This work presents an overview of the techni-cal details behind a high-performance reinforcement learning policy deployment with the Spot RL Researcher Development Kit for low-level motor access on Boston Dynamic's Spot. This represents the first public demonstration of an end-to-end reinforcement learning policy deployed on Spot hardware with training code publicly available through Nvidia IsaacLab and deployment code available through Boston Dynamics. We utilize Wasserstein Distance and Maximum Mean Discrepancy to quantify the distributional dissimilarity of data collected on hardware and in simulation to measure our sim-to-real gap. We use these measures as a scoring function for the Covariance Matrix Adaptation Evolution Strategy to optimize simulated parameters that are unknown or difficult to measure from Spot. Our procedure for modeling and training produces high-quality reinforcement learning policies capable of multiple gaits, including a flight phase. We deploy policies capable of over 5.2m/s locomotion, more than triple Spot's default controller maximum speed, robustness to slippery surfaces, disturbance rejection, and overall agility previously unseen on Spot. We detail our method and release our code to support future work on Spot with the low-level API.

We present Diffuse-CLoC, a guided diffusion framework for physics-based look-ahead control that enables intuitive, steerable, and physically realistic motion generation. While existing kinematics motion generation with diffusion models offer intuitive steering capabilities with inference-time conditioning, they often fail to produce physically viable motions. In contrast, recent diffusion-based control policies have shown promise in generating physically realizable motion sequences, but the lack of kinematics prediction limits their steerability. Diffuse-CLoC addresses these challenges through a key insight: modeling the joint distribution of states and actions within a single diffusion model makes action generation steerable by conditioning it on the predicted states. This approach allows us to leverage established conditioning techniques from kinematic motion generation while producing physically realistic motions. As a result, we achieve planning capabilities without the need for a high-level planner. Our method handles a diverse set of unseen long-horizon downstream tasks through a single pre-trained model, including static and dynamic obstacle avoidance, motion in-betweening, and task-space control. Experimental results show that our method significantly outperforms the traditional hierarchical framework of high-level motion diffusion and low-level tracking.

Adaptive falling and recovery skills greatly extend the applicability of robot deployments. In the case of legged mobile manipulators, the robot arm could adaptively stop the fall and assist the recovery. Prior works on falling and recovery strategies for legged mobile manipulators usually rely on assumptions such as inelastic collisions and falling in defined directions to enable real-time computation. This paper presents a learning-based approach to reducing fall damage and recovery. An asymmetric actor-critic training structure is used to train a time-invariant policy with time-varying reward functions. In simulated experiments, the policy recovers from 98.9% of initial falling configurations. It reduces base contact impulse, peak joint internal forces, and base acceleration during the fall compared to the baseline methods. The trained control policy is deployed and extensively tested on the ALMA robot hardware. A video summarizing the proposed method and the hardware tests is available at https://youtu.be/avwg2HqGi8s

Legged robots are designed to perform highly dynamic motions. However, it remains challenging for users to retarget expressive motions onto these complex systems. In this paper, we present a Differentiable Optimal Control (DOC) framework that facilitates the transfer of rich motions from either animals or animations onto these robots. Interfacing with either motion capture or animation data, we formulate retargeting objectives whose parameters make them agnostic to differences in proportions and numbers of degrees of freedom between input and robot. Optimizing these parameters over the manifold spanned by optimal state and control trajectories, we minimize the retargeting error. We demonstrate the utility and efficacy of our modeling by applying DOC to a Model-Predictive Control (MPC) formulation, showing retargeting results for a family of robots of varying proportions and mass distribution. With a hardware deployment, we further show that the retargeted motions are physically feasible, while MPC ensures that the robots retain their capability to react to unexpected disturbances.

