Performing acrobatic maneuvers involving long aerial phases, such as precise dives or multiple backflips from significant heights, remains an open challenge in legged robot autonomy. Such aggressive motions often require accurate state predictions over long horizons with multiple contacts and extended flight phases. Most existing trajectory optimization (TO) methods rely on Euler or Runge-Kutta integration, which can accumulate significant prediction errors over long planning horizons. In this work, we propose a novel whole-body TO method using variational integration (VI) and full-body nonlinear dynamics for long-flight aggressive maneuvers. Compared to traditional Euler-based TO, our approach using VI preserves energy and momentum properties of the continuous-time system and reduces error between predicted and executed trajectories by factors of between 2 - 10 while achieving similar planning time. We successfully demonstrate long-flight triple backflips on a quadruped A1 robot model and backflips on a bipedal HECTOR robot model for various heights and distances, achieving landing angle errors of only a few degrees. In contrast, TO with Euler integration fails to achieve accurate landings in equivalent circumstances, e.g., with landing angle errors greater than 90° for triple backflips. We provide an open-source implementation of our VI -discretized TO to support further research on accurate dynamic maneuvers for multi-rigid-body robot systems with contact: https://github.com/DRCL-USC/VI_discretized_TO

Teleoperated humanoid robot systems have made substantial advancements in recent years, offering a physical avatar that harnesses human skills and decision-making while safeguarding users from hazardous environments. However, current telelocomotion interfaces often fail to accurately represent the robot's environment, limiting the user's ability to effectively navigate the robot through unstructured terrain. This paper presents an initial telelocomotion framework that integrates the ForceBot locomotion interface with the small-sized humanoid robot, HECTOR V2. The framework utilizes ForceBot to simulate walking motion and estimate the user's Center of Mass (CoM) trajectory, which serves as a tracking reference for the robot. On the robot side, a model predictive control (MPC) approach, based on a reduced-order single rigid body model, is employed to track the user's scaled trajectory. We present experimental results on ForceBot's CoM estimation and the robot's tracking performance, demonstrating the feasibility of this approach.

Current humanoid push-recovery strategies often use whole-body motion, yet they tend to overlook posture regulation. For instance, in manipulation tasks, the upper body may need to stay upright and have minimal recovery displacement. This paper introduces a novel approach to enhancing humanoid push-recovery performance under unknown disturbances and regulating body posture by tailoring the recovery stepping strategy. We propose a hierarchical-MPC-based scheme that analyzes and detects instability in the prediction window and quickly recovers through adapting gait frequency. Our approach integrates a high-level nonlinear MPC, a posture-aware gait frequency adaptation planner, and a low-level convex locomotion MPC. The planners predict the center of mass (CoM) state trajectories that can be assessed for precursors of potential instability and posture deviation. In simulation, we demonstrate improved maximum recoverable impulse by 131 % on average compared with baseline approaches. In hardware experiments, a 125 ms advancement in recovery stepping timing/reflex has been observed with the proposed approach. We also demonstrate improved push-recovery performance and minimized body attitude change under 0.2 rad.

Achieving precise target jumping with legged robots poses a significant challenge due to the long flight phase and the uncertainties inherent in contact dynamics and hardware. Forcefully attempting these agile motions on hardware could result in severe failures and potential damage. Motivated by this challenge, we propose an Iterative Learning Control (ILC) approach to learn and refine jumping skills from easy to difficult, instead of directly learning these challenging tasks. We verify that learning from simplicity can enhance safety and target jumping accuracy over trials. Compared to other ILC approaches for legged locomotion, our method can tackle the problem of a long flight phase where control input is not available. In addition, our approach allows the robot to apply what it learns from a simple jumping task to accomplish more challenging tasks within a few trials directly in hardware, instead of learning from scratch. We validate the method through extensive experiments on the Al model and hardware for various tasks. Starting from a small jump (e.g., a forward jump 40cm), our learning approach empowers the robot to accomplish a variety of challenging targets, including jumping onto a 20cm high box, leaping to a greater distance of up to 60cm, as well as performing jumps while carrying an unknown payload of 2kg. Our framework allows the robot to reach the desired position and orientation targets with approximate errors of 1 cm and 10within a few trials.

