Publications

2026

1. Skill Learning

   

   UNIC: Learning Unified Multimodal Extrinsic Contact Estimation

   Zhengtong Xu and Yuki Shirai

   Submitted to ICRA2026, 2026

   Abs

   A unified multimodal framework for extrinsic contact estimation that operates without any prior knowledge or camera calibration.

2. Skill Learning

   

   Goal-Conditioned Residual Diffusion Policy via Pretrained Policy Data Augmentation

   Yuki Shirai, Zhengtong Xu, Kei Ota, and Diego Romeres

   In preparation to RAL, 2026

2025

1. Skill Learning

   

   Learning Pivoting Manipulation with Force and Vision Feedback Using Optimization-based Demonstrations

   Yuki Shirai, Kei Ota, Devesh K Jha, and Diego Romeres

   Submitted to RAL and Accepted for 2025 NeurIPS Workshop on Embodied World Models for Decision Making, 2025

   Abs arXiv Video

   

   Non-prehensile manipulation is challenging due to complex contact interactions between objects, the environment, and robots. Model-based approaches can efficiently generate complex trajectories of robots and objects under contact constraints. However, they tend to be sensitive to model inaccuracies and require access to privileged information (e.g., object mass, size, pose), making them less suitable for novel objects. In contrast, learning-based approaches are typically more robust to modeling errors but require large amounts of data. In this paper, we bridge these two approaches to propose a framework for learning closed-loop pivoting manipulation. By leveraging computationally efficient Contact-Implicit Trajectory Optimization (CITO), we design demonstration-guided deep Reinforcement Learning (RL), leading to sample-efficient learning. We also present a sim-to-real transfer approach using a privileged training strategy, enabling the robot to perform pivoting manipulation using only proprioception, vision, and force sensing without access to privileged information. Our method is evaluated on several pivoting tasks, demonstrating that it can successfully perform sim-to-real transfer.

2. Contact Optimization

   

   Is Linear Feedback on Smoothed Dynamics Sufficient for Stabilizing Contact-Rich Plans?

   Yuki Shirai, Tong Zhao, H.J. Terry Suh, Huaijiang Zhu, and 4 more authors

   In 2025 IEEE International Conference on Robotics and Automation (ICRA), May 2025

   🎥 Featured in IEEE Spectrum Video Friday

   Abs DOI arXiv Video Poster Website

   

   Designing planners and controllers for contact-rich manipulation is extremely challenging as contact violates the smoothness conditions that many gradient-based controller synthesis tools assume. Contact smoothing approximates a non-smooth system with a smooth one, allowing one to use these synthesis tools more effectively. However, applying classical control synthesis methods to smoothed contact dynamics remains relatively under-explored. This paper analyzes the efficacy of linear controller synthesis using differential simulators based on contact smoothing. We introduce natural baselines for leveraging contact smoothing to compute (a) open-loop plans robust to uncertain conditions and/or dynamics, and (b) feedback gains to stabilize around open-loop plans. Using robotic bimanual whole-body manipulation as a testbed, we perform extensive empirical experiments on over 300 trajectories and analyze why LQR seems insufficient for stabilizing contact-rich plans.

3. Contact Optimization

   

   Hierarchical Contact-Rich Trajectory Optimization for Multi-Modal Manipulation Using Tight Convex Relaxations

   Yuki Shirai, Arvind Raghunathan, and Devesh K. Jha

   In 2025 IEEE International Conference on Robotics and Automation (ICRA), May 2025

   🎥 Featured in IEEE Spectrum Video Friday

   Abs DOI arXiv Video Poster

   

   Designing trajectories for manipulation through contact is challenging as it requires reasoning of object & robot trajectories as well as complex contact sequences simultaneously. In this paper, we present a novel framework for simultaneously designing trajectories of robots, objects, and contacts efficiently for contact-rich manipulation. We propose a hierarchical optimization framework where Mixed-Integer Linear Program (MILP) selects optimal contacts between robot & object using approximate dynamical constraints, and then a NonLinear Program (NLP) optimizes trajectory of the robot(s) and object considering full nonlinear constraints. We present a convex relaxation of bilinear constraints using binary encoding technique such that MILP can provide tighter solutions with better computational complexity. The proposed framework is evaluated on various manipulation tasks where it can reason about complex multi-contact interactions while providing computational advantages. We also demonstrate our framework in hardware experiments using a bimanual robot system.

