Optimization based predictive control is a powerful tool that has improved the ability of legged robots to execute dynamic maneuvers and traverse increasingly difficult terrains. However, it is often challenging and unintuitive to design meaningful cost functions and build high-fidelity models while adhering to timing restrictions. A novel framework to extract and design principled regularization heuristics for legged locomotion optimization control is presented. By allowing a simulation to fully explore the cost space offline, certain states and actions can be constrained or isolated. Data is fit with simple models relating the desired commands, optimal control actions, and robot states to identify new heuristic candidates. Basic parameter learning and adaptation laws are then applied to the models online. This method extracts simple, but powerful heuristics that can approximate complex dynamics and account for errors stemming from model simplifications and parameter uncertainty without the loss of physical intuition while generalizing the parameter tuning process. Results on the Mini Cheetah robot verify the increased capabilities due to the newly extracted heuristics without any modification to the controller structure or gains.

Legged robots have been highlighted as promising mobile platforms for disaster response and rescue scenarios because of their rough terrain locomotion capability. In cluttered environments, small robots are desirable as they can maneuver through small gaps, narrow paths, or tunnels. However small robots have their own set of difficulties such as limited space for sensors, limited obstacle clearance, and scaled-down walking speed. In this paper, we extensively address these difficulties via effective sensor integration and exploitation of dynamic locomotion and jumping. We integrate two Intel RealSense sensors into the MIT Mini-Cheetah, a 0.3 m tall, 9 kg quadruped robot. Simple and effective filtering and evaluation algorithms are used for foothold adjustment and obstacle avoidance. We showcase the exploration of highly irregular terrain using dynamic trotting and jumping with the small-scale, fully sensorized Mini-Cheetah quadruped robot.

Animal-level agility and robustness in robots cannot be accomplished by solely relying on blind locomotion controllers. A significant portion of a robot's ability to traverse terrain comes from reacting to the external world through visual sensing. However, embedding the sensors and compute that provide sufficient accuracy at high speeds is challenging, especially if the robot has significant space limitations. In this paper, we propose a system integration of a small-scale quadruped robot, the MIT Mini-Cheetah Vision, that exteroceptively senses the terrain and dynamically explores the world around it at high velocities. Through extensive hardware and software development, we demonstrate a fully untethered robot with all hardware onboard running a locomotion controller that combines state-of-the-art Regularized Predictive Control (RPC) with Whole-Body Impulse Control (WBIC). We devise a hierarchical state estimator that integrates kinematic, IMU, and localization sensor data to provide state estimates specific to path planning and locomotion tasks. Our integrated system has demonstrated robust autonomous waypoint tracking in dynamic real-world environments at speeds of over 1 m/s with high rates of success.

This work presents a successful implementation of a nonlinear optimization-based Regularized Predictive Control (RPC) for legged locomotion on the MIT Cheetah 3 robot platform. Footstep placements and ground reaction forces at the contact feet are simultaneously solved for over a prediction horizon in real-time. Often in academic literature not enough attention is given to the implementation details that make the theory work in practice and many times it is precisely these details that end up being critical to the success or failure of the theory in real world applications. Nonlinear optimization for real-time legged locomotion control in particular is one of the techniques that has shown promise, but falls short when implemented on hardware systems subjected to computation limits and undesirable local minima. We discuss various algorithms and techniques developed to overcome some of the challenges faced when implementing nonlinear optimization-based controllers for dynamic legged locomotion.

As legged robots are sent into unstructured environments, the ability to robustly manage contact transitions will be a critical skill. This paper introduces an approach to probabilistically fuse contact models, managing uncertainty in terrain geometry, dynamic modeling, and kinematics to improve the robustness of contact initiation at touchdown. A discrete-time extension of the generalized-momentum disturbance observer is presented to increase the accuracy of proprioceptive force control estimates. This information is fused with other contact priors under a framework of Kalman Filtering to increase robustness of the method. This approach results in accurate contact detection with 99.3 % accuracy and a small 4-5ms delay. Using this new detector, an Event-Based Finite State Machine is implemented to deal with unexpected early and late contacts. This allows the robot to traverse cluttered environments by modifying the control actions for each individual leg based on the estimated contact state rather than adhering to a rigid time schedule regardless of actual contact state. Experiments with the MIT Cheetah 3 robot show the success of both the detection algorithm, as well as the Event-Based FSM while making unexpected contacts during trotting.

This paper introduces a new robust, dynamic quadruped, the MIT Cheetah 3. Like its predecessor, the Cheetah 3 exploits tailored mechanical design to enable simple control strategies for dynamic locomotion and features high-bandwidth proprioceptive actuators to manage physical interaction with the environment. A new leg design is presented that includes proprioceptive actuation on the abduction/adduction degrees of freedom in addition to an expanded range of motion on the hips and knees. To make full use of these new capabilities, general balance and locomotion controllers for Cheetah 3 are presented. These controllers are embedded into a modular control architecture that allows the robot to handle unexpected terrain disturbances through reactive gait modification and without the need for external sensors or prior environment knowledge. The efficiency of the robot is demonstrated by a low Cost of Transport (CoT) over multiple gaits at moderate speeds, with the lowest CoT of 0.45 found during trotting. Experiments showcase the ability to blindly climb up stairs as a result of the full system integration. These results collectively represent a promising step toward a platform capable of generalized dynamic legged locomotion.

This paper presents an implementation of model predictive control (MPC) to determine ground reaction forces for a torque-controlled quadruped robot. The robot dynamics are simplified to formulate the problem as convex optimization while still capturing the full 3D nature of the system. With the simplified model, ground reaction force planning problems are formulated for prediction horizons of up to 0.5 seconds, and are solved to optimality in under 1 ms at a rate of 20-30 Hz. Despite using a simplified model, the robot is capable of robust locomotion at a variety of speeds. Experimental results demonstrate control of gaits including stand, trot, flying-trot, pronk, bound, pace, a 3-legged gait, and a full 3D gallop. The robot achieved forward speeds of up to 3 m/s, lateral speeds up to 1 m/s, and angular speeds up to 180 deg/sec. Our approach is general enough to perform all these behaviors with the same set of gains and weights.

This paper introduces a new policy-regularized model-predictive control (PR-MPC) approach to automatically generate and stabilize a diverse set of quadrupedal gaits. Model-predictive methods offer great promise to address balance in dynamic robots, yet require the solution of challenging nonlinear optimization problems when applied to legged systems. The new proposed PR-MPC approach aims to improve the conditioning of these problems by adding regularization based on heuristic reference policies. With this approach, a unified MPC formulation is shown to generate and stabilize trotting, bounding, and galloping without retuning any cost-function parameters. Intuitively, the added regularization biases the solution of the MPC towards common heuristics from the literature that are based on simple physics. Simulation results show that PR-MPC improves the computation time and closed-loop outcomes of applying MPC to stabilize quadrupedal gaits.