Dynamic locomotion in rough terrain requires accurate foot placement, collision avoidance, and planning of the underactuated dynamics of the system. Reliably optimizing for such motions and interactions in the presence of imperfect and often incomplete perceptive information is challenging. We present a complete perception, planning, and control pipeline, which can optimize motions for all degrees of freedom of the robot in real time. To mitigate the numerical challenges posed by the terrain, a sequence of convex inequality constraints is extracted as local approximations of foothold feasibility and embedded into an online model-predictive controller. Steppability classification, plane segmentation, and a signed distance field are precomputed per elevation map to minimize the computational effort during the optimization. A combination of multiple-shooting, real-time iteration, and a filter-based line search is used to solve the formulated problem reliably and at high rate. We validate the proposed method in scenarios with gaps, slopes, and stepping stones in simulation and experimentally on the ANYmal quadruped platform, resulting in state-of-the-art dynamic climbing.

This article presents a hybrid motion planning and control approach applicable to various ground robot types and morphologies. Our two-step approach uses a sampling-based planner to compute an approximate motion, which is then fed to numerical optimization for refinement. The sampling-based stage finds a long-term global plan consisting of a contact schedule and sequence of keyframes, i.e., stable whole-body configurations. Subsequently, the optimization refines the solution with a short-term planning horizon to satisfy all nonlinear dynamics constraints. The proposed hybrid planner can compute plans for scenarios that would be difficult for trajectory optimization or sampling planner alone. We present tasks of traversing challenging terrain that requires discovering a contact schedule, navigating nonconvex obstacles, and coordinating many degrees of freedom. Our hybrid planner has been applied to three different robots: a quadruped, a wheeled quadruped, and a legged excavator. We validate our hybrid locomotion planner in the real world and simulation, generating behaviors we could not achieve with previous methods. The results show that computing and executing hybrid locomotion plans is possible on hardware in real time.

In this paper, we present a real-time whole-body planner for collision-free legged mobile manipulation. We enforce both self-collision and environment-collision avoidance as soft constraints within a Model Predictive Control (MPC) scheme that solves a multi-contact optimal control problem. By penalizing the signed distances among a set of representative primitive collision bodies, the robot is able to safely execute a variety of dynamic maneuvers while preventing any self-collisions. Moreover, collision-free navigation and manipulation in both static and dynamic environments are made viable through efficient queries of distances and their gradients via a euclidean signed distance field. We demonstrate through a comparative study that our approach only slightly increases the computational complexity of the MPC planning. Finally, we validate the effectiveness of our framework through a set of hardware experiments involving dynamic mobile manipulation tasks with potential collisions, such as locomotion balancing with the swinging arm, weight throwing, and autonomous door opening.

This paper introduces a novel approach for whole-body motion planning and dynamic occlusion avoidance. The proposed approach reformulates the visibility constraint as a likelihood maximization of visibility probability. In this formulation, we augment the primary cost function of a whole-body model predictive control scheme through a relaxed log barrier function yielding a relaxed log-likelihood maximization formulation of visibility probability. The visibility probability is computed through a probabilistic shadow field that quantifies point light source occlusions. We provide the necessary algorithms to obtain such a field for both 2D and 3D cases. We demonstrate 2D implementations of this field in simulation and 3D implementations through real-time hardware experiments. We show that due to the linear complexity of our shadow field algorithm to the map size, we can achieve high update rates, which facilitates onboard execution on mobile platforms with limited computational power. Lastly, we evaluate the performance of the proposed MPC reformulation in simulation for a quadrupedal mobile manipulator.

Model Predictive Control (MPC) schemes have proven their efficiency in controlling high degree-of-freedom (DoF) complex robotic systems. However, they come at a high computational cost and an update rate of about tens of hertz. This relatively slow update rate hinders the possibility of stable haptic teleoperation of such systems since the slow feedback loops can cause instabilities and loss of transparency to the operator. This work presents a novel framework for transparent teleoperation of MPC-controlled complex robotic systems. In particular, we employ a feedback MPC approach [1] and exploit its structure to account for the operator input at a fast rate which is independent of the update rate of the MPC loop itself. We demonstrate our framework on a mobile manipulator platform and show that it significantly improves haptic teleoperation's transparency and stability. We also highlight that the proposed feedback structure is constraint satisfactory and does not violate any constraints defined in the optimal control problem. To the best of our knowledge, this work is the first realization of the bilateral teleoperation of a legged manipulator using a whole-body MPC framework.