4. Nonlinear Optimization

   

   Analytic Conditions for Differentiable Collision Detection in Trajectory Optimization

   Akshay Jaitly, Devesh K Jha, Kei Ota, and Yuki Shirai

   In 2025 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Oct 2025

   Abs arXiv Video Poster

   

   Optimization-based methods are widely used for computing fast, diverse solutions for complex tasks such as collision-free movement or planning in the presence of contacts. However, most of these methods require enforcing non-penetration constraints between objects, resulting in a non-trivial and computationally expensive problem. This makes the use of optimization-based methods for planning and control challenging. In this paper, we present a method to efficiently enforce non-penetration of sets while performing optimization over their configuration, which is directly applicable to problems like collision-aware trajectory optimization. We introduce novel differentiable conditions with analytic expressions to achieve this. To enforce non-collision between non-smooth bodies using these conditions, we introduce a method to approximate polytopes as smooth semi-algebraic sets. We present several numerical experiments to demonstrate the performance of the proposed method and compare the performance with other baseline methods recently proposed in the literature.

5. Climbing Robots

   

   SCALER: Versatile Multilimbed Robot for Free-Climbing in Extreme Terrains

   Yusuke Tanaka, Yuki Shirai, Alexander Schperberg, Xuan Lin, and 1 more author

   IEEE Transactions on Robotics, 2025

   🏆 SICE SIYA-IROS2022 Awards

   Abs DOI arXiv Video Website

   

   This article presents Spine-enhanced Climbing Autonomous Limbed Exploration Robot (SCALER), a versatile free-climbing multilimbed robot that is designed to achieve tightly coupled simultaneous locomotion and dexterous grasping. While existing quadrupedal-limbed robots have demonstrated impressive dexterous capabilities, achieving a balance between power-demanding locomotion and precise grasping remains a critical challenge. We design a torso mechanism and a parallel–serial limb to meet the conflicting requirements that pose unique challenges in hardware design. SCALER employs underactuated two-fingered GOAT grippers that can mechanically adapt and offer seven modes of grasping, enabling SCALER to traverse extreme terrains with multimodal grasping strategies. We study the whole-body approach, where SCALER utilizes its body and limbs to generate additional forces for stable grasping in various environments, thereby further enhancing its versatility. Furthermore, we improve the GOAT gripper actuation speed to realize more dynamic climbing in a closed-loop control fashion. With these proposed technologies, SCALER can traverse vertical, overhanging, upside-down, slippery terrains and bouldering walls with nonconvex-shaped climbing holds under the Earth’s gravity.

2024

1. Contact Optimization

   

   Robust Pivoting Manipulation Using Contact Implicit Bilevel Optimization

   Yuki Shirai, Devesh K. Jha, and Arvind U. Raghunathan

   IEEE Transactions on Robotics, 2024

   🏆 Oral Presentation (3 out of 17 papers) — 2022 RSS Workshop on The Science of Bumping Into Things

   Abs DOI arXiv Video Poster

   

   Generalizable manipulation requires that robots be able to interact with novel objects and environment. This requirement makes manipulation extremely challenging as a robot has to reason about complex frictional interactions with uncertainty in physical properties of the object and the environment. In this article, we study robust optimization for planning of pivoting manipulation in the presence of uncertainties. We present insights about how friction can be exploited to compensate for inaccuracies in the estimates of the physical properties during manipulation. Under certain assumptions, we derive analytical expressions for stability margin provided by friction during pivoting manipulation. This margin is then used in a contact implicit bilevel optimization framework to optimize a trajectory that maximizes this stability margin to provide robustness against uncertainty in several physical parameters of the object. We present analysis of the stability margin with respect to several parameters involved in the underlying bilevel optimization problem. We demonstrate our proposed method using a 6 DoF manipulator for manipulating several different objects. We also design and validate an MPC controller using the proposed algorithm which can track and regulate the position of the object during manipulation.

2. 