Bipedal locomotion control is essential for humanoid robots to navigate complex, human-centric environments. While optimization-based control designs are popular for integrating sophisticated models of humanoid robots, they often require labor-intensive manual tuning. In this work, we address the challenges of parameter selection in bipedal locomotion control using DiffTune, a model-based autotuning method that leverages differential programming for efficient parameter learning. A major difficulty lies in balancing model fidelity with differentiability. We address this difficulty using a low-fidelity model for differentiability, enhanced by a Ground Reaction Force-and-Moment Network (GRFM-Net) to capture discrepancies between MPC commands and actual control effects. We validate the parameters learned by DiffTune with GRFM-Net in hardware experiments, which demonstrates the parameters’ optimality in a multi-objective setting compared with baseline parameters, reducing the total loss by up to 40.5% compared with the expert-tuned parameters. The results confirm the GRFM-Net’s effectiveness in mitigating the sim-to-real gap, improving the transferability of simulation-learned parameters to real hardware.

Dynamic loco-manipulation calls for effective whole-body control and contact-rich interactions with the object and the environment. Existing learning-based control synthesis relies on training low-level skill policies and explicitly switching with a high-level policy or a hand-designed finite state machine, leading to quasi-static behaviors. In contrast, dynamic tasks such as soccer require the robot to run towards the ball, decelerate to an optimal approach to dribble, and eventually kick a goal—a continuum of smooth motion. To this end, we propose Preferenced Oracle Guided Multi-mode Policies (OGMP) to learn a single policy mastering all the required modes and preferred sequence of transitions to solve uni-object loco-manipulation tasks. We design hybrid automatons as oracles to generate references with continuous dynamics and discrete mode jumps to perform a guided policy optimization through bounded exploration. To enforce learning a desired sequence of mode transitions, we present a task-agnostic preference reward that enhances performance. The proposed approach demonstrates successful loco-manipulation for tasks like soccer and moving boxes omnidirectionally through whole-body control. In soccer, a single policy learns to optimally reach the ball, transition to contact-rich dribbling, and execute successful goal kicks and ball stops. Leveraging the oracle’s abstraction, we solve each loco-manipulation task on robots with varying morphologies, including HECTOR V1, Berkeley Humanoid, Unitree G1, and H1, using the same reward definition and weights.

In the context of legged robots, adaptive behavior involves adaptive balancing and adaptive swing foot reflection. While adaptive balancing counteracts perturbations to the robot, adaptive swing foot reflection helps the robot to navigate intricate terrains without foot entrapment. In this paper, we manage to bring both aspects of adaptive behavior to quadruped locomotion by combining RL and MPC while improving the robustness and agility of blind legged locomotion. This integration leverages MPC’s strength in predictive capabilities and RL’s adeptness in drawing from past experiences. Unlike traditional locomotion controls that separate stance foot control and swing foot trajectory, our innovative approach unifies them, addressing their lack of synchronization. At the heart of our contribution is the synthesis of stance foot control with swing foot reflection, improving agility and robustness in locomotion with adaptive behavior. A hallmark of our approach is robust blind stair climbing through swing foot reflection. Moreover, we intentionally designed the learning module as a general plugin for different robot platforms. We trained the policy and implemented our approach on the Unitree A1 robot, achieving impressive results: a peak turn rate of 8.5 rad/s, a peak running speed of 3 m/s, and steering at a speed of 2.5 m/s. Remarkably, this framework also allows the robot to maintain stable locomotion while bearing an unexpected load of 10 kg, or 83% of its body mass. We further demonstrate the generalizability and robustness of the same policy where it realizes zero-shot transfer to different robot platforms like Go1 and AlienGo robots for load carrying. Code is made available for the use of the research community at https://github.com/DRCL-USC/RL_augmented_MPC.git