A kitchen assistant needs to operate human-scale objects, such as cabinets and ovens, in unmapped environments with dynamic obstacles. Autonomous interactions in such environments require integrating dexterous manipulation and fluid mobility. While mobile manipulators in different form factors provide an extended workspace, their real-world adoption has been limited. Executing a high-level task for general objects requires a perceptual understanding of the object as well as adaptive whole-body control among dynamic obstacles. In this paper, we propose a two-stage architecture for autonomous interaction with large articulated objects in unknown environments. The first stage, object-centric planner, only focuses on the object to provide an action-conditional sequence of states for manipulation using RGB-D data. The second stage, agent-centric planner, formulates the whole-body motion control as an optimal control problem that ensures safe tracking of the generated plan, even in scenes with moving obstacles. We show that the proposed pipeline can handle complex static and dynamic kitchen settings for both wheel-based and legged mobile manipulators. Compared to other agent-centric planners, our proposed planner achieves a higher success rate and a lower execution time. We also perform hardware tests on a legged mobile manipulator to interact with various articulated objects in a kitchen. For additional material, please check: www.pair.toronto.edularticulated-mm/.

Terrain geometry is, in general, nonsmooth, nonlinear, nonconvex, and, if perceived through a robot-centric visual unit, appears partially occluded and noisy. This article presents the complete control pipeline capable of handling the aforementioned problems in real-time. We formulate a trajectory optimization problem that jointly optimizes over the base pose and footholds, subject to a height map. To avoid converging into undesirable local optima, we deploy a graduated optimization technique. We embed a compact, contact-force free stability criterion that is compatible with the nonflat ground formulation. Direct collocation is used as transcription method, resulting in a nonlinear optimization problem that can be solved online in less than ten milliseconds. To increase robustness in the presence of external disturbances, we close the tracking loop with a momentum observer. Our experiments demonstrate stair climbing, walking on stepping stones, and over gaps, utilizing various dynamic gaits.

We present a model predictive controller (MPC) that automatically discovers collision-free locomotion while simultaneously taking into account the system dynamics, friction constraints, and kinematic limitations. A relaxed barrier function is added to the optimization’s cost function, leading to collision avoidance behavior without increasing the problem’s computational complexity. Our holistic approach does not require any heuristics and enables legged robots to find whole-body motions in the presence of static and dynamic obstacles. We use a dynamically generated euclidean signed distance field for static collision checking. Collision checking for dynamic obstacles is modeled with moving cylinders, increasing the responsiveness to fast-moving agents. Furthermore, we include a Kalman filter motion prediction for moving obstacles into our receding horizon planning, enabling the robot to anticipate possible future collisions. Our experiments1demonstrate collision-free motions on a quadrupedal robot in challenging indoor environments. The robot handles complex scenes like overhanging obstacles and dynamic agents by exploring motions at the robot’s dynamic and kinematic limits.

Planning for legged-wheeled machines is typically done using trajectory optimization because of many degrees of freedom, thus rendering legged-wheeled planners prone to falling prey to bad local minima. We present a combined sampling and optimization-based planning approach that can cope with challenging terrain. The sampling-based stage computes whole-body configurations and contact schedule, which speeds up the optimization convergence. The optimization-based stage ensures that all the system constraints, such as non-holonomic rolling constraints, are satisfied. The evaluations show the importance of good initial guesses for optimization. Furthermore, they suggest that terrain/collision (avoidance) constraints are more challenging than the robot model’s constraints. Lastly, we extend the optimization to handle general terrain representations in the form of elevation maps.