   Optimization-based Planning and Control for Robust and Dexterous Locomotion and Manipulation through Contact

   Yuki Shirai

   Jan 2024

   PDF Video
3. Stochastic Optimization

   

   Chance-constrained optimization for contact-rich systems using mixed integer programming

   Yuki Shirai, Devesh K. Jha, Arvind U. Raghunathan, and Diego Romeres

   Nonlinear Analysis: Hybrid Systems, Jan 2024

   Abs DOI

   Stochastic and robust optimization of uncertain contact-rich systems is relatively unexplored. This paper presents a chance-constrained formulation for robust trajectory optimization during manipulation. In particular, we present chance-constrained optimization of Stochastic Discrete-time Linear Complementarity Systems (SDLCS). The optimization problem is formulated as a Mixed-Integer Quadratic Program with Chance Constraints (MIQPCC). In our formulation, we explicitly consider joint chance constraints for complementarity variables and states to capture the stochastic evolution of dynamics. Additionally, we demonstrate the use of our proposed approach for designing a Stochastic Model Predictive Controller (SMPC) with complementarity constraints for a planar pushing system. We evaluate the robustness of our optimized trajectories in simulation on several systems. The proposed approach outperforms some recent approaches for robust trajectory optimization for SDLCS.

2023

1. Tactile Learning

   

   Tactile Tool Manipulation

   Yuki Shirai, Devesh K. Jha, Arvind U. Raghunathan, and Dennis Hong

   In 2023 IEEE International Conference on Robotics and Automation (ICRA), May 2023

   🏆 1st Prize — 2023 ICRA Workshop on Embracing Contacts

   🎥 Featured in IEEE Spectrum Video Friday

   Abs DOI arXiv Supp Video Poster

   

   Humans can effortlessly perform very complex, dexterous manipulation tasks by reacting to sensor observations. In contrast, robots can not perform reactive manipulation and they mostly operate in open-loop while interacting with their environment. Consequently, the current manipulation algorithms either are inefficient in performance or can only work in highly structured environments. In this paper, we present closed-loop control of a complex manipulation task where a robot uses a tool to interact with objects. Manipulation using a tool leads to complex kinematics and contact constraints that need to be satisfied for generating feasible manipulation trajectories. We first present an open-loop controller design using Non-Linear Programming (NLP) that satisfies these constraints. In order to design a closed-loop controller, we present a pose estimator of objects and tools using tactile sensors. Using our tactile estimator, we design a closed-loop controller based on Model Predictive Control (MPC). The proposed algorithm is verified using a 6 DoF manipulator on tasks using a variety of objects and tools. We verify that our closed-loop controller can successfully perform tool manipulation under several unexpected contacts.

2. Stochastic Optimization

   

   Covariance Steering for Uncertain Contact-rich Systems

   Yuki Shirai, Devesh K. Jha, and Arvind U. Raghunathan

   In 2023 IEEE International Conference on Robotics and Automation (ICRA), May 2023

   Abs DOI arXiv Video

   

   Planning and control for uncertain contact systems is challenging as it is not clear how to propagate uncertainty for planning. Contact-rich tasks can be modeled efficiently using complementarity constraints among other techniques. In this paper, we present a stochastic optimization technique with chance constraints for systems with stochastic complementarity constraints. We use a particle filter-based approach to propagate moments for stochastic complementarity system. To circumvent the issues of open-loop chance constrained planning, we propose a contact-aware controller for covariance steering of the complementarity system. Our optimization problem is formulated as Non-Linear Programming (NLP) using bilevel optimization. We present an important-particle algorithm for numerical efficiency for the underlying control problem. We verify that our contact-aware closed-loop controller is able to steer the covariance of the states under stochastic contact-rich tasks.

3. Stochastic Optimization

   

   Chance-Constrained Optimization in Contact-rich Systems

   Yuki Shirai, Devesh K. Jha, Arvind U. Raghunathan, and Diego Romeres

   In 2023 American Control Conference (ACC), May 2023

   Abs DOI arXiv

   

   This paper presents a chance-constrained formulation for robust trajectory optimization during manipulation. In particular, we present a chance-constrained optimization for Stochastic Discrete-time Linear Complementarity Systems (SDLCS). To solve the optimization problem, we formulate Mixed-Integer Quadratic Programming with Chance Constraints (MIQPCC). In our formulation, we explicitly consider joint chance constraints for complementarity as well as states to capture the stochastic evolution of dynamics. We evaluate robustness of our optimized trajectories in simulation on several systems. The proposed approach outperforms some recent approaches for robust trajectory optimization for SDLCS.