Many applications require the deployment of legged-robot teams to effectively and efficiently carry out missions. The use of multiple robots allows tasks to be executed concurrently, expediting mission completion. It also enhances resilience by enabling task transfer in case of a robot failure. This paper presents a formulation based on Mixed Integer Linear Programming (MILP) for allocating tasks to robots by taking into account travel time and ensuring efficient execution of collaborative tasks. We extended the MILP formulation to account for complexities with legged robot teams. Our results demonstrate that this approach leads to improved performance in terms of the makespan of the mission. We demonstrate the usefulness of this approach using a case study involving the disinfection of a building consisting of multiple rooms.

In recent years, the field of legged robotics has seen growing interest in enhancing the capabilities of these robots through the integration of articulated robotic arms. However, achieving successful loco-manipulation, especially involving interaction with heavy objects, is far from straightforward, as object manipulation can introduce substantial disturbances that impact the robot’s locomotion. This paper presents a novel framework for legged loco-manipulation that considers whole-body coordination through a hierarchical optimization-based control framework. First, an online manipulation planner computes the manipulation forces and manipulated object task-based reference trajectory. Then, pose optimization aligns the robot’s trajectory with kinematic constraints. The resultant robot reference trajectory is executed via a linear MPC controller incorporating the desired manipulation forces into its prediction model. Our approach has been validated in simulation and hardware experiments, highlighting the necessity of whole-body optimization compared to the baseline locomotion MPC when interacting with heavy objects. Experimental results with Unitree Aliengo, equipped with a custom-made robotic arm, showcase its ability to lift and carry an 8kg payload and manipulate doors.

Agile-legged robots have proven to be highly effective in navigating and performing tasks in complex and challenging environments, including disaster zones and industrial settings. However, these applications commonly require the capability of carrying heavy loads while maintaining dynamic motion. Therefore, this paper presents a novel methodology for incorporating adaptive control into a force-based control system. Recent advancements in the control of quadruped robots show that force control can effectively realize dynamic locomotion over rough terrain. By integrating adaptive control into the force-based controller, our proposed approach can maintain the advantages of the baseline framework while adapting to significant model uncertainties and unknown terrain impact models. Experimental validation was successfully conducted on the Unitree A1 robot. With our approach, the robot can carry heavy loads (up to 50% of its weight) while performing dynamic gaits such as fast trotting and bounding across uneven terrains.

We present a new framework for implementing real-time embedded safety-critical controllers which utilizes hybrid computing to address the issue of limited computational resources, a problem that is particularly prevalent in microrobotics. In our approach, the nominal stabilizing control algorithm is implemented digitally while the safety-critical quadratic program is solved via a dedicated analog resistor array. We apply this hybrid computing architecture to a simulated collision avoidance task for a micro-aerial vehicle and show the benefit relative to a purely-digital implementation. By leveraging analog quadratic programming on the Crazyflie 2.1 micro quadrotor, a reduction in overall processing time from 8.9 ms to 0.6 ms is estimated for this computationally-limited system. We further display the viability of our proposed safety-critical control framework through real-time flight demonstrations, utilizing a novel prototype analog circuit tethered to the Crazyflie. The flight results confirm the functionality of the control structure and prototype circuit while highlighting the overall capabilities of hybrid computing.

Recent studies on quadruped robots have focused on either locomotion or mobile manipulation using a robotic arm. However, legged robots can manipulate large objects using non-prehensile manipulation primitives, such as planar pushing, to drive the object to the desired location. This paper presents a novel hierarchical model predictive control (MPC) for contact optimization of the manipulation task. Using two cascading MPCs, we split the loco-manipulation problem into two parts: the first to optimize both contact force and contact location between the robot and the object, and the second to regulate the desired interaction force through the robot locomotion. Our method is successfully validated in both simulation and hardware experiments. While the baseline locomotion MPC fails to follow the desired trajectory of the object, our proposed approach can effectively control both object's position and orientation with minimal tracking error. This capability also allows us to perform obstacle avoidance for both the robot and the object during the loco-manipulation task.