Modern, torque-controlled service robots can regulate contact forces when interacting with their environment. Model Predictive Control (MPC) is a powerful method to solve the underlying control problem, allowing to plan for whole-body motions while including different constraints imposed by the robot dynamics or its environment. However, an accurate model of the robot-environment is needed to achieve a satisfying closed-loop performance. Currently, this necessity undermines the performance and generality of MPC in manipulation tasks. In this work, we combine an MPC-based whole-body controller with two adaptive schemes, derived from online system identification and adaptive control. As a result, we enable a general mobile manipulator to interact with unknown environments, without any need for re-tuning parameters or pre-modeling the interacting objects. In combination with the MPC controller, the two adaptive approaches are validated and benchmarked with a ball-balancing manipulator in door opening and object lifting tasks.

We present a learning algorithm for training a single policy that imitates multiple gaits of a walking robot. To achieve this, we use and extend MPC-Net, which is an Imitation Learning approach guided by Model Predictive Control (MPC). The strategy of MPC-Net differs from many other approaches since its objective is to minimize the control Hamiltonian, which derives from the principle of optimality. To represent the policies, we employ a mixture-of-experts network (MEN) and observe that the performance of a policy improves if each expert of a MEN specializes in controlling exactly one mode of a hybrid system, such as a walking robot. We introduce new loss functions for single- and multi-gait policies to achieve this kind of expert selection behavior. Moreover, we benchmark our algorithm against Behavioral Cloning and the original MPC implementation on various rough terrain scenarios. We validate our approach on hardware and show that a single learned policy can replace its teacher to control multiple gaits.

Quadrupedal robots are skillful at locomotion tasks while lacking manipulation skills, not to mention dexterous manipulation abilities. Inspired by the animal behavior and the duality between multi-legged locomotion and multi-fingered manipulation, we showcase a circus ball challenge on a quadrupedal robot, ANYmal. We employ a model-free reinforcement learning approach to train a deep policy that enables the robot to balance and manipulate a light-weight ball robustly using its limbs without any contact measurement sensor. The policy is trained in the simulation, in which we randomize many physical properties with additive noise and inject random disturbance force during manipulation, and achieves zero-shot deployment on the real robot without any adjustment. In the hardware experiments, dynamic performance is achieved with a maximum rotation speed of 15 °/s, and robust recovery is showcased under external poking. To our best knowledge, it is the first work that demonstrates the dexterous dynamic manipulation on a real quadrupedal robot.

The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time version of the well-known Differential Dynamic Programming (DDP) technique with a Gauss-Newton Hessian approximation. This family of methods has gained popularity in the robotics community due to its efficiency in solving complex trajectory optimization problems. However, one major drawback of DDP-based formulations is their inability to properly incorporate path constraints. In this paper, we address this issue by devising a constrained SLQ algorithm that handles a mixture of constraints with a previously implemented projection technique and a new augmented-Lagrangian approach. By providing an appropriate multiplier update law, and by solving a single inner and outer loop iteration, we are able to retrieve suboptimal solutions at rates suitable for real-time model-predictive control applications. We particularly focus on the inequality-constrained case, where three augmented-Lagrangian penalty functions are introduced, along with their corresponding multiplier update rules. These are then benchmarked against a relaxed log-barrier formulation in a cart-pole swing up example, an obstacle-avoidance task, and an object-pushing task with a quadrupedal mobile manipulator.