4. Force Control

   

   Adaptive Force Controller for Contact-Rich Robotic Systems using an Unscented Kalman Filter

   Alexander Schperberg, Yuki Shirai, Xuan Lin, Yusuke Tanaka, and 1 more author

   In 2023 IEEE-RAS 22nd International Conference on Humanoid Robots (Humanoids), Dec 2023

   Abs DOI arXiv Video

   

   In multi-point contact systems, precise force control is crucial for achieving stable and safe interactions between robots and their environment. Thus, we demonstrate an admittance controller with auto-tuning that can be applied for these systems. The controller’s objective is to track the target wrench profiles of each contact point while considering the additional torque due to rotational friction. Our admittance controller is adaptive during online operation by using an auto-tuning method that tunes the gains of the controller while following user-specified training objectives. These objectives include facilitating controller stability, such as tracking the wrench profiles as closely as possible, ensuring control outputs are within force limits that minimize slippage, and avoiding configurations that induce kinematic singularity. We demonstrate the robustness of our controller on hardware for both manipulation and locomotion tasks using a multi-limbed climbing robot.

2022

1. Contact Optimization

   

   Simultaneous Contact-Rich Grasping and Locomotion via Distributed Optimization Enabling Free-Climbing for Multi-Limbed Robots

   Yuki Shirai, Xuan Lin, Alexander Schperberg, Yusuke Tanaka, and 3 more authors

   In 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Oct 2022

   Abs DOI arXiv Video Poster

   

   While motion planning of locomotion for legged robots has shown great success, motion planning for legged robots with dexterous multi-finger grasping is not mature yet. We present an efficient motion planning framework for simultaneously solving locomotion (e.g., centroidal dynamics), grasping (e.g., patch contact), and contact (e.g., gait) problems. To accelerate the planning process, we propose distributed optimization frameworks based on Alternating Direction Methods of Multipliers (ADMM) to solve the original large-scale Mixed-Integer NonLinear Programming (MINLP). The resulting frameworks use Mixed-Integer Quadratic Programming (MIQP) to solve contact and NonLinear Programming (NLP) to solve nonlinear dynamics, which are more computationally tractable and less sensitive to parameters. Also, we explicitly enforce patch contact constraints from limit surfaces with micro-spine grippers. We demonstrate our proposed framework in the hardware experiments, showing that the multi-limbed robot is able to realize various motions including free-climbing at a slope angle 45° with a much shorter planning time.

2. Climbing Robots

   

   SCALER: A Tough Versatile Quadruped Free-Climber Robot

   Yusuke Tanaka, Yuki Shirai, Xuan Lin, Alexander Schperberg, and 4 more authors

   In 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Oct 2022

   🏆 SICE SIYA-IROS2022 Awards

   Abs DOI arXiv Video Website

   

   This paper introduces SCALER, a quadrupedal robot that demonstrates climbing on bouldering walls, over-hangs, ceilings and trotting on the ground. SCALER is one of the first high-degrees of freedom four-limbed robots that can free-climb under the Earth’s gravity and one of the most mechanically efficient quadrupeds on the ground. Where other state-of-the-art climbers specialize in climbing, SCALER promises practical free-climbing with payload and ground locomotion, which realizes true versatile mobility. A new climbing gait, SKATE gait, increases the payload by utilizing the SCALER body linkage mechanism. SCALER achieves a maximum normalized locomotion speed of 1.87 /s, or 0.56 m/s on the ground and 1.0 /min, or 0.35 m/min in bouldering wall climbing. Payload capacity reaches 233 % of the SCALER weight on the ground and 35 % on the vertical wall. Our GOAT gripper, a mechanically adaptable underactuated two-finger gripper, successfully grasps convex and non-convex objects and supports SCALER.