Legged robots have shown remarkable advantages in navigating uneven terrain. However, realizing effective loco-motion and manipulation tasks on quadruped robots is still challenging. In addition, object and terrain parameters are generally unknown to the robot in these problems. Therefore, this paper proposes a hierarchical adaptive control framework that enables legged robots to perform loco-manipulation tasks without any given assumption on the object's mass, the friction coefficient, or the slope of the terrain. In our approach, we first present an adaptive manipulation control to regulate the contact force to manipulate an unknown object on unknown terrain. We then introduce a unified model predictive control (MPC) for loco-manipulation that takes into account the manipulation force in our robot dynamics. The proposed MPC framework thus can effectively regulate the interaction force between the robot and the object while keeping the robot balance. Experimental validation of our proposed approach is successfully conducted on a Unitree A1 robot, allowing it to manipulate an unknown time-varying load up to 7 kg (60% of the robot's weight). Moreover, our framework enables fast adaptation to unknown slopes or different surfaces with different friction coefficients.

In this paper, we propose a novel framework for synthesizing a single multimodal control policy capable of generating diverse behaviors (or modes) and emergent inherent transition maneuvers for bipedal locomotion. In our method, we first learn efficient latent encodings for each behavior by training an autoencoder from a dataset of rough reference motions. These latent encodings are used as commands to train a multimodal policy through an adaptive sampling of modes and transitions to ensure consistent performance across different behaviors. We validate the policy's performance in simulation for various distinct locomotion modes such as walking, leaping, jumping on a block, standing idle, and all possible combinations of inter-mode transitions. Finally, we integrate a task-based planner to rapidly generate open-loop mode plans for the trained multimodal policy to solve high-level tasks like reaching a goal position on a challenging terrain. Complex parkour-like motions by smoothly combining the discrete locomotion modes were generated in$\sim 3$min. to traverse tracks with a gap of width 0.45 m, a plateau of height 0.2 m, and a block of height 0.4 m, which are all significant compared to the dimensions of our mini-biped platform.

Despite the potential benefits of collaborative robots, effective manipulation tasks with quadruped robots remain difficult to realize. In this paper, we propose a hierarchical control system that can handle real-world collaborative manipulation tasks, including uncertainties arising from object properties, shape, and terrain. Our approach consists of three levels of controllers. Firstly, an adaptive controller computes the required force and moment for object manipulation without prior knowledge of the object's properties and terrain. The computed force and moment are then optimally distributed between the team of quadruped robots using a Quadratic Programming (QP)-based controller. This QP-based controller optimizes each robot's contact point location with the object while satisfying constraints associated with robot-object contact. Finally, a decentralized loco-manipulation controller is designed for each robot to apply manipulation force while maintaining the robot's stability. We successfully validated our approach in a high-fidelity simulation environment where a team of quadruped robots manipulated an unknown object weighing up to 18 kg on different terrains while following the desired trajectory.

Deep reinforcement learning has emerged as a popular and powerful way to develop locomotion controllers for quadruped robots. Common approaches have largely focused on learning actions directly in joint space, or learning to modify and offset foot positions produced by trajectory generators. Both approaches typically require careful reward shaping and training for millions of time steps, and with trajectory generators introduce human bias into the resulting control policies. In this paper, we present a learning framework that leads to the natural emergence of fast and robust bounding policies for quadruped robots. The agent both selects and controls actions directly in task space to track desired velocity commands subject to environmental noise including model uncertainty and rough terrain. We observe that this framework improves sample efficiency, necessitates little reward shaping, leads to the emergence of natural gaits such as galloping and bounding, and eases the sim-to-real transfer at running speeds. Policies can be learned in only a few million time steps, even for challenging tasks of running over rough terrain with loads of over 100% of the nominal quadruped mass. Training occurs in PyBullet, and we perform a sim-to-sim transfer to Gazebo and sim-to-real transfer to the Unitree A1 hardware. For sim-to-sim, our results show the quadruped is able to run at over 4 m/s without a load, and 3.5 m/s with a 10 kg load, which is over 83% of the nominal quadruped mass. For sim-to-real, the Unitree A1 is able to bound at 2 m/s with a 5 kg load, representing 42% of the nominal quadruped mass.