A high-quality free-motion rendering is one of the most vital traits to achieve an immersive human-robot interaction. Rendering free-motion is notably challenging for rehabilitation exoskeletons due to their relatively high weight and powerful actuators required for strength training and support. In the presence of dynamic human movements, accurate feedback linearization of the robot's dynamics is necessary to allow for a linear synthesis of interaction wrench controllers. Hence, we introduce a virtual model controller that uses two 6-DoF force sensors to control the interaction wrenches of a multi-DoF torque-controlled exoskeleton over the joint accelerations and inverse dynamics. Furthermore, we propose a disturbance observer for controlling the joint acceleration to diminish the influence of modeling errors on the inverse dynamics. To provide a high-bandwidth, low-bias estimation of the system's acceleration, we introduce a bias-observer which fuses the information from joint encoders and seven low priced IMUs. We have validated the performance of our proposed control structure on the shoulder and arm exoskeleton ANYexo. The experimental comparison of the controllers shows a reduction of the felt inertia and maximum reflected joint torque by a factor of more than three compared to state of the art. The controllers' robustness w.r.t. a model mismatch is validated. The experiments show that the closed-loop acceleration control improves the tracking, particularly at joints with low inertia. The proposed controllers' performance sets a new benchmark in haptic transparency for comparable devices and should be transferable to other applications.

Locomotion planning for legged systems requires reasoning about suitable contact schedules. The contact sequence and timings constitute a hybrid dynamical system and prescribe a subset of achievable motions. State-of-the-art approaches cast motion planning as an optimal control problem. In order to decrease computational complexity, one common strategy separates footstep planning from motion optimization and plans contacts using heuristics. In this paper, we propose to learn contact schedule selection from high-level task descriptors using Bayesian Optimization. A bi-level optimization is defined in which a Gaussian Process model predicts the performance of trajectories generated by a motion planning nonlinear program. The agent, therefore, retains the ability to reason about suitable contact schedules, while explicit computation of the corresponding gradients is avoided. We delineate the algorithm in its general form and provide results for planning single-legged hopping. Our method is capable of learning contact schedule transitions that align with human intuition. It performs competitively against a heuristic baseline in predicting task appropriate contact schedules.

We present a fully-integrated sensing and control system which enables mobile manipulator robots to execute building tasks with millimeter-scale accuracy on building construction sites. The approach leverages multi-modal sensing capabilities for state estimation, tight integration with digital building models, and integrated trajectory planning and whole-body motion control. A novel method for high-accuracy localization updates relative to the known building structure is proposed. The approach is implemented on a real platform and tested under realistic construction conditions. We show that the system can achieve sub-cm end-effector positioning accuracy during fully autonomous operation using solely onboard sensing.

The computational power of mobile robots is currently insufficient to achieve torque level whole-body Model Predictive Control (MPC) at the update rates required for complex dynamic systems such as legged robots. This problem is commonly circumvented by using a fast tracking controller to compensate for model errors between updates. In this work, we show that the feedback policy from a Differential Dynamic Programming (DDP) based MPC algorithm is a viable alternative to bridge the gap between the low MPC update rate and the actuation command rate. We propose to augment the DDP approach with a relaxed barrier function to address inequality constraints arising from the friction cone. A frequency-dependent cost function is used to reduce the sensitivity to high-frequency model errors and actuator bandwidth limits. We demonstrate that our approach can find stable locomotion policies for the torque-controlled quadruped, ANYmal, both in simulation and on hardware.

In this paper, we present an efficient Dynamic Programing framework for optimal planning and control of legged robots. First we formulate this problem as an optimal control problem for switched systems. Then we propose a multi-level optimization approach to find the optimal switching times and the optimal continuous control inputs. Through this scheme, the decomposed optimization can potentially be done more efficiently than the combined approach. Finally, we present a continuous-time constrained LQR algorithm which simultaneously optimizes the feedforward and feedback controller with O(n) time-complexity. In order to validate our approach, we show the performance of our framework on a quadrupedal robot. We choose the Center of Mass dynamics and the full kinematic formulation as the switched system model where the switching times as well as the contact forces and the joint velocities are optimized for different locomotion tasks such as gap crossing, walking and trotting.

This work addresses the problem of kinematic trajectory planning for mobile manipulators with non-holonomic constraints, and holonomic operational-space tracking constraints. We obtain whole-body trajectories and time-varying kinematic feedback controllers by solving a Constrained Sequential Linear Quadratic Optimal Control problem. The employed algorithm features high efficiency through a continuous-time formulation that benefits from adaptive step-size integrators and through linear complexity in the number of integration steps. In a first application example, we solve kinematic trajectory planning problems for a 26 DoF wheeled robot. In a second example, we apply Constrained SLQ to a real-world mobile manipulator in a receding-horizon optimal control fashion, where we obtain optimal controllers and plans at rates up to 100 Hz.