3. Hybrid Optimization

   

   Multi-Modal Multi-Agent Optimization for LIMMS, A Modular Robotics Approach to Delivery Automation

   Xuan Lin, Gabriel I. Fernandez, Yeting Liu, Taoyuanmin Zhu, and 2 more authors

   In 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Oct 2022

   Abs DOI arXiv

   

   In this paper we present a motion planner for LIMMS, a modular multi-agent, multi-modal package delivery platform. A single LIMMS unit is a robot that can operate as an arm or leg depending on how and what it is attached to, e.g., a manipulator when it is anchored to walls within a delivery vehicle or a quadruped robot when 4 are attached to a box. Coordinating amongst multiple LIMMS, when each one can take on vastly different roles, can quickly become complex. For such a planning problem we first compose the necessary logic and constraints. The formulation is then solved for skill exploration and can be implemented on hardware after refinement. To solve this optimization problem we use alternating direction method of multipliers (ADMM). The proposed planner is experimented under various scenarios which shows the capability of LIMMS to enter into different modes or combinations of them to achieve their goal of moving shipping boxes.

4. Contact Optimization

   

   Robust Pivoting: Exploiting Frictional Stability Using Bilevel Optimization

   Yuki Shirai, Devesh K. Jha, Arvind U. Raghunathan, and Diego Romeres

   In 2022 International Conference on Robotics and Automation (ICRA), May 2022

   Abs DOI arXiv Video Poster

   

   Generalizable manipulation requires that robots be able to interact with novel objects and environment. This requirement makes manipulation extremely challenging as a robot has to reason about complex frictional interaction with uncertainty in physical properties of the object. In this paper, we study robust optimization for control of pivoting manipulation in the presence of uncertainties. We present insights about how friction can be exploited to compensate for the inaccuracies in the estimates of the physical properties during manipulation. In particular, we derive analytical expressions for stability margin provided by friction during pivoting manipulation. This margin is then used in a bilevel trajectory optimization algorithm to design a controller that maximizes this stability margin to provide robustness against uncertainty in physical properties of the object. We demonstrate our proposed method using a 6 DoF manipulator for manipulating several different objects.

2021

1. Dexterous Grasping

   

   An Under-Actuated Whippletree Mechanism Gripper based on Multi-Objective Design Optimization with Auto-Tuned Weights

   Yusuke Tanaka, Yuki Shirai, Zachary Lacey, Xuan Lin, and 2 more authors

   In 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Sep 2021

   Abs DOI arXiv Video Website

   

   Current rigid linkage grippers are limited in flexibility, and gripper design optimality relies on expertise, experiments, or arbitrary parameters. Our proposed rigid gripper can accommodate irregular and off-center objects through a whippletree mechanism, improving adaptability. We present a whippletree-based rigid under-actuated gripper and its parametric design multi-objective optimization for a one-wall climbing task. Our proposed objective function considers kinematics and grasping forces simultaneously with a mathematical metric based on a model of an object environment. Our multi-objective problem is formulated as a single kinematic objective function with auto-tuning force-based weight. Our results indicate that our proposed objective function determines optimal parameters and kinematic ranges for our under-actuated gripper in the task environment with sufficient grasping forces.

2. Motion Planning

   

   LTO: Lazy Trajectory Optimization with Graph-Search Planning for High DOF Robots in Cluttered Environments

   Yuki Shirai, Xuan Lin, Ankur Mehta, and Dennis Hong

   In 2021 IEEE International Conference on Robotics and Automation (ICRA), May 2021

   Abs DOI arXiv Video

   

   Although Trajectory Optimization (TO) is one of the most powerful motion planning tools, it suffers from expensive computational complexity as a time horizon increases in cluttered environments. It can also fail to converge to a globally optimal solution. In this paper, we present Lazy Trajectory Optimization (LTO) that unifies local short-horizon TO and global Graph-Search Planning (GSP) to generate a long-horizon global optimal trajectory. LTO solves TO with the same constraints as the original long-horizon TO with improved time complexity. We also propose a TO-aware cost function that can balance both solution cost and planning time. Since LTO solves many nearly identical TO in a roadmap, it can provide an informed warm-start for TO to accelerate the planning process. We also present proofs of the computational complexity and optimality of LTO. Finally, we demonstrate LTO’s performance on motion planning problems for a 2 DOF free-flying robot and a 21 DOF legged robot, showing that LTO outperforms existing algorithms in terms of its runtime and reliability.

