on an enormous robot hand composed of four KUKA LWR IV+ representing fingers cooperatively manipulating a 9kg box with total 28 actuated DOF and six virtual DOF representing the object as additional free-floating robot link. Finally, we validate the same approach on ANYmal, a floating-base quadruped with 12 actuated DOF. Experiments are performed both in simulation and real world.

We propose a model-based control framework for multi-arm manipulation of a rigid object subject to external disturbances. The control framework, based on projected inverse dynamics, decomposes the control law into constrained and unconstrained subspaces. Unconstrained components accomplish the motion task with a desired 6-DOF Cartesian impedance behaviour against external disturbances. Meanwhile, the constrained component enforces contact and friction constraints by optimising for contact forces within the constrained subspace. External disturbances are explicitly compensated for without using force/torque sensors at the contact points. The approach is evaluated on a dual-arm platform manipulating a rigid object while coping with unknown object dynamics and human interaction.

Legged robots have many potential applications in real-world scenarios where the tasks are too dangerous for humans, and compliance is needed to protect the system against external disturbances and impacts. In this paper, we propose a model-based controller for hierarchical tasks of legged systems subject to external disturbance. The control framework is based on projected inverse dynamics controller, such that the control law is decomposed into two orthogonal subspaces, i.e., the constrained and the unconstrained subspaces. The unconstrained component controls multiple desired tasks with impedance responses. The constrained space controller maintains the contact subject to unknown external disturbances, without the use of any force/torque sensing at the contact points. By explicitly modelling the external force, our controller is robust to external disturbances and errors arising from incorrect dynamic model information. The main contributions of this paper include (1) incorporating an impedance controller to control external disturbances and allow impedance shaping to adjust the behaviour of the motion under external disturbances, (2) optimising contact forces within the constrained subspace that also takes into account the external disturbances without using force/torque sensors at the contact locations. The techniques are evaluated on the ANYmal quadruped platform under a variety of scenarios.

Many human skills can be described in terms of performing a set of prioritised tasks. While a number of tools have become available that recover the underlying control policy from constrained movements, few have explicitly considered learning how constraints should be imposed in order to perform the control policy. In this paper, a method for learning the self-imposed constraints present in movement observations is proposed. The problem is formulated into the operational space control framework, where the goal is to estimate the constraint matrix and its null space projection that decompose the task space and any redundant degrees of freedom. The proposed method requires no prior knowledge about either the dimensionality of the constraints nor the underlying control policies. The techniques are evaluated on a simulated three degree-of-freedom arm and on the AR10 humanoid hand.

Many everyday human skills can be considered in terms of performing some task subject to a set of self-imposed or environmental constraints. In recent years, a number of new tools have become available in the learning and robotics community that allow data from constrained and/or redundant systems to be used to uncover underlying consistent behaviours that may be otherwise masked by the constraints. However, while a wide variety of work for generalisation of movements have been proposed, few have explicitly considered learning the constraints of the motion and ways to cope with unknown environment. In this paper, we propose a method to learn the constraints such that some previously learnt behaviours can be adapted to new environment in an appropriate way. In particular, we consider learning the null space projection matrix of a kinematically constrained system, and see how previously learnt policies can be adapted to novel constraints.

An accurate model of patient survival time can help in the treatment and care of cancer patients. The common practice of providing survival time estimates based only on population averages for the site and stage of cancer ignores many important individual differences among patients. In this paper, we propose a local regression method for learning patient-specific survival time distribution based on patient attributes such as blood tests and clinical assessments. When tested on a cohort of more than 2000 cancer patients, our method gives survival time predictions that are much more accurate than popular survival analysis models such as the Cox and Aalen regression models. Our results also show that using patient-specific attributes can reduce the prediction error on survival time by as much as 20% when compared to using cancer site and stage only.