We present an algorithm that generates walking motions for quadruped robots without the use of an explicit footstep planner by simultaneously optimizing over both the Center of Mass (CoM) trajectory and the footholds. Feasibility is achieved by imposing stability constraints on the CoM related to the Zero Moment Point and explicitly enforcing kinematic constraints between the footholds and the CoM position. Given a desired goal state, the problem is solved online by a Nonlinear Programming solver to generate the walking motion. Experimental trials show that the algorithm is able to generate walking gaits for multiple steps in milliseconds that can be executed on a real quadruped robot.

We introduce a robust control architecture for the whole-body motion control of torque controlled robots with arms and legs. The method is based on the robust control of contact forces in order to track a planned Center of Mass trajectory. Its appeal lies in the ability to guarantee robust stability and performance despite rigid body model mismatch, actuator dynamics, delays, contact surface stiffness, and unobserved ground profiles. Furthermore, we introduce a task space decomposition approach which removes the coupling effects between contact force controller and the other non-contact controllers. Finally, we verify our control performance on a quadruped robot and compare its performance to a standard inverse dynamics approach on hardware.

This paper presents a framework for real-time, full-state feedback, unconstrained, nonlinear model predictive control that combines trajectory optimization and tracking control in a single, unified approach. The proposed method uses an iterative optimal control algorithm, namely Sequential Linear Quadratic (SLQ), in a Model Predictive Control (MPC) setting to solve the underlying nonlinear control problem and simultaneously derive the optimal feedforward and feedback terms. Our customized solver can generate trajectories of multiple seconds within only a few milliseconds. The performance of the approach is validated on two different hardware platforms, an AscTec Firefly hexacopter and the ball balancing robot Rezero. In contrast to similar approaches, we perform experiments that require leveraging the full system dynamics.

In recent years impressive results have been presented illustrating the potential of quadrotors to solve challenging tasks. Generally, the derivation of the controllers involve complex analytical manipulation of the dynamics and are very specific to the task at hand. In addition, most approaches construct a trajectory and then design a stabilizing controller in a separate step, whereas a fully optimal solution requires finding both simultaneously. In this paper, a generalized approach is presented using an iterative optimal control algorithm. A series of complex tasks are thus solved using the same algorithm without the need for manual manipulation of the system dynamics, heuristic simplifications, or manual trajectory generation. First, aggressive maneuvers are performed by requiring the quadrotor to pass with a slung load through a window not high enough for the load to pass while hanging straight down. Second, go-to-goal tasks with single and double rotor failure are demonstrated. The adaptability and applicability of this unified approach to such diverse tasks with a nonlinear, underactuated, constrained, and in the case of the slung load, hybrid quadrotor systems is thus shown.

Learning motion control as a unified process of designing the reference trajectory and the controller is one of the most challenging problems in robotics. The complexity of the problem prevents most of the existing optimization algorithms from giving satisfactory results. While model-based algorithms like iterative linear-quadratic-Gaussian (iLQG) can be used to design a suitable controller for the motion control, their performance is strongly limited by the model accuracy. An inaccurate model may lead to degraded performance of the controller on the physical system. Although using machine learning approaches to learn the motion control on real systems have been proven to be effective, their performance depends on good initialization. To address these issues, this paper introduces a two-step algorithm which combines the proven performance of a model-based controller with a model-free method for compensating for model inaccuracy. The first step optimizes the problem using iLQG. Then, in the second step this controller is used to initialize the policy for our PI2-01 reinforcement learning algorithm. This algorithm is a derivation of the PI2algorithm enabling more stable and faster convergence. The performance of this method is demonstrated both in simulation and experimental results.