This paper proposes a novel approach to controlling wheel-legged quadrupedal robots using pose optimization and force-based control via quadratic programming (QP). Our method allows the robot to leverage the whole-body motion and the wheel actuation to roll over high obstacles while keeping wheel traction with the terrain. In detail, we first present linear rigid body dynamics with wheels that can be used for real-time balancing control of wheel-legged robots. We then introduce an effective pose optimization method for wheel-legged robot's locomotion over steep ramp and stair terrains. The pose optimization solves for optimal poses to enhance stability and enforce collision-free constraints at critical pose locations for rolling over high obstacles. Experimental validation of the real robot demonstrated the capability of rolling up on a 0.36 m obstacle. The robot can also successfully roll up and down multiple stairs without lifting its legs or colliding with the terrain.

Performing highly agile acrobatic motions with a long flight phase requires perfect timing, high accuracy, and coordination of the full-body motion. To address these challenges, we present a novel approach on timings and trajectory optimization framework for legged robots performing aggressive 3D jumping. In our method, we firstly utilize an effective optimization framework using simplified rigid body dynamics to solve for contact timings and a reference trajectory of the robot body. The solution of this module is then used to formulate a full-body trajectory optimization based on the full nonlinear dynamics of the robot. This combination allows us to effectively optimize for contact timings while ensuring that the jumping trajectory can be effectively realized in the robot hardware. We first validate the efficiency of the proposed framework on the A1 robot model for various 3D jumping tasks such as double-backflips off the high altitude of 2m. Experimental validation was then successfully conducted for various aggressive 3D jumping motions such as diagonal jumps, barrel roll, and double barrel roll from a box of heights 0.4m and 0.9m, respectively.

This paper presents a novel omnidirectional gait design and feedback control of a radially symmetric tripedal friction-driven robot. The robot features 3 servo motors mounted on a 3-D printed chassis 7 cm from the center of mass and separated 120 degrees. These motors drive limbs, which impart frictional reactive forces on the body. We first introduce a mathematical model for the robot motion, then show experimental observations performed on a uniform friction surface, which validated the accuracy of the model. This model was then used to create an omnidirectional gait that allows the robot to translate in any direction. Based on this gait, we also introduce a Proportional-Integral (PI) feedback control framework that enables the robot to closely follow a desired path. Contrasting with feedforward motion generation, the proposed feedback controller reduced the tracking error by approximately 46%. We have successfully demonstrated the approach in our robot hardware for the problem of line following using live feedback from an overhead tracking camera. Our controller is also able to correct for aerodynamic disturbances generated by a high-volume industrial fan with a mean flow speed of 5.5ms−1, reducing path error by 65% relative to the basic position update procedure.

Adaptive control can address model uncertainty in control systems. However, it is preliminarily designed for tracking control. Recent advancements in the control of quadruped robots show that force control can effectively realize agile and robust locomotion. In this paper, we present a novel adaptive force-based control framework for legged robots. We introduce a new architecture in our proposed approach to incorporate adaptive control into quadratic programming (QP) force control. Since our approach is based on force control, it also retains the advantages of the baseline framework, such as robustness to uneven terrain, controllable friction constraints, or soft impacts. Our method is successfully validated in both simulation and hardware experiments. While the baseline QP control has shown a significant degradation in the body tracking error with a small load, our proposed adaptive force-based control can enable the 12-kg Unitree A1 robot to walk on rough terrains while carrying a heavy load of up to 6 kg (50% of the robot weight). When standing with four legs, our proposed adaptive control can even allow the robot to carry up to 11 kg of load (92% of the robot weight) with less than 5-cm tracking error in the robot height.