2020

1. Climbing Robots

   

   Risk-Aware Motion Planning for a Limbed Robot with Stochastic Gripping Forces Using Nonlinear Programming

   Yuki Shirai, Xuan Lin, Yusuke Tanaka, Ankur Mehta, and 1 more author

   IEEE Robotics and Automation Letters, Oct 2020

   Abs DOI arXiv Video Website

   

   We present a motion planning algorithm with probabilistic guarantees for limbed robots with stochastic gripping forces. Planners based on deterministic models with a worst-case uncertainty can be conservative and inflexible to consider the stochastic behavior of the contact, especially when a gripper is installed. Our proposed planner enables the robot to simultaneously plan its pose and contact force trajectories while considering the risk associated with the gripping forces. Our planner is formulated as a nonlinear programming problem with chance constraints, which allows the robot to generate a variety of motions based on different risk bounds. To model the gripping forces as random variables, we employ Gaussian Process regression. We validate our proposed motion planning algorithm on an 11.5 kg six-limbed robot for two-wall climbing. Our results show that our proposed planner generates various trajectories (e.g., avoiding low friction terrain under the low risk bound, choosing an unstable but faster gait under the high risk bound) by changing the probability of risk based on various specifications.

2019

1. Motion Planning

   

   Gait Planning for a Free-Climbing Robot Based on Tumble Stability

   Kentaro Uno, Warley F. R. Ribeiro, William Jones, Yuki Shirai, and 3 more authors

   In 2019 IEEE/SICE International Symposium on System Integration (SII), Jan 2019

   Abs DOI

   

   Conventional wheeled or tracked robots are unable to traverse rough, uneven, or steep terrain. A multi-legged robot that has grippers at the tips of each leg is capable of grasping irregularities in the terrain, allowing for free climbing motion through a variety of challenging environments. To execute safe and reliable free-climbing locomotion, the motion of the robot should be planned in consideration of three aspects: optimal selection of gripping points along the path to the goal, tumble stability of the robot including the performance of the gripper, and feasibility of motion on the basis of kinematics. In this paper, we propose a method to satisfy these three conditions and verify the validity of the proposed method with a free-climbing robot walking simulation on inclined terrain with randomly distributed discrete grippable points.

2018

1. Climbing Robots

   

   Passive Spine Gripper for Free-Climbing Robot in Extreme Terrain

   Kenji Nagaoka, Hayato Minote, Kyohei Maruya, Yuki Shirai, and 4 more authors

   IEEE Robotics and Automation Letters, Jul 2018

   Abs DOI Video

   

   In this letter, we present a passive spine gripper that can hold rough rocky surfaces of boulders on cliff walls, and we discuss its application to a four-limbed robot for free-climbing in extreme terrain. The limbed robot has four degrees of freedom in each limb, where three are to drive joints of the limb and one for releasing the gripper. The fine spine of the proposed gripper also enables it to passively and adaptively latch on to microscopic asperities of the rough surface, and it is thus an efficient mechanism. In this letter, we present the fundamental design and mechanism of the proposed gripper, after which we introduce its static gripping model. We verify the gripping model by the experimental gripping performance of the prototype gripper. We show a lightweight four-limbed robot that is equipped with the grippers mounted on each limb. To evaluate the climbing capabilities of the robot, we use it to perform climbing experiments on a rugged and steep slope. The results show that the prototype can safely climb over such challenging terrain that is similar to a gravity offload system.

2. Motion Planning

   

   Gait analysis of a free-climbing robot on sloped terrain for lunar and planetary exploration

   Yuki Shirai, Hayato Minote, Kenji Nagaoka, and Kazuya Yoshida

   In Proc. Int. Symp. Artif. Intell. Robot. Autom, Jul 2018

   Abs PDF

   

   In this paper, we discuss free-climbing gaits on sloped terrains based on tumble stability margin and manipulability in a quantitative way. The tumble stability margin considers a tumbling moment according to forces and moments acting on a robot with legs, and the manipulability considers the movements of the legs. Considering these parameters, we propose a more suitable gait called hybrid gait for slope walking. Hybrid gait increases the tumble stability margin by shifting the main body of the robot to improve stability during slope walking. To validate the proposed gait, we conducted numerical simulations and experiments using a prototype robot. The result shows that although the robot overturns during different gaits, such as adaptive gait and sway compensation gait, it does not tumble when using the hybrid gait on sloped terrain. Our findings confirm that the proposed gait achieves the most stable locomotion on slopes.