In this paper, we introduce a kinodynamic model predictive control (MPC) framework that exploits unidirectional parallel springs (UPS) to improve the energy efficiency of dynamic legged robots. The proposed method employs a hierarchical control structure, where the solution of MPC with simplified dynamic models is used to warm-start the kinody-namic MPC, which accounts for nonlinear centroidal dynamics and kinematic constraints. The proposed approach enables energy efficient dynamic hopping on legged robots by using UPS to reduce peak motor torques and energy consumption during stance phases. Simulation results demonstrated a 38.8% reduction in the cost of transport (CoT) for a monoped robot equipped with UPS during high-speed hopping. Additionally, preliminary hardware experiments show a 14.8% reduction in energy consumption.

This paper proposes a hybrid planning framework that generates complex dynamic motion plans for jumping legged robots to traverse challenging terrains. By employing a motion primitive, the original problem is decoupled as path planning followed by a trajectory optimization (TO) module that handles dynamics. A variant of a kinodynamic Rapidly-exploring Random Trees (RRT) planner finds a path as a parabola sequence between stance phases. To make this fast, a reachability informed control sampling scheme leverages a precomputed velocity reachability map. The path is post-processed to eliminate redundant jumps and passed to the TO module to find a dynamically feasible trajectory. Simulation results are presented where the proposed hybrid planner solves challenging terrains by executing multiple consecutive jumps, producing novel strategies to leap over large gaps by leveraging dynamics. In a physical experiment, the hybrid planner is tested on a real robot successfully traversing a challenging terrain.

This paper introduces HOPPY, an open-source, low-cost, robust, and modular kit for robotics education. The robot dynamically hops around a rotating gantry with a fixed base. The kit is intended to lower the entry barrier for studying dynamic robots and legged locomotion with real systems. It bridges the theoretical content of fundamental robotic courses with real dynamic robots by facilitating and guiding the software and hardware integration. This paper describes the topics which can be studied using the kit, lists its components, discusses preferred practices for implementation, presents results from experiments with the simulator and the real system, and suggests further improvements. A simple heuristic-based controller is described to achieve velocities up to 1.7m/s, navigate small objects, and mitigate external disturbances when the robot is aided by a counterweight. HOPPY was utilized as the subject of a semester-long project for the Robot Dynamics and Control course at the University of Illinois at Urbana-Champaign. The positive feedback from the students and instructors about the hands-on activities during the course motivates us to share this kit and continue improving it in the future.

This article presents a novel representation-free model predictive control (RF-MPC) framework for controlling various dynamic motions of a quadrupedal robot in three-dimensional (3-D) space. Our formulation directly represents the rotational dynamics using the rotation matrix, which liberates us from the issues associated with the use of Euler angles and quaternion as the orientation representations. With a variation-based linearization scheme and a carefully constructed cost function, the MPC control law is transcribed to the standard quadratic program form. The MPC controller can operate at real-time rates of 250 Hz on a quadruped robot. Experimental results including periodic quadrupedal gaits and a controlled backflip validate that our control strategy could stabilize dynamic motions that involve singularity in 3-D maneuvers.

This paper proposes a kinodynamic motion plan-ning framework for multi-legged robot jumping based on the mixed-integer convex program (MICP), which simultaneously reasons about centroidal motion, contact points, wrench, and gait sequences. This method uniquely combines configuration space discretization and the construction of feasible wrench polytope (FWP) to encode kinematic constraints, actuator limit, friction cone constraint, and gait sequencing into a single MICP. The MICP could be efficiently solved to the global optimum by off-the-shelf numerical solvers and provide highly dynamic jumping motions without requiring initial guesses. Simulation and experimental results demonstrate that the proposed method could find novel and dexterous maneuvers that are directly deployable on the two-legged robot platform to traverse through challenging terrains.

This paper presents a new Model Predictive Control (MPC) framework for controlling various dynamic movements of a quadrupedal robot. System dynamics are represented by linearizing single rigid body dynamics in three-dimensional (3D) space. Our formulation linearizes rotation matrices without resorting to parameterizations like Euler angles and quaternions, avoiding issues of singularity and unwinding phenomenon, respectively. With a carefully chosen configuration error function, the MPC control law is transcribed into a Quadratic Program (QP) which can be solved efficiently in realtime. Our formulation can stabilize a wide range of periodic quadrupedal gaits and acrobatic maneuvers. We show various simulation as well as experimental results to validate our control strategy. Experiments prove the application of this framework with a custom QP solver could reach execution rates of 160 Hz on embedded platforms.

This paper proposes a mixed-integer convex programming formulation for dynamic motion planning. Many dynamic constraints such as the actuator torque constraint are nonlinear and non-convex due to the trigonometrical terms from the Jacobian matrix. This often causes the optimization problem to converge to local optima or even infeasible set. In this paper, we convexify the torque constraint by formulating a mixed-integer quadratically-constrained program (MIQCP). More specifically, the workspace is discretized into a union of disjoint polytopes and torque constraint is enforced upon a convex outer approximation of the torque ellipsoid, obtained by solving a semidefinite program (SDP). Bilinear terms are approximated by McCormick envelope convex relaxation. The proposed MIQCP framework could be solved efficiently to global optimum and the generated trajectories could exploit the rich features of the rough terrain without any initial guess from the designer. The demonstrated experiment results prove that this approach is currently capable of planning consecutive jumps that navigates a single-legged robot through challenging terrains.

This paper introduces a novel method for actuator design that exploits electromagnetic motors' torque and speed potential in jumping applications. We proposed a nonlinear optimization process that integrates (a) the control design to obtain the optimal ground reaction force, and (b) the mechanical design to narrow down the choices of motor/gearbox pair. Based on this method, actuators were designed and assembled into a leg prototype with two actuated degrees of freedom. Experiments demonstrated that the leg could achieve a maximum vertical jumping height of 0.62 m (2.4 times of leg length) and maximum forward jumping distance of 0.72 m (2.7 times of